Percentage Increase and Decrease: Worksheets with Answers
Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. And best of all they all (well, most!) come with answers.
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Mathster is a fantastic resource for creating online and paper-based assessments and homeworks. They have kindly allowed me to create 3 editable versions of each worksheet, complete with answers.
| Worksheet Name | 1 | 2 | 3 |
|---|---|---|---|
| Increase and Decrease by a Percentage | |||
| Find Percentage Increase and Decrease |
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Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. It really is one of the very best websites around.
| Name | Questions | Solutions |
|---|---|---|
| Percentages: increasing/decreasing by | ||
| Percentages: change | | |
| Percentages: multipliers | |
Solved Examples on Percentage
The solved examples on percentage will help us to understand how to solve step-by-step different types of percentage problems. Now we will apply the concept of percentage to solve various real-life examples on percentage.
Solved examples on percentage:
1. In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate.
Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
2. A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.
Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 8% of 400
= 8/100 × 400
= 3200/100
= 32
Therefore, total number of rotten fruits = 90 + 32 = 122
Therefore Number of fruits in good condition = 1000 - 122 = 878
Therefore Percentage of fruits in good condition = (878/1000 × 100)%
= (87800/1000)%
= 87.8%
3. Aaron had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he take along with him?
Solution:
Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
Therefore, the money he took for shopping is $ 3000.
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Solving Problems with Percentages
March 12, 2023.
Scheme of work: GCSE Higher: Year 10: Term 1: Solving Problems with Percentages
Prerequisite Knowledge
- Multiply and divide by powers of ten.
- Recognise the per cent symbol (%)
- Understand that per cent relates to number of parts per hundred.
- Write one number as a fraction of another
- Calculate equivalent fractions
Success Criteria
- Define percentage as a number of parts per hundred.
- Interpret fractions and percentages as operators
- Interpret percentages as a fraction or a decimal
- Interpret percentages changes as a fraction or a decimal
- Interpret percentage changes multiplicatively
- Express one quantity as a percentage of another
- Compare two quantities using percentages
- Work with percentages greater than 100%;
- Solve problems involving percentage change
- Solve problems involving percentage increase/decrease
- Solve problems involving original value problems
- Solve problems involving simple interest including in financial mathematics
- Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes
Key Concepts
- Use the place value table to illustrate the equivalence between fractions, decimals and percentages.
- To calculate a percentage of an amount without calculator students need to be able to calculate 10% of any number by dividing by 10.
- To calculate a percentage of an amount with a calculator students should be able to convert percentages to decimals mentally and use the percentage function.
- Equivalent ratios are useful for calculating the original amount after a percentage change.
- To calculate the multiplier for a percentage change students need to understand 100% as the original amount. E.g., 10% decrease represents 10% less than 100% = 0.9.
- Students need to have a secure understanding of the difference between simple and compound interest.
Common Misconceptions
- Students often consider percentages to be limited to 100%. A key learning point is to understand how percentages can exceed 100%.
- Students sometimes confuse 70% with a magnitude of 70 rather than 0.7.
- Students can confuse 65% with 1/65 rather than 65/100.
- Compound interest is often confused with simple interest, i.e., 10% compound interest = 110% = 1.1 2, not 220% (2.2).
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Mixed Worded Fractions Decimals Percentages Questions (Exam Style)
Subject: Mathematics
Age range: 7-11
Resource type: Worksheet/Activity
Last updated
20 December 2017
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