lesson 9.5 homework answer key

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9.5: Homework

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• Page ID 70336

• Julie Harland
• MiraCosta College
• Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
• Start a new module on the front side of a new page and write the module number on the top center of the page.
• Answers without supporting work will receive no credit.
• Some solutions are given in the solutions manual.
• You may work with classmates but do your own work.

Do each of the following steps using your C-strips.

• State how many C-strips (each an equal part of the whole) make up one unit.
• State which C-strip makes up one part of the whole.
• State the fraction that the C-strip in part b represents.
• State how many of the C-strips in part b you need to make into a train.
• State which C-strip is the length of the train you made in part c

a. If S represents 1 unit, then which C-strip represents \(\frac{7}{11}\)?

b. If H represents 1 unit, then which C-strip represents \(\frac{2}{3}\)?

c. If P represents 1 unit, then which C-strip represents \(\frac{3}{2}\)?

d. If L represents 1 unit, then which C-strip represents 3 ?

e. If Y represents 1 unit, then which C-strip represents \(\frac{6}{5}\)?

f. If O represents 1 unit, then which C-strip represents \(\frac{1}{2}\)?

g. If B represents 1 unit, then which C-strip represents \(\frac{4}{3}\)?

Do each step using your C-strips.

• State how many C-strips will make up the named C-strip stated in the problem.
• Which C-strip makes up one equal part?
• State how many of the C-strips in part b will make up one unit.
• Form the unit by making a train from the equal parts (C-strip in part b) and state which C-strip has the same length as that train.

a. If O represents \(\frac{5}{6}\), then which C-strip is 1 unit?

b. If W represents \(\frac{1}{7}\), then which C-strip is 1 unit?

c. If D represents \(\frac{3}{2}\), then which C-strip is 1 unit?

d. If N represents \(\frac{4}{3}\), then which C-strip is 1 unit?

e. If D represents 3, then which C-strip is 1 unit?

f. If K represents \(\frac{7}{9}\), then which C-strip is 1 unit?

• State which C-strip is one unit.
• State which C-strip is the answer.

a. If N represents \(\frac{2}{3}\), then which C-strip represents \(\frac{1}{4}\)?

b. If D represents \(\frac{3}{4}\), then which C-strip represents \(\frac{3}{2}\)?

c. If B represents \(\frac{3}{2}\), this which C-strip represents \(\frac{4}{3}\)?

Use your fraction arrays to determine all fractions on the fraction array that are equivalent to 3/4. Do this by finding 3/4 on the array, and seeing what other numbers are the same length. Include a diagram.

Use your multiple strips to write 6 fractions equivalent to 5/6. Draw the strips.

Use your multiple strips to write 6 fractions equivalent to 3/8 Draw the strips.

Compare 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.

Add 3/8 and 1/3 using models. Show all of the steps, and explain the procedure as shown in this module.

Do the following subtraction using models: 3/5 – 1/4. Show all of the steps, and explain the procedure as shown in this module.

Do the following multiplications using models. Show all of the steps, and explain the procedure as shown in this module.

a. 3/8 \(\cdot\) 2/5

b. 4/7 \(\cdot\) 2/3

By looking at the final drawing someone made to model a multiplication of two fractions, determine which multiplication was performed, and then state the answer.

a. 5/6 \(\cdot\) 2/3 OR 2/3 \(\cdot\) 5/6

b. 1/2 \(\cdot\) 7/8 OR 7/8 \(\cdot\) 1/2

If all of the dots shown for each problem represent 1 unit, determine the multiplication problem that someone did to get the answer, and state the answer.

Fill in the chart showing how to do the following multiplications using C-strips. The multiplication is in the first column. State an appropriate choice for the unit (name a C-strip, or sum of two C-strips) in the second column. Write the C-strip obtained after the first part of the multiplication (which is the second fraction as a part of the unit) in the third column. Then, do the final multiplication, and write the C-strip obtained in the fourth column. In the fifth column, write a fraction using C-strips putting the final unit obtained in the fourth column as the numerator, and the unit in the denominator. Then, in the last column, write the answer as a fraction. Do not simplify.

Perform the following division using the box and dot methods. First define the unit. Then explain and show all of the steps. Include diagrams.

a. 5 \(\div\) 1/3

b. 3/4 \(\div\) 1/3

Determine if the following statements are true or false by comparing cross products.

a. 19/23 = 57/69

b. 24/37 = 68/91

Write each fraction in simplest form using each of the two methods:

(1) prime factorization and

(2) finding GCF.

a. \(\frac{216}{420}\)

b. \(\frac{195}{286}\)

Use cross products to compare each of the following fractions. Use < or >.

a. 18/23 and 5/8

b. 11/18 and 121/250

Find 3 rational numbers, written with a common denominator, between 3/8 and 5/8.

Find 3 rational numbers, written with a common denominator, between 1/2 and 4/7.

a. 21 of John's students have cats at home. This represents 7/10 of John's students. How many students are in John's class? Solve the problem using models. Explain how the model works.

b. At an elementary school, 38 teachers drive alone to work. This represents 2/3 of the teachers. How many teachers work at the school? Solve the problem using models. Explain how the model works.

Write in words how to read each of the following decimals.

Multiply the following decimals mentally then do it again by showing the same steps as shown in this module..

a. (0.3)(0.8)

b. (1.2)(0.4)

c. (1.22)(2.3)

d. (3.2)(2.41)

For each fraction, determine if it can be written as an equivalent fraction with a power of ten in the denominator. If a fraction cannot be written as a terminal decimal, explain why not. Otherwise, show ALL of the steps to write it as a terminal decimal.

a. \(\frac{11}{16}\)

b. \(\frac{3}{125}\)

c. \(\frac{1}{12}\)

d. \(\frac{9}{40}\)

e. \(\frac{21}{56}\)

Rewrite each of the following decimals as simplified fractions. For repeating decimals, use the techniques shown in this module. Then, check your answer using a calculator by dividing the numerator by the denominator to see if the result matches the original problem.

a. \(0.\bar{7}\)

b. \(0.\overline{72}\)

c. \(0.\overline{235}\)

d. \(0.2\bar{5}\)

e. \(0.3\overline{42}\)

x = 4 3 , x = −4 3 x = 4 3 , x = −4 3

y = 3 3 , y = −3 3 y = 3 3 , y = −3 3

x = 7 , x = −7 x = 7 , x = −7

m = 4 , m = −4 m = 4 , m = −4

c = 2 3 i , c = −2 3 i c = 2 3 i , c = −2 3 i

c = 2 6 i , c = −2 6 i c = 2 6 i , c = −2 6 i

x = 2 10 , x = −2 10 x = 2 10 , x = −2 10

y = 2 7 , y = −2 7 y = 2 7 , y = −2 7

r = 6 5 5 , r = − 6 5 5 r = 6 5 5 , r = − 6 5 5

t = 8 3 3 , t = − 8 3 3 t = 8 3 3 , t = − 8 3 3

a = 3 + 3 2 , a = 3 − 3 2 a = 3 + 3 2 , a = 3 − 3 2

b = −2 + 2 10 , b = −2 − 2 10 b = −2 + 2 10 , b = −2 − 2 10

x = 1 2 + 5 2 x = 1 2 + 5 2 , x = 1 2 − 5 2 x = 1 2 − 5 2

y = − 3 4 + 7 4 , y = − 3 4 − 7 4 y = − 3 4 + 7 4 , y = − 3 4 − 7 4

a = 5 + 2 5 , a = 5 − 2 5 a = 5 + 2 5 , a = 5 − 2 5

b = −3 + 4 2 , b = −3 − 4 2 b = −3 + 4 2 , b = −3 − 4 2

r = − 4 3 + 2 2 i 3 , r = − 4 3 − 2 2 i 3 r = − 4 3 + 2 2 i 3 , r = − 4 3 − 2 2 i 3

t = 4 + 10 i 2 , t = 4 − 10 i 2 t = 4 + 10 i 2 , t = 4 − 10 i 2

m = 7 3 , m = −1 m = 7 3 , m = −1

n = − 3 4 , n = − 7 4 n = − 3 4 , n = − 7 4

ⓐ ( a − 10 ) 2 ( a − 10 ) 2 ⓑ ( b − 5 2 ) 2 ( b − 5 2 ) 2 ⓒ ( p + 1 8 ) 2 ( p + 1 8 ) 2

ⓐ ( b − 2 ) 2 ( b − 2 ) 2 ⓑ ( n + 13 2 ) 2 ( n + 13 2 ) 2 ⓒ ( q − 1 3 ) 2 ( q − 1 3 ) 2

x = −5 , x = −1 x = −5 , x = −1

y = 1 , y = 9 y = 1 , y = 9

y = 5 + 15 i , y = 5 − 15 i y = 5 + 15 i , y = 5 − 15 i

z = −4 + 3 i , z = −4 − 3 i z = −4 + 3 i , z = −4 − 3 i

x = 8 + 4 3 , x = 8 − 4 3 x = 8 + 4 3 , x = 8 − 4 3

y = −4 + 3 3 , y = −4 − 3 3 y = −4 + 3 3 , y = −4 − 3 3

a = −7 , a = 3 a = −7 , a = 3

b = −10 , b = 2 b = −10 , b = 2

p = 5 2 + 61 2 , p = 5 2 − 61 2 p = 5 2 + 61 2 , p = 5 2 − 61 2

q = 7 2 + 37 2 , q = 7 2 − 37 2 q = 7 2 + 37 2 , q = 7 2 − 37 2

c = −9 , c = 3 c = −9 , c = 3

d = 11 , d = −7 d = 11 , d = −7

m = −7 , m = −1 m = −7 , m = −1

n = −2 , n = 8 n = −2 , n = 8

r = − 7 3 , r = 3 r = − 7 3 , r = 3

t = − 5 2 , t = 2 t = − 5 2 , t = 2

x = − 3 8 + 41 8 , x = − 3 8 − 41 8 x = − 3 8 + 41 8 , x = − 3 8 − 41 8

y = 5 3 + 10 3 , y = 5 3 − 10 3 y = 5 3 + 10 3 , y = 5 3 − 10 3

y = 1 , y = 2 3 y = 1 , y = 2 3

z = 1 , z = − 3 2 z = 1 , z = − 3 2

a = −3 , a = 5 a = −3 , a = 5

b = −6 , b = −4 b = −6 , b = −4

m = −6 + 15 3 , m = −6 − 15 3 m = −6 + 15 3 , m = −6 − 15 3

n = −2 + 2 6 5 , n = −2 − 2 6 5 n = −2 + 2 6 5 , n = −2 − 2 6 5

a = 1 4 + 31 4 i , a = 1 4 − 31 4 i a = 1 4 + 31 4 i , a = 1 4 − 31 4 i

b = − 1 5 + 19 5 i , b = − 1 5 − 19 5 i b = − 1 5 + 19 5 i , b = − 1 5 − 19 5 i

x = −1 + 6 , x = −1 − 6 x = −1 + 6 , x = −1 − 6

y = 1 + 2 , y = 1 − 2 y = 1 + 2 , y = 1 − 2

c = 2 + 7 3 , c = 2 − 7 3 c = 2 + 7 3 , c = 2 − 7 3

d = 9 + 33 4 , d = 9 − 33 4 d = 9 + 33 4 , d = 9 − 33 4

r = −5 r = −5

t = 4 5 t = 4 5

ⓐ 2 complex solutions; ⓑ 2 real solutions; ⓒ 1 real solution

ⓐ 2 real solutions; ⓑ 2 complex solutions; ⓒ 1 real solution

ⓐ factoring; ⓑ Square Root Property; ⓒ Quadratic Formula

ⓐ Quadratic Forumula; ⓑ Factoring or Square Root Property ⓒ Square Root Property

x = 2 , x = − 2 , x = 2 , x = −2 x = 2 , x = − 2 , x = 2 , x = −2

x = 7 , x = − 7 , x = 2 , x = −2 x = 7 , x = − 7 , x = 2 , x = −2

x = 3 , x = 1 x = 3 , x = 1

y = −1 , y = 1 y = −1 , y = 1

x = 9 , x = 16 x = 9 , x = 16

x = 4 , x = 16 x = 4 , x = 16

x = −8 , x = 343 x = −8 , x = 343

x = 81 , x = 625 x = 81 , x = 625

x = 4 3 x = 2 x = 4 3 x = 2

x = 2 5 , x = 3 4 x = 2 5 , x = 3 4

The two consecutive odd integers whose product is 99 are 9, 11, and −9, −11

The two consecutive even integers whose product is 128 are 12, 14 and −12, −14.

The height of the triangle is 12 inches and the base is 76 inches.

The height of the triangle is 11 feet and the base is 20 feet.

The length of the garden is approximately 18 feet and the width 11 feet.

The length of the tablecloth is approximatel 11.8 feet and the width 6.8 feet.

The length of the flag pole’s shadow is approximately 6.3 feet and the height of the flag pole is 18.9 feet.

The distance between the opposite corners is approximately 7.2 feet.

The arrow will reach 180 feet on its way up after 3 seconds and again on its way down after approximately 3.8 seconds.

The ball will reach 48 feet on its way up after approximately .6 second and again on its way down after approximately 5.4 seconds.

The speed of the jet stream was 100 mph.

The speed of the jet stream was 50 mph.

Press #1 would take 12 hours, and Press #2 would take 6 hours to do the job alone.

The red hose take 6 hours and the green hose take 3 hours alone.

ⓐ up; ⓑ down

ⓐ down; ⓑ up

ⓐ x = 2 ; x = 2 ; ⓑ ( 2 , −7 ) ( 2 , −7 )

ⓐ x = 1 ; x = 1 ; ⓑ ( 1 , −5 ) ( 1 , −5 )

y -intercept: ( 0 , −8 ) ( 0 , −8 ) x -intercepts ( −4 , 0 ) , ( 2 , 0 ) ( −4 , 0 ) , ( 2 , 0 )

y -intercept: ( 0 , −12 ) ( 0 , −12 ) x -intercepts ( −2 , 0 ) , ( 6 , 0 ) ( −2 , 0 ) , ( 6 , 0 )

y -intercept: ( 0 , 4 ) ( 0 , 4 ) no x -intercept

y -intercept: ( 0 , −5 ) ( 0 , −5 ) x -intercepts ( −1 , 0 ) , ( 5 , 0 ) ( −1 , 0 ) , ( 5 , 0 )

The minimum value of the quadratic function is −4 and it occurs when x = 4.

The maximum value of the quadratic function is 5 and it occurs when x = 2.

It will take 4 seconds for the stone to reach its maximum height of 288 feet.

It will 6.5 seconds for the rocket to reach its maximum height of 676 feet.

ⓑ The graph of g ( x ) = x 2 + 1 g ( x ) = x 2 + 1 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 1 unit. The graph of h ( x ) = x 2 − 1 h ( x ) = x 2 − 1 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted down 1 unit.

ⓑ The graph of h ( x ) = x 2 + 6 h ( x ) = x 2 + 6 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 6 units. The graph of h ( x ) = x 2 − 6 h ( x ) = x 2 − 6 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted down 6 units.

ⓑ The graph of g ( x ) = ( x + 2 ) 2 g ( x ) = ( x + 2 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 2 units. The graph of h ( x ) = ( x − 2 ) 2 h ( x ) = ( x − 2 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shift right 2 units.

ⓑ The graph of g ( x ) = ( x + 5 ) 2 g ( x ) = ( x + 5 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 5 units. The graph of h ( x ) = ( x − 5 ) 2 h ( x ) = ( x − 5 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted right 5 units.

f ( x ) = −4 ( x + 1 ) 2 + 5 f ( x ) = −4 ( x + 1 ) 2 + 5

f ( x ) = 2 ( x − 2 ) 2 − 5 f ( x ) = 2 ( x − 2 ) 2 − 5

ⓐ f ( x ) = 3 ( x − 1 ) 2 + 2 f ( x ) = 3 ( x − 1 ) 2 + 2 ⓑ

ⓐ f ( x ) = −2 ( x − 2 ) 2 + 1 f ( x ) = −2 ( x − 2 ) 2 + 1 ⓑ

f ( x ) = ( x − 3 ) 2 − 4 f ( x ) = ( x − 3 ) 2 − 4

f ( x ) = ( x + 3 ) 2 − 1 f ( x ) = ( x + 3 ) 2 − 1

ⓑ ( −4 , −2 ) ( −4 , −2 )

ⓑ ( − ∞ , 2 ] ∪ [ 6 , ∞ ) ( − ∞ , 2 ] ∪ [ 6 , ∞ )

ⓑ ( −1 , 5 ) ( −1 , 5 )

ⓑ ( − ∞ , 2 ] ∪ [ 8 , ∞ ) ( − ∞ , 2 ] ∪ [ 8 , ∞ )

( − ∞ , −4 ] ∪ [ 2 , ∞ ) ( − ∞ , −4 ] ∪ [ 2 , ∞ )

[ −3 , 5 ] [ −3 , 5 ]

[ −1 − 2 , −1 + 2 ] [ −1 − 2 , −1 + 2 ]

( − ∞ , 4 − 2 ) ∪ ( 4 + 2 , ∞ ) ( − ∞ , 4 − 2 ) ∪ ( 4 + 2 , ∞ )

ⓐ ( − ∞ , ∞ ) ( − ∞ , ∞ ) ⓑ no solution

ⓐ no solution ⓑ ( − ∞ , ∞ ) ( − ∞ , ∞ )

Section 9.1 Exercises

a = ± 7 a = ± 7

r = ± 2 6 r = ± 2 6

u = ± 10 3 u = ± 10 3

m = ± 3 m = ± 3

x = ± 6 x = ± 6

x = ± 5 i x = ± 5 i

x = ± 3 7 i x = ± 3 7 i

x = ± 9 x = ± 9

a = ± 2 5 a = ± 2 5

p = ± 4 7 7 p = ± 4 7 7

y = ± 4 10 5 y = ± 4 10 5

u = 14 , u = −2 u = 14 , u = −2

m = 6 ± 2 5 m = 6 ± 2 5

r = 1 2 ± 3 2 r = 1 2 ± 3 2

y = − 2 3 ± 2 2 9 y = − 2 3 ± 2 2 9

a = 7 ± 5 2 a = 7 ± 5 2

x = −3 ± 2 2 x = −3 ± 2 2

c = − 1 5 ± 3 3 5 i c = − 1 5 ± 3 3 5 i

x = 3 4 ± 7 2 i x = 3 4 ± 7 2 i

m = 2 ± 2 2 m = 2 ± 2 2

x = 3 + 2 3 , x = 3 − 2 3 x = 3 + 2 3 , x = 3 − 2 3

x = − 3 5 , x = 9 5 x = − 3 5 , x = 9 5

x = − 7 6 , x = 11 6 x = − 7 6 , x = 11 6

r = ± 4 r = ± 4

a = 4 ± 2 7 a = 4 ± 2 7

w = 1 , w = 5 3 w = 1 , w = 5 3

a = ± 3 2 a = ± 3 2

p = 1 3 ± 7 3 p = 1 3 ± 7 3

m = ± 2 2 i m = ± 2 2 i

u = 7 ± 6 2 u = 7 ± 6 2

m = 4 ± 2 3 m = 4 ± 2 3

x = −3 , x = −7 x = −3 , x = −7

c = ± 5 6 6 c = ± 5 6 6

x = 6 ± 2 i x = 6 ± 2 i

Answers will vary.

Section 9.2 Exercises

ⓐ ( m − 12 ) 2 ( m − 12 ) 2 ⓑ ( x − 11 2 ) 2 ( x − 11 2 ) 2 ⓒ ( p − 1 6 ) 2 ( p − 1 6 ) 2

ⓐ ( p − 11 ) 2 ( p − 11 ) 2 ⓑ ( y + 5 2 ) 2 ( y + 5 2 ) 2 ⓒ ( m + 1 5 ) 2 ( m + 1 5 ) 2

u = −3 , u = 1 u = −3 , u = 1

x = −1 , x = 21 x = −1 , x = 21

m = −2 ± 2 10 i m = −2 ± 2 10 i

r = −3 ± 2 i r = −3 ± 2 i

a = 5 ± 2 5 a = 5 ± 2 5

x = − 5 2 ± 33 2 x = − 5 2 ± 33 2

u = 1 , u = 13 u = 1 , u = 13

r = −2 , r = 6 r = −2 , r = 6

v = 9 2 ± 89 2 v = 9 2 ± 89 2

x = 5 ± 30 x = 5 ± 30

x = −7 , x = 3 x = −7 , x = 3

m = −11 , m = 1 m = −11 , m = 1

n = 1 ± 14 n = 1 ± 14

c = −2 , c = 3 2 c = −2 , c = 3 2

x = −5 , x = 3 2 x = −5 , x = 3 2

p = − 7 4 ± 161 4 p = − 7 4 ± 161 4

x = 3 10 ± 191 10 i x = 3 10 ± 191 10 i

Section 9.3 Exercises

m = −1 , m = 3 4 m = −1 , m = 3 4

p = 1 2 , p = 3 p = 1 2 , p = 3

p = −4 , p = −3 p = −4 , p = −3

r = −3 , r = 11 r = −3 , r = 11

u = −7 ± 73 6 u = −7 ± 73 6

a = 3 ± 3 2 a = 3 ± 3 2

x = −4 ± 2 5 x = −4 ± 2 5

y = −2 , y = 1 3 y = −2 , y = 1 3

x = − 3 4 ± 15 4 i x = − 3 4 ± 15 4 i

x = 3 8 ± 7 8 i x = 3 8 ± 7 8 i

v = 2 ± 2 13 v = 2 ± 2 13

y = −4 , y = 7 y = −4 , y = 7

b = −2 ± 11 6 b = −2 ± 11 6

c = − 3 4 c = − 3 4

q = − 3 5 q = − 3 5

ⓐ no real solutions no real solutions ⓑ 1 1 ⓒ 2 2

ⓐ 1 1 ⓑ no real solutions no real solutions ⓒ 2 2

ⓐ factor factor ⓑ square root square root ⓒ Quadratic Formula Quadratic Formula

ⓐ Quadratic Formula Quadratic Formula ⓑ square root square root ⓒ factor factor

Section 9.4 Exercises

x = ± 3 , x = ± 2 x = ± 3 , x = ± 2

x = ± 15 , x = ± 2 i x = ± 15 , x = ± 2 i

x = ± 1 , x = ± 6 2 x = ± 1 , x = ± 6 2

x = ± 3 , x = ± 2 2 x = ± 3 , x = ± 2 2

x = −1 , x = 12 x = −1 , x = 12

x = − 5 3 , x = 0 x = − 5 3 , x = 0

x = 0 , x = ± 3 x = 0 , x = ± 3

x = ± 11 2 , x = ± 7 x = ± 11 2 , x = ± 7

x = 25 x = 25

x = 4 x = 4

x = 1 4 x = 1 4

x = 1 25 , x = 9 4 x = 1 25 , x = 9 4

x = −1 , x = −512 x = −1 , x = −512

x = 8 , x = −216 x = 8 , x = −216

x = 27 8 , x = − 64 27 x = 27 8 , x = − 64 27

x = 27 512 , x = 125 x = 27 512 , x = 125

x = 1 , x = 49 x = 1 , x = 49

x = −2 , x = − 3 5 x = −2 , x = − 3 5

x = −2 , x = 4 3 x = −2 , x = 4 3

Section 9.5 Exercises

Two consecutive odd numbers whose product is 255 are 15 and 17, and −15 and −17.

The first and second consecutive odd numbers are 24 and 26, and −26 and −24.

Two consecutive odd numbers whose product is 483 are 21 and 23, and −21 and −23.

The width of the triangle is 5 inches and the height is 18 inches.

The base is 24 feet and the height of the triangle is 10 feet.

The length of the driveway is 15.0 feet and the width is 3.3 feet.

The length of table is 8 feet and the width is 3 feet.

The length of the legs of the right triangle are 3.2 and 9.6 cm.

The length of the diagonal fencing is 7.3 yards.

The ladder will reach 24.5 feet on the side of the house.

The arrow will reach 400 feet on its way up in 2.8 seconds and on the way down in 11 seconds.

The bullet will take 70 seconds to hit the ground.

The speed of the wind was 49 mph.

The speed of the current was 4.3 mph.

The less experienced painter takes 6 hours and the experienced painter takes 3 hours to do the job alone.

Machine #1 takes 3.6 hours and Machine #2 takes 4.6 hours to do the job alone.

Section 9.6 Exercises

ⓐ down ⓑ up

ⓐ x = −4 x = −4 ; ⓑ ( −4 , −17 ) ( −4 , −17 )

ⓐ x = 1 x = 1 ; ⓑ ( 1 , 2 ) ( 1 , 2 )

y -intercept: ( 0 , 6 ) ; ( 0 , 6 ) ; x -intercept ( −1 , 0 ) , ( −6 , 0 ) ( −1 , 0 ) , ( −6 , 0 )

y -intercept: ( 0 , 12 ) ; ( 0 , 12 ) ; x -intercept ( −2 , 0 ) , ( −6 , 0 ) ( −2 , 0 ) , ( −6 , 0 )

y -intercept: ( 0 , −19 ) ; ( 0 , −19 ) ; x -intercept: none

y -intercept: ( 0 , 13 ) ; ( 0 , 13 ) ; x -intercept: none

y -intercept: ( 0 , −16 ) ; ( 0 , −16 ) ; x -intercept ( 5 2 , 0 ) ( 5 2 , 0 )

y -intercept: ( 0 , 9 ) ; ( 0 , 9 ) ; x -intercept ( −3 , 0 ) ( −3 , 0 )

The minimum value is − 9 8 − 9 8 when x = − 1 4 . x = − 1 4 .

The maximum value is 6 when x = 3.

The maximum value is 16 when x = 0.

In 5.3 sec the arrow will reach maximum height of 486 ft.

In 3.4 seconds the ball will reach its maximum height of 185.6 feet.

20 computers will give the maximum of $400 in receipts.

He will be able to sell 35 pairs of boots at the maximum revenue of $1,225.

The length of the side along the river of the corral is 120 feet and the maximum area is 7,200 square feet.

The maximum area of the patio is 800 feet.

Section 9.7 Exercises

ⓑ The graph of g ( x ) = x 2 + 4 g ( x ) = x 2 + 4 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 4 units. The graph of h ( x ) = x 2 − 4 h ( x ) = x 2 − 4 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shift down 4 units.

ⓑ The graph of g ( x ) = ( x − 3 ) 2 g ( x ) = ( x − 3 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted right 3 units. The graph of h ( x ) = ( x + 3 ) 2 h ( x ) = ( x + 3 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 3 units.

f ( x ) = −3 ( x + 2 ) 2 + 7 f ( x ) = −3 ( x + 2 ) 2 + 7

f ( x ) = 3 ( x + 1 ) 2 − 4 f ( x ) = 3 ( x + 1 ) 2 − 4

ⓐ f ( x ) = ( x + 3 ) 2 − 4 f ( x ) = ( x + 3 ) 2 − 4 ⓑ

ⓐ f ( x ) = ( x + 2 ) 2 − 1 f ( x ) = ( x + 2 ) 2 − 1 ⓑ

ⓐ f ( x ) = ( x − 3 ) 2 + 6 f ( x ) = ( x − 3 ) 2 + 6 ⓑ

ⓐ f ( x ) = − ( x − 4 ) 2 + 0 f ( x ) = − ( x − 4 ) 2 + 0 ⓑ

ⓐ f ( x ) = − ( x + 2 ) 2 + 6 f ( x ) = − ( x + 2 ) 2 + 6 ⓑ

ⓐ f ( x ) = 5 ( x − 1 ) 2 + 3 f ( x ) = 5 ( x − 1 ) 2 + 3 ⓑ

ⓐ f ( x ) = 2 ( x − 1 ) 2 − 1 f ( x ) = 2 ( x − 1 ) 2 − 1 ⓑ

ⓐ f ( x ) = −2 ( x − 2 ) 2 − 2 f ( x ) = −2 ( x − 2 ) 2 − 2 ⓑ

ⓐ f ( x ) = 2 ( x + 1 ) 2 + 4 f ( x ) = 2 ( x + 1 ) 2 + 4 ⓑ

ⓐ f ( x ) = − ( x − 1 ) 2 − 3 f ( x ) = − ( x − 1 ) 2 − 3 ⓑ

f ( x ) = ( x + 1 ) 2 − 5 f ( x ) = ( x + 1 ) 2 − 5

f ( x ) = 2 ( x − 1 ) 2 − 3 f ( x ) = 2 ( x − 1 ) 2 − 3

Section 9.8 Exercises

ⓑ ( − ∞ , −5 ) ∪ ( −1 , ∞ ) ( − ∞ , −5 ) ∪ ( −1 , ∞ )

ⓑ [ −3 , −1 ] [ −3 , −1 ]

ⓑ ( − ∞ , −6 ] ∪ [ 3 , ∞ ) ( − ∞ , −6 ] ∪ [ 3 , ∞ )

ⓑ [ −3 , 4 ] [ −3 , 4 ]

( − ∞ , −4 ] ∪ [ 1 , ∞ ) ( − ∞ , −4 ] ∪ [ 1 , ∞ )

( 2 , 5 ) ( 2 , 5 )

( − ∞ , −5 ) ∪ ( −3 , ∞ ) ( − ∞ , −5 ) ∪ ( −3 , ∞ )

[ 2 − 2 , 2 + 2 ] [ 2 − 2 , 2 + 2 ]

( − ∞ , 5 − 6 ) ∪ ( 5 + 6 , ∞ ) ( − ∞ , 5 − 6 ) ∪ ( 5 + 6 , ∞ )

( − ∞ , − 5 2 ] ∪ [ − 2 3 , ∞ ) ( − ∞ , − 5 2 ] ∪ [ − 2 3 , ∞ )

[ − 1 2 , 4 ] [ − 1 2 , 4 ]

( − ∞ , ∞ ) . ( − ∞ , ∞ ) .

no solution

Review Exercises

y = ± 12 y = ± 12

a = ± 5 a = ± 5

r = ± 4 2 i r = ± 4 2 i

w = ± 5 3 w = ± 5 3

p = −1 , 9 p = −1 , 9

x = 1 4 ± 3 4 x = 1 4 ± 3 4

n = 4 ± 10 2 n = 4 ± 10 2

n = −5 ± 2 3 n = −5 ± 2 3

( x + 11 ) 2 ( x + 11 ) 2

( a − 3 2 ) 2 ( a − 3 2 ) 2

d = −13 , −1 d = −13 , −1

m = −3 ± 10 i m = −3 ± 10 i

v = 7 ± 3 2 v = 7 ± 3 2

m = −9 , −1 m = −9 , −1

a = 3 2 ± 41 2 a = 3 2 ± 41 2

u = −6 ± 2 2 u = −6 ± 2 2

p = 0 , 6 p = 0 , 6

y = − 1 2 , 2 y = − 1 2 , 2

c = − 1 3 ± 2 7 3 c = − 1 3 ± 2 7 3

x = 3 2 ± 1 2 i x = 3 2 ± 1 2 i

x = 1 4 , 1 x = 1 4 , 1

r = −6 , 7 r = −6 , 7

v = −1 ± 21 8 v = −1 ± 21 8

m = −4 ± 10 3 m = −4 ± 10 3

a = 5 12 ± 23 12 i a = 5 12 ± 23 12 i

u = 5 ± 21 u = 5 ± 21

p = 4 ± 5 5 p = 4 ± 5 5

c = − 1 2 c = − 1 2

ⓐ 1 ⓑ 2 ⓒ 2 ⓓ 2

ⓐ factor ⓑ Quadratic Formula ⓒ square root

x = ± 2 , x = ± 2 3 x = ± 2 , x = ± 2 3

x = ± 1 , x = ± 1 2 x = ± 1 , x = ± 1 2

x = 16 x = 16

x = 64 , x = 216 x = 64 , x = 216

Two consecutive even numbers whose product is 624 are 24 and 26, and −24 and −26.

The height is 14 inches and the width is 10 inches.

The length of the diagonal is 3.6 feet.

The width of the serving table is 4.7 feet and the length is 16.1 feet.

The speed of the wind was 30 mph.

One man takes 3 hours and the other man 6 hours to finish the repair alone.

ⓐ up ⓑ down

x = 2 ; ( 2 , −7 ) x = 2 ; ( 2 , −7 )

y : ( 0 , 15 ) x : ( 3 , 0 ) , ( 5 , 0 ) y : ( 0 , 15 ) x : ( 3 , 0 ) , ( 5 , 0 )

y : ( 0 , −46 ) x : none y : ( 0 , −46 ) x : none

y : ( 0 , −64 ) x : ( −8 , 0 ) y : ( 0 , −64 ) x : ( −8 , 0 )

The maximum value is 2 when x = 2.

The length adjacent to the building is 90 feet giving a maximum area of 4,050 square feet.

f ( x ) = 2 ( x − 1 ) 2 − 6 f ( x ) = 2 ( x − 1 ) 2 − 6

ⓐ f ( x ) = 3 ( x − 1 ) 2 − 4 f ( x ) = 3 ( x − 1 ) 2 − 4 ⓑ

ⓐ f ( x ) = −3 ( x + 2 ) 2 + 7 f ( x ) = −3 ( x + 2 ) 2 + 7 ⓑ

ⓑ ( − ∞ , −2 ) ∪ ( 3 , ∞ ) ( − ∞ , −2 ) ∪ ( 3 , ∞ )

[ −2 , 1 ] [ −2 , 1 ]

( 2 , 4 ) ( 2 , 4 )

[ 3 − 5 , 3 + 5 ] [ 3 − 5 , 3 + 5 ]

Practice Test

w = −2 , w = −8 w = −2 , w = −8

m = 1 , m = 3 2 m = 1 , m = 3 2

y = 2 3 y = 2 3

y = 1 , y = −27 y = 1 , y = −27

ⓐ down ⓑ x = −4 x = −4 ⓒ ( −4 , 0 ) ( −4 , 0 ) ⓓ y : ( 0 , 16 ) ; x : ( −4 , 0 ) y : ( 0 , 16 ) ; x : ( −4 , 0 ) ⓔ minimum value of −4 −4 when x = 0 x = 0

( − ∞ , − 5 2 ) ∪ ( 2 , ∞ ) ( − ∞ , − 5 2 ) ∪ ( 2 , ∞ )

The diagonal is 3.8 units long.

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• Authors: Lynn Marecek
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• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-9

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Math Expressions Grade 5 Unit 5 Lesson 9 Answer Key Division Practice

Solve the questions in Math Expressions Grade 5 Homework and Remembering Answer Key Unit 5 Lesson 9 Answer Key Division Practice to attempt the exam with higher confidence. https://mathexpressionsanswerkey.com/math-expressions-grade-5-unit-5-lesson-9-answer-key/

Math Expressions Common Core Grade 5 Unit 5 Lesson 9 Answer Key Division Practice

Math Expressions Grade 5 Unit 5 Lesson 9 Homework

Unit 5 Lesson 9 Division Practice Math Expressions Question 1.

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 350  ÷ 7

Set up the problem with the long division bracket. Put the dividend inside the bracket and the divisor on the outside to the left.

Put 350, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 7, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 35 by the divisor, 7.

35 divided by 7 is 5, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 7 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 35 ÷ 0.7 = 50

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 2400  ÷ 6

Put 2400, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 6, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first three numbers of the dividend, 240 by the divisor, 6.

240 divided by 6 is 4, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 6 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 24 ÷ 0.06 = 400

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 6.4  ÷ 8

Put 6.4, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 8, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first  numbers of the dividend, 6.4 by the divisor, 8.

6.4 divided by 8 is 0.8, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 6 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 6.4 ÷ 0.8 = 0.8

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 1800  ÷ 3

Put 1800, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 3, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first three numbers of the dividend, 180 by the divisor, 3.

180 divided by 3 is 60, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 6 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 18 ÷ 0.03 = 600

Put 33, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 3, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first  numbers of the dividend, 33 by the divisor, 3.

33 divided by 3 is 11, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 3 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 33 ÷ 3 = 11

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 6500  ÷ 5

Put 6500, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 5, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 65 by the divisor, 5.

65 divided by 5 is 1, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 1 so you have 15. 15 divided by 5 is 3, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 0.65 ÷ 0.05 = 13

Put 72, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 12, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first  numbers of the dividend, 72 by the divisor, 12.

72 divided by 12 is 6, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 12 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 72 ÷ 12 = 6

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 1156  ÷4

Put 1156, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 4, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 11 by the divisor, 4.

11 divided by 4 is 2, with a remainder of 3. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 3 so you have 5. 35 divided by 4 is 8, with a remainder of 3. Bring down the next number of the dividend and insert it after the 3 so you have 6. 36 divided by 4 is 9, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 11.56 ÷ 0.04 = 289

Put 216, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 8, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 21 by the divisor, 8.

21 divided by 8 is 2, with a remainder of 5. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 5 so you have 56. 56 divided by 8 is 7, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 216 ÷ 8 = 27

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 4904  ÷ 8

Put 4904, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 8, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 49 by the divisor, 8.

49 divided by 8 is 6, with a remainder of 1. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 1 so you have 10 10 divided by 8 is 1, with a remainder of 2. Bring down the next number of the dividend and insert it after the 2 so you have 4. 24 divided by 8 is 3, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 490.4 ÷ 0.8 = 613

Put 2380, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 28, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first three numbers of the dividend, 224 by the divisor, 28.

224 divided by 28 is 8, with a remainder of 14. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 14 so you have 140. 140 divided by 28 is 5, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 2380 ÷ 28 = 85

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 5148  ÷ 33

Put 5148, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 33, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 51 by the divisor, 33.

51 divided by 33 is 1, with a remainder of 18. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 18 so you have 184. 184 divided by 33 is 5, with a remainder of 19. Bring down the next number of the dividend and insert it after the 19 so you have 198. 198 divided by 33 is 6, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 5.148 ÷ 0.033 = 156

Solve. Explain how you know your answer is reasonable.

Question 13. Georgia works as a florist. She has 93 roses to arrange in vases. Each vase holds 6 roses. How many roses will Georgia have left over? Answer:  Georgia will be left with 15.5 roses.

Put 93, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 6, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first  numbers of the dividend, 9 by the divisor, 6.

9 divided by 6 is 1, with a remainder of 3. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 3 so you have 33. 33 divided by 6 is 5, with a remainder of 3. Bring down the next number of the dividend and insert it after the 3 so you have 30. 30 divided by 6 is 5, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 93 ÷ 6 = 15.5

Totally, Georgia will be left with 15.5 roses.

Question 14. Julia is jarring peaches. She has 25.5 cups of peaches. Each jar holds 3 cups. How many jars will Julia need to hold all the peaches? Answer: Julia will need 8.5 jars to  hold the peaches.

Put 25.5, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 3, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 25 by the divisor, 3.

25 divided by 3 is 8, with a remainder of 1. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 1 so you have 15. 15 divided by 3 is 5, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 25.5 ÷ 3 = 8.5

Thus, Julia will need 8.5 jars to  hold the peaches.

Question 15. The area of a room is 114 square feet. The length of the room is 9.5 feet. What is the width of the room? Answer: The width of the room is 12 feet.

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 1140  ÷ 95

Put 1140, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 95, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 114 by the divisor, 95.

114 divided by 9.5 is 95, with a remainder of 1. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 19 so you have 190. 190 divided by 95 is 2, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 114 ÷ 9.5 = 12

Thus, The width of the room is 12 feet.

Math Expressions Grade 5 Unit 5 Lesson 9 Remembering

Add or Subtract.

Explanation: By simplifying the given fractions, 1\(\frac{1}{2}\) = \(\frac{2 + 1}{2}\) = \(\frac{3}{2}\) \(\frac{3}{2}\)  can be written as 1.5 5\(\frac{5}{6}\) = \(\frac{30 + 5}{6}\) = \(\frac{35}{6}\) \(\frac{35}{6}\)  can be written as 15.83 Now add both the decimal numbers Then, 1.5 + 5.83 = 7.33.

Explanation: By simplifying the given fractions, 2\(\frac{2}{5}\) = \(\frac{10 + 3}{5}\) = \(\frac{13}{5}\) \(\frac{13}{5}\)  can be written as 2.6 5\(\frac{3}{10}\) = \(\frac{50 + 3}{10}\) = \(\frac{53}{10}\) \(\frac{53}{10}\)  can be written as 5.3 Now add both the decimal numbers Then, 2.6 + 5.3 = 7.9.

Explanation: By simplifying the given fractions, 1\(\frac{1}{3}\) = \(\frac{3 + 1}{3}\) = \(\frac{4}{3}\) \(\frac{4}{3}\)  can be written as 1.33 \(\frac{1}{6}\)  can be written as 0.16 Now substract both the decimal numbers Then, 1.33 – 0.16 = 1.17.

Explanation: By simplifying the given fractions, 7\(\frac{3}{10}\) = \(\frac{70 + 3}{10}\) = \(\frac{73}{10}\) \(\frac{73}{10}\)  can be written as 7.3 2\(\frac{1}{5}\) = \(\frac{10 + 1}{5}\) = \(\frac{11}{5}\) \(\frac{11}{5}\)  can be written as 2.2 Now add both the decimal numbers Then, 7.3 + 2.2 = 9.5.

Explanation: By simplifying the given fractions, 9\(\frac{1}{8}\) = \(\frac{72 + 1}{8}\) = \(\frac{73}{8}\) \(\frac{73}{8}\)  can be written as 9.125 2\(\frac{3}{4}\) = \(\frac{8 + 3}{4}\) = \(\frac{11}{4}\) \(\frac{11}{4}\)  can be written as 2.75 Now substract both the decimal numbers Then, 9.125 – 2.75 = 6.375.

Explanation: By simplifying the given fractions, 5\(\frac{2}{3}\) = \(\frac{15 + 2}{3}\) = \(\frac{17}{3}\) \(\frac{17}{3}\)  can be written as 5.66 Now substract both the numbers Then, 12 – 5.66 = 6.34.

Find each product.

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 640  ÷ 8

Put 640, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 8, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 64 by the divisor, 8.

64 divided by 8 is 8, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 0. 0 divided by 8 is 0, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 6.4 ÷ 0.08 = 80

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 72  ÷ 8

Put 72, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 8, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first  numbers of the dividend, 72 by the divisor, 8.

72 divided by 8 is 9, with a remainder of 0. You can ignore the remainder for now. Since the remainder is 0, your long division is done.

So, 7.2 ÷ 0.8 = 9

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 567  ÷ 7

Put 567, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 7, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 56 by the divisor, 7.

56 divided by 7 is 8, with a remainder of 0. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 0 so you have 07. 7 divided by 7 is 1, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 5.67 ÷ 0.07 = 81

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 533.6  ÷ 58

Put 533.6, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 58, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first three numbers of the dividend, 533 by the divisor, 58.

533 divided by 58 is 9, with a remainder of 11. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 11 so you have 116. 116 divided by 58 is 2, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 5.336 ÷ 0.58 = 9.2

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 63  ÷ 9

Put 63, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 9, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first three numbers of the dividend, 63 by the divisor, 9.

63 divided by 9 is 7, with a remainder of 0. You can ignore the remainder for now. Since the remainder is 0, your long division is done.

So, 6.3 ÷ 0.9 = 7

If the divisor is a decimal number, move the decimal all the way to the right. Count the number of places and move the decimal in the dividend the same number of places. Add zeroes if needed. Then we have 175  ÷ 5

Put 175, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 5, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 17 by the divisor, 5.

17 divided by 5 is 3, with a remainder of 2. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 2 so you have 25. 25 divided by 5 is 5, with a remainder of 0. Since the remainder is 0, your long division is done.

So, 1.75 ÷ 0.05 = 35

Question 19. Stretch Your Thinking Write a real world division problem for which you would drop the remainder. Answer: Alex and joy have 147 awesome unicorn stickers, if they can only fir 13 stickers on each page of their sticker book, How many pages will be full of stickers?

Put 147, the dividend, on the inside of the bracket. The dividend is the number you’re dividing. Put 13, the divisor, on the outside of the bracket. The divisor is the number you’re dividing by. Divide the first two numbers of the dividend, 14 by the divisor, 13.

14 divided by 13 is 1, with a remainder of 1. You can ignore the remainder for now. Bring down the next number of the dividend and insert it after the 1 so you have 17. 17 divided by 13 is 1, with a remainder of 4. Bring down the next number of the dividend and insert it after the 4 so you have 40. 40 divided by 13 is 3, with a remainder of  10. Since the remainder is 10, your long division is done.

So, 147 ÷ 13 = 11.3.

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Home > CC1 > Chapter 9 > Lesson 9.1.1

Lesson 9.1.1, lesson 9.1.2, lesson 9.2.1, lesson 9.2.2, lesson 9.2.3, lesson 9.2.4.

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Go Math Grade 2 Chapter 9 Answer Key Pdf Length in Metric Units

Go Math Grade 2 Chapter 9 Answer Key Pdf : Hey guys!!! Are you searching for the grade 2 answer key on various websites? If yes then you can stop your search now. Here you can get detailed explanations for all the questions on this page. As per your convenience, we have provided the Go Math Grade 2 Answer Key Chapter 9 Length in Metric Units in pdf format. Hence Download HMH Go Math Grade 2 Chapter 9 Solution Key Length in Metric Units Concepts for free of cost.

Length in Metric Units Go Math Grade 2 Chapter 9 Answer Key Pdf

Check out the topics before starting your preparation for the exams. We have provided solutions for all the questions as per the textbook. Test yourself by solving the problems given in the mid-chapter checkpoint and review test. By solving the review test problems you can know how much you have learned from this chapter. Click on the below-given links and kickstart your preparation.

Chapter: 9 – Length in Metric Units

• Length in Metric Units Show What You Know – Page 600
• Length in Metric Units Vocabulary Builder – Page 601
• Length in Metric Units Game Estimating Length – Page 602
• Length in Metric Units Vocabulary Game – Page(602A-602B) 

Lesson: 1 Measure with a Centimeter Model

• Lesson 9.1 Measure with a Centimeter Model – Page(603-608)
• Measure with a Centimeter Model Homework & Practice 9.1 – Page(607-608)

Lesson: 2 Estimate Lengths in Centimeters

• Lesson 9.2 Estimate Lengths in Centimeters – Page(609-614)
• Estimate Lengths in Centimeters Homework & Practice 9.2 – Page(613-614)

Lesson: 3 Measure with a Centimeter Ruler

• Lesson 9.3 Measure with a Centimeter Ruler – Page(615-620)
• Measure with a Centimeter Ruler Homework & Practice 9.3 – Page(619-620)

Lesson: 4 Problem Solving • Add and Subtract Lengths

• Lesson 9.4 Problem Solving • Add and Subtract Lengths – Page(621-626)
• Problem Solving • Add and Subtract Lengths Homework & Practice 9.4 – Page(625-626)

Mid-Chapter Checkpoint

• Length in Metric Units Mid-Chapter Checkpoint – Page 624

Lesson: 5 Centimeters and Meters

• Lesson 9.5 Centimeters and Meters – Page(627-632)
• Centimeters and Meters Homework & Practice 9.5 – Page(631-632)

Lesson: 6 Estimate Lengths in Meters

• Lesson 9.6 Estimate Lengths in Meters – Page(633-638)
• Estimate Lengths in Meters Homework & Practice 9.6 – Page(637-638)

Lesson: 7 Measure and Compare Lengths

• Lesson 9.7 Measure and Compare Lengths – Page(639-644)
• Measure and Compare Lengths Homework & Practice 9.7 – Page(643-644)

Review/Test

• Length in Metric Units Review/Test – Page(645-648)

Length in Metric Units Show What You Know

Explanation: Use the cube to measure the length of the pencil. The estimated measure of a pencil is 7

Question 3.

Explanation: Use the cube to measure the length of the pen. The estimated measure of a pen is 7.

Length in Metric Units Vocabulary Builder

Length in Metric Units Game Estimating Length

• Take turns choosing a picture. Find the real object.
• Each player estimates the length of the object in cubes and then makes a cube train for his or her estimate.
• Compare the cube trains to the length of the object. The player with the closer estimate puts a counter on the picture. If there is a tie, both players put a counter on the picture.

Length in Metric Units Vocabulary Game

For 3 players Materials

• 4 sets of word cards

How to Play

• Every player is dealt 5 cards. Put the rest face-down in a draw pile.
• If the player has the word card, he or she gives it to you. Put both cards in front of you. Take another turn.
• If the player does not have the word, he or she answers, “Go fish.” Take a card from the pile. If the word you get matches one you are holding, put both cards in front of you. Take another turn. If it does not match, your turn is over.

The Write Way Reflect Choose one idea. Write about it in the space below.

• Compare a centimeter to a meter. Explain how they are alike and how they are different.

Lesson 9.1 Measure with a Centimeter Model

Essential Question How do you use a centimeter model to measure the lengths of objects?

Listen and Draw

HOME CONNECTION • Your child used unit cubes as an introduction to measurement of length before using metric measurement tools.

MATHEMATICAL PRACTICES Use Tools Describe how to use unit cubes to measure an object’s length. Answer: We can measure the length of the object by locating the unit cubes in a sequence.

Share and Show

On Your Own

Problem Solving • Applications

TAKE HOME ACTIVITY • Have your child compare the lengths of other objects to those in this lesson.

Measure with a Centimeter Model Homework & Practice 9.1

Go Math Grade 2 Pdf Download Free Question 5. WRITE Write about using a unit cube to measure lengths in this lesson. ______________ _____________ Answer: Let us say your cube has the dimensions of 3 × 4 × 5 to find the area of the cube in the cubic measure you would multiply the three dimensions together and divide by the area of the cubes.

Question 4. Dan has a paper strip that is 28 inches long. He tears 6 inches off the strip. How long is the paper strip now? _________ inches Answer:  22 inches.

Explanation: Given Dan has a paper strip that is 28 inches long He tears 6 inches off the strip so 28 inches – 6 inches = 22 inches 22 inches long is the paper strip.

Question 5. Rita has 1 quarter, 1 dime, and 2 pennies. What is the total value of Rita’s coins? $ ______ or ______ cents Answer: Quarter = 25 cents dime = 10 cents 2 pennies = 2 cents 25 + 10 + 2 = 37 cents Thus the total value of Rita’s coins 37 cents.

Lesson 9.2 Estimate Lengths in Centimeters

Essential Question How do you use known lengths to estimate unknown lengths?

Find three classroom objects that are shorter than your 10-centimeter strip. Draw the objects. Write estimates for their lengths. about ________ centimeters

about ________ centimeters

HOME CONNECTION • Your child used a 10-centimeter strip of paper to practice estimating the lengths of some classroom objects.

Question 8. MATHEMATICAL PRACTICE Analyze Mr. Lott has 250 more centimeters of tape than Mrs. Sanchez. Mr. Lott has 775 centimeters of tape. How many centimeters of tape does Mrs. Sanchez have? ________ centimeters Answer: 525 centimeters

Explanation: Given, Mr. Lott has 250 more centimeters of tape than Mrs. Sanchez. Mr. Lott has 775 centimeters of tape. To find the length of tape we have to subtract 250 from 775 775 – 250 = 525 centimeters

TAKE HOME ACTIVITY • Give your child an object that is about 5 centimeters long. Have him or her use it to estimate the lengths of some other objects.

Estimate Lengths in Centimeters Homework & Practice 9.2

Question 4. WRITE Choose one exercise above. Describe how you decided which estimate was the best choice. Answer: Lesson 9.2 Estimate Lengths in Centimeters in this exercise we estimate the length of an object by comparing with the other object. So, this was the best choice.

Question 3. What is the sum? 14 + 65 = ______ Answer: 79

Question 4. Adrian has a cube train that is 13 inches long. He adds 6 inches of cubes to the train. How long is the cube train now? _______ inches Answer: 19 inches

Explanation: Given, Adrian has a cube train that is 13 inches long. He adds 6 inches of cubes to the train. 13 + 6 = 19 inches

Lesson 9.3 Measure with a Centimeter Ruler

Essential Question How do you use a centimeter ruler to measure lengths?

HOME CONNECTION • Your child used unit cubes to measure the lengths of some classroom objects as an introduction to measuring lengths in centimeters.

Question 8. GO DEEPER A marker is almost 13 centimeters long. This length ends between which two centimeter-marks on a ruler? ____________________ _____________________ Answer: It ends between 13 cm and 14 cm mark.

Explanation: Since this marker in the above question is almost 13 centimeters long and definitely ends between two centimeter marks, the two centimeters that the length of this marker ends between on a ruler should be 13cm and 14 cm marks on the ruler.

Explanation: Shown in the given figure that length of the crayon is between 3 to 11 cms hence 11-3 we get 8 centimeters

TAKE HOME ACTIVITY • Have your child measure the lengths of some objects using a centimeter ruler.

Measure with a Centimeter Ruler Homework & Practice 9.3

Question 4. WRITE Measure the length of the top of your desk in centimeters. Describe how you found the length. ___________________ ___________________ Answer: 12 centimeters by using rulers find the length of the desk

Lesson 9.4 Problem Solving • Add and Subtract Lengths

Essential Question How can drawing a diagram help when solving problems about lengths?

Nate had 23 centimeters of string. He gave 9 centimeters of string to Myra. How much string does Nate have now?

Unlock the Problem What information do I need to use? Nate had _________ centimeters of string. He gave _______ centimeters of string to Myra.

Answer: Nate has 14 centimeters of string now.

HOME CONNECTION • Your child drew a diagram to represent a problem about lengths. The diagram can be used to choose the operation for solving the problem.

Try Another Problem

MATHEMATICAL PRACTICES Explain how your diagram shows what happened in the first problem. Answer:

TAKE HOME ACTIVITY • Have your child explain how he or she used a diagram to solve one problem in this lesson.

Problem Solving • Add and Subtract Lengths Homework & Practice 9.4

Question 3. What is another way to write the time half past 7? _____ : ______ Answer: 07 : 30

Length in Metric Units Mid-Chapter Checkpoint

Concepts and Skills

Lesson 9.5 Centimeters and Meters

Essential Question How is measuring in meters different from measuring in centimeters?

MATHEMATICAL PRACTICES Describe how the lengths of the yarn and the sheet of paper are different. Answer:

TAKE HOME ACTIVITY • Have your child describe how centimeters and meters are different.

Centimeters and Meters Homework & Practice 9.5

Problem Solving Question 3. Sally will measure the length of a wall in both centimeters and meters. Will there be fewer centimeters or fewer meters? Explain. _________________ _________________ Answer: There would be fewer meters. Since 1 m=100 cm. Fewer centimeters because there will be fewer centimeters

Question 4. WRITE Would you measure the length of a bench in centimeters or in meters? Explain your choice. Answer: Meters

Step-by-step explanation: Reason: Usually, the bench length is bigger than the length of the chair and the table. So it will be measured using meters. If we use a meter it will be easy to measure and accurate because it is somewhat bigger in length than a chair and table. 1 meter = 100 centimeters. The standard length of a bench will be 1.5 meters to 2 meters. Usually, 3 to 4 people will sit on the bench.

Question 3. Janet has a poster that is about 3 feet long. Fill in the blanks with the word inches or feet to make the statement true. 3 ______ is longer than 12 ________. Answer: The measurement of feets is longer than inches. 1 feet = 12 inches So, 3 feet is longer than 12 inches.

Question 5. List a group of coins with a value of $1.00. ______________ _____________ Answer: 100 pennies, 20 nickels, 10 dimes, or 4 quarters

Lesson 9.6 Estimate Lengths in Meters

Essential Question How do you estimate the lengths of objects in meters?

Is there a classroom object that is about 50 centimeters long? Draw and label it. Answer: No

MATHEMATICAL PRACTICES Describe how the lengths of the two real objects compare. Answer: Measure the length of an object twice, using length units of different lengths for the two measurements

Model and Draw

TAKE HOME ACTIVITY • With your child, estimate the lengths of some objects in meters.

Estimate Lengths in Meters Homework & Practice 9.6

Problem Solving Question 3. Barbara and Luke each placed 2 meter sticks end-to-end along the length of a large table. About how long is the table? about ________ meters Answer: 4 meters

Question 4. WRITE Choose one object from above. Describe how you estimated its length. __________________ __________________ Answer: Table By comparing with the real world we can estimate the length of the table.

Spiral Review Question 3. Sara has two $1 bills, 3 quarters, and 1 dime. How much money does she have? $ ____ . _____ Answer: $1 + $0.25 + $0.10 = $1.35

Lesson 9.7 Measure and Compare Lengths

Essential Question How do you find the difference between the lengths of two objects?

HOME CONNECTION • Your child measured these lengths as an introduction to measuring and then comparing lengths.

MATHEMATICAL PRACTICES Name a classroom object that is longer than the paintbrush. Explain how you know. Answer: Chalkboard as it is 2 meters long which is more than a paintbrush

Analyze Relationships Question 6. Mark has a rope that is 23 centimeters long. He cuts 15 centimeters off. What is the length of the rope now? _________ centimeters Answer: 8 centimeters

Question 7. The yellow ribbon is 15 centimeters longer than the green ribbon. The green ribbon is 29 centimeters long. What is the length of the yellow ribbon? _________ centimeters Answer: 44 centimeters

TAKE HOME ACTIVITY • Have your child tell you how he or she solved one of the problems in this lesson.

Measure and Compare Lengths Homework & Practice 9.7

Explanation: The length of the craft stick is 8 centimeters The length of the chalk is 6 centimeters 11 – 8 = 3 Thus the craft stick is 3 centimeters longer than the chalk.

Problem Solving

Solve. Write or draw to explain. Question 2. A string is 11 centimeters long, a ribbon is 24 centimeters long, and a large paper clip is 5 centimeters long. How much longer is the ribbon than the string? ________ centimeters longer Answer: 19 centimeters longer

Question 3. WRITE Suppose the lengths of two strings are 10 centimeters and 17 centimeters. Describe how the lengths of these two strings compare. _____________________ ______________________ Answer: The length of the second string is 7 centimeters longer than the first string.

Question 3. What is a reasonable estimate for the length of a real chalkboard? _______ feet Answer: 5 feet

Question 4. Cindy leaves at half past 2. At what time does Cindy leave? ___ : ___ Answer: 02:30

Length in Metric Units Review/Test

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Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice

Access the Answer Key for Go Math Grade 3 Chapter 9 Compare Fractions Extra Practice and use them as a quick reference. Get the Homework Help Go Math Grade 3 Answer Key Chapter 9 Compare Fractions Extra Practice and test your preparation standard. We provide the Step by Step Solution for all the Problems in 3rd Grade Go Math Ch 9 Extra Practice for better understanding.

Grade 3 Go Math Answer Key Chapter 9 Compare Fractions Extra Practice

Before you begin your preparation make sure to check out the topics list in 3rd Grade Go Math Ch 9 Answer Key Compare Fractions. You have different methods for solving the Comparing Fractions. Avail the quick links and get to know the concepts better. Practice the Problems in 3rd Grade Go Math Ch 9 on your own and verify the solutions in the Go Math Answer Key Grade 3 Chapter 9 Compare Fractions.

Common Core – Page No. 189000

Solve. Show your work.

Explanation:

Compare the fractions \(\frac{4}{8}\) and \(\frac{7}{8}\) The denominator of both the fractions is the same. So, compare the numerators. The numerator with the greatest number will be the greatest fraction. 7 is greater than 4. \(\frac{7}{8}\) > \(\frac{4}{8}\) Therefore Ed finished the greater part of his homework.

Answer: \(\frac{2}{3}\)

Rafael walked \(\frac{2}{3}\) mile and then rode his scooter \(\frac{2}{6}\) mile. The numerator of both the fractions is the same but the denominators are different. The fraction is smaller if the denominator is greater. Thus \(\frac{2}{3}\) > \(\frac{2}{6}\) \(\frac{2}{3}\) mile is farther.

Lessons 9.2–9.3

Compare. Write <, >, or =.

Question 3. \(\frac{2}{6}\) _____ \(\frac{3}{6}\)

Answer: \(\frac{2}{6}\) < \(\frac{3}{6}\)

Compare the fractions \(\frac{2}{6}\) and \(\frac{3}{6}\) The denominators are the same and the numerators are different. So compare the numerators of two fractions. 2 is less than 3. So, \(\frac{2}{6}\) < \(\frac{3}{6}\)

Question 4. \(\frac{6}{8}\) _____ \(\frac{1}{8}\)

Answer: \(\frac{6}{8}\) > \(\frac{1}{8}\)

Compare \(\frac{6}{8}\) and \(\frac{1}{8}\) The denominators are the same and the numerators are different. 6 is greater than 1. \(\frac{6}{8}\) > \(\frac{1}{8}\)

Question 5. \(\frac{3}{8}\) _____ \(\frac{3}{4}\)

Answer: \(\frac{3}{8}\) < \(\frac{3}{4}\)

Compare the fractions \(\frac{3}{8}\) and \(\frac{3}{4}\) The numerators are the same and denominators are different. Compare the denominators of two fractions. The fraction with lesser number will be the greatest. \(\frac{3}{8}\) < \(\frac{3}{4}\)

Question 6. \(\frac{1}{6}\) _____ \(\frac{1}{8}\)

Answer: \(\frac{1}{6}\) > \(\frac{1}{8}\)

The numerator of both the fractions is the same. The denominator with the greatest number will be the smallest fraction. So, \(\frac{1}{6}\) > \(\frac{1}{8}\)

Question 7. \(\frac{2}{3}\) _____ \(\frac{2}{6}\)

Answer: \(\frac{2}{3}\) > \(\frac{2}{6}\)

The numerator of both the fractions is the same. The denominator with the greatest number will be the smallest fraction. \(\frac{2}{3}\) > \(\frac{2}{6}\)

Question 8. \(\frac{1}{8}\) _____ \(\frac{3}{8}\)

Answer: \(\frac{1}{8}\) < \(\frac{3}{8}\)

The denominator of both the fractions is the same. So, compare the numerators. The fraction with the small number will be the smallest fraction. \(\frac{1}{8}\) < \(\frac{3}{8}\)

Compare. Write <, >, or = . Write the strategy you used.

Question 9. \(\frac{2}{8}\) _____ \(\frac{2}{3}\)

Answer: \(\frac{2}{8}\) < \(\frac{2}{3}\)

The numerator of both the fractions is the same. Compare the denominators. The denominator with the greatest number will be the smallest fraction. \(\frac{2}{8}\) < \(\frac{2}{3}\)

Question 10. \(\frac{5}{6}\) _____ \(\frac{1}{6}\)

Answer: \(\frac{5}{6}\) > \(\frac{1}{6}\)

The denominator of both the fractions is the same. The fraction with the small number will be the smallest fraction. 5 is greater than 1. \(\frac{5}{6}\) > \(\frac{1}{6}\)

Question 11. \(\frac{7}{8}\) _____ \(\frac{3}{4}\)

Answer: \(\frac{7}{8}\) > \(\frac{3}{4}\)

Compare \(\frac{7}{8}\) and \(\frac{3}{4}\) Make the denominators equal to compare the fractions. \(\frac{3}{4}\) × \(\frac{8}{8}\) = \(\frac{24}{32}\) \(\frac{7}{8}\) × \(\frac{4}{4}\) = \(\frac{28}{32}\) \(\frac{28}{32}\) > \(\frac{24}{32}\) \(\frac{7}{8}\) > \(\frac{3}{4}\)

Common Core – Page No. 190000

Write the fractions in order from greatest to least.

Question 1. \(\frac{1}{2}, \frac{1}{4}, \frac{1}{3}\) Type below: __________

Answer: \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

The numerator of the three fractions is the same. So, the order from greatest to least is \(\frac{1}{2}, \frac{1}{3}, \frac{1}{4}\)

Question 2. \(\frac{4}{6}, \frac{1}{6}, \frac{2}{6}\) Type below: __________

Answer: \(\frac{4}{6}, \frac{2}{6}, \frac{1}{6}\)

The denominator of the three fractions is the same. Compare the numerator of the fraction. 4 > 2 > 1 \(\frac{4}{6}, \frac{2}{6}, \frac{1}{6}\)

Question 3. \(\frac{3}{6}, \frac{3}{4}, \frac{3}{8}\) Type below: __________

Answer: \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}\)

The numerator of the three fractions is the same. So, the order is \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}\)

Question 4. \(\frac{6}{8}, \frac{3}{8}, \frac{5}{8}\) Type below: __________

Answer: \(\frac{6}{8}, \frac{5}{8}, \frac{3}{8}\)

The denominator of the three fractions is the same. Compare the numerator and write the order from greatest to least fraction. \(\frac{6}{8}, \frac{5}{8}, \frac{3}{8}\)

Lessons 9.6–9.7

Shade the model. Then divide the pieces to find the equivalent fraction.

Answer: \(\frac{1}{4}\) = \(\frac{2} {8}\)

\(\frac{1}{4}\) = \(\frac{2} {8}\)

Answer: \(\frac{2}{3}\) = \(\frac{4} {6}\)

\(\frac{2}{3}\) = \(\frac{4} {6}\)

Use the number line to find the equivalent fraction.

Answer: \(\frac{1}{2}\) = \(\frac{4} {8}\)

Answer: \(\frac{2}{2}\) = \(\frac{6} {6}\)

Each shape is 1 whole. Shade the model to find the equivalent fraction.

Answer: \(\frac{3}{4}\) = \(\frac{6} {8}\)

\(\frac{3}{4}\) = \(\frac{6} {8}\)

Answer: \(\frac{1}{2}\) = \(\frac{3} {6}\)

\(\frac{1}{2}\) = \(\frac{3} {6}\)

Learn the fundamentals right from the young age and become pro in the subject. To help you understand the concepts better we even drew pictures. Utilize Go Math Grade 3 Answer Key Chapter 9 Extra Practice and score better grades in the exams. To Clear all your queries check out Go Math Grade 3 Answer Key Chapter 9 Compare Fractions PDF.

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