What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The symbol for percentage is %. For example, 50% means 50 out of 100.

Why Do We Use Percentages?

Percentages are useful because they help us compare different quantities easily. For example, if you have 20 apples and 10 are red, you can say that 50% of the apples are red.

How to Find Percentages

Step-by-Step Guide

  1. Understand the Total: First, know the total amount you are working with.
  2. Identify the Part: Determine the part of the total that you want to find the percentage of.
  3. Use the Percentage Formula: The formula to find a percentage is:\text{Percentage} = \left( \frac{\text{Part}}{\text{Total}} \right) \times 100

Example 1: Finding 25% of 80

  1. Total: 80
  2. Part: We want to find 25% of 80.
  3. Calculate:\text{Percentage} = \left( \frac{25}{100} \times 80 \right) = 20

So, 25% of 80 is 20.

Example 2: Finding the Percentage of Students

Imagine there are 30 students in a class, and 12 students are girls. To find the percentage of girls:

  1. Total: 30 students
  2. Part: 12 girls
  3. Calculate:\text{Percentage} = \left( \frac{12}{30} \right) \times 100 = 40%

So, 40% of the students are girls.

Key Rules to Remember

  1. Always Divide the Part by the Total: This gives you a fraction.
  2. Multiply by 100: This converts the fraction into a percentage.
  3. Simplify When Possible: Sometimes, simplifying the fraction can make calculations easier.

Tips and Tricks

  • Use Benchmarks: Remember that 50% is half, 25% is a quarter, and 75% is three-quarters. This can help you estimate quickly.
  • Draw a Pie Chart: Visuals can help you see how parts make up a whole.
  • Practice with Real-Life Examples: Try finding percentages on prices when shopping or in sports scores.

Questions on Finding Percentages

Easy Level Questions

  1. What is 10% of 50?
  2. Find 20% of 100.
  3. What is 50% of 60?
  4. Calculate 25% of 80.
  5. What is 30% of 90?
  6. Find 40% of 50.
  7. What is 5% of 200?
  8. Calculate 15% of 60.
  9. What is 75% of 40?
  10. Find 60% of 80.

Medium Level Questions

  1. What is 20% of 150?
  2. Calculate 10% of 250.
  3. Find 35% of 200.
  4. What is 45% of 220?
  5. Calculate 80% of 90.
  6. What is 12% of 160?
  7. Find 25% of 120.
  8. Calculate 55% of 180.
  9. What is 70% of 300?
  10. Find 90% of 50.

Hard Level Questions

  1. If there are 240 students and 60% are boys, how many boys are there?
  2. A shirt costs £80. If there is a 25% discount, what is the sale price?
  3. In a race, 30% of runners are women. If there are 120 runners, how many are women?
  4. A book costs £15, and there is a 10% tax. What is the total price?
  5. If you scored 85 out of 100 in a test, what percentage is that?
  6. A toy is reduced in price from £50 to £37. What percentage discount is that?
  7. If 45% of a group of 200 people are adults, how many adults are there?
  8. A pizza is cut into 8 slices, and you eat 3. What percentage of the pizza did you eat?
  9. If a car depreciates by 20% and is worth £12,000, what was its original price?
  10. A student answered 28 out of 35 questions correctly. What percentage did they get right?

Answers and Explanations

Easy Level Answers

  1. 5
  2. 20
  3. 30
  4. 20
  5. 27
  6. 20
  7. 10
  8. 9
  9. 30
  10. 48

Medium Level Answers

  1. 30
  2. 25
  3. 70
  4. 99
  5. 72
  6. 19.2
  7. 30
  8. 99
  9. 210
  10. 45

Hard Level Answers

  1. 144
  2. £60
  3. 36
  4. £16.50
  5. 85%
  6. 26%
  7. 90
  8. 37.5%
  9. £15,000
  10. 80%

By practising these problems, you will become more confident in finding percentages. Keep up the great work!