Introduction

Hello Year 6! Today we are going to learn about percentages, decimals, and fractions. These three concepts are all related. Understanding how to change between them will make your maths much easier. Let’s dive in!

What is a Percentage?

A percentage is a way to express a number as a part of 100. For example, if you have 25 out of 100 apples, we say you have 25%.

Key Rule:

  • To find a percentage, divide the part by the whole and then multiply by 100.

Example:

If you scored 15 out of 20 on a test, the percentage would be:

\text{Percentage} = \left(\frac{15}{20}\right) \times 100 = 75%

What is a Decimal?

A decimal is a way to express numbers that are not whole. For example, 0.25 is a decimal that means 25 out of 100.

Key Rule:

  • To convert a percentage to a decimal, divide by 100.

Example:

To convert 25% to a decimal:

\text{Decimal} = \frac{25}{100} = 0.25

What is a Fraction?

A fraction is a way to show a part of a whole using two numbers. The top number is called the numerator, and the bottom number is the denominator.

Key Rule:

  • To convert a percentage to a fraction, put the percentage over 100 and simplify if possible.

Example:

To convert 25% to a fraction:

\text{Fraction} = \frac{25}{100} = \frac{1}{4} \text{ (after simplifying)}

Quick Summary

  • Percentage to Decimal: Divide by 100.
  • Percentage to Fraction: Put over 100 and simplify.
  • Decimal to Percentage: Multiply by 100.
  • Fraction to Percentage: Divide the numerator by the denominator, then multiply by 100.

Tips and Tricks

  1. Practice makes perfect! The more you work with percentages, decimals, and fractions, the easier it gets.
  2. Use a calculator for tricky numbers but try to do simple ones in your head.
  3. Draw visuals like pie charts to see how percentages, fractions, and decimals relate.

Questions

Easy Level Questions

  1. Convert 50% to a decimal.
  2. Convert 25% to a fraction.
  3. What is 75% as a decimal?
  4. Convert 10% to a fraction.
  5. What is 1/2 as a percentage?
  6. Convert 0.5 to a percentage.
  7. What is 20% as a decimal?
  8. Convert 1/4 to a percentage.
  9. What is 60% as a decimal?
  10. Convert 0.75 to a fraction.

Medium Level Questions

  1. What is 33% as a decimal?
  2. Convert 2/5 to a percentage.
  3. What is 45% as a decimal?
  4. Convert 0.2 to a percentage.
  5. What is 80% as a fraction?
  6. Convert 1/8 to a decimal.
  7. What is 12.5% as a fraction?
  8. Convert 0.04 to a percentage.
  9. What is 90% as a decimal?
  10. Convert 3/10 to a percentage.

Hard Level Questions

  1. Convert 7.5% to a decimal.
  2. What is 125% as a fraction?
  3. Convert 0.6 to a percentage.
  4. What is 15% as a decimal?
  5. Convert 5/12 to a percentage.
  6. What is 1/3 as a decimal?
  7. Convert 0.125 to a percentage.
  8. What is 22% as a fraction?
  9. Convert 250% to a decimal.
  10. What is 9/20 as a percentage?

Answers

Easy Level Answers

  1. 0.50
  2. 1/4
  3. 0.75
  4. 1/10
  5. 50%
  6. 50%
  7. 0.20
  8. 25%
  9. 0.60
  10. 3/4

Medium Level Answers

  1. 0.33
  2. 40%
  3. 0.45
  4. 20%
  5. 4/5
  6. 0.125
  7. 1/8
  8. 4%
  9. 0.90
  10. 30%

Hard Level Answers

  1. 0.075
  2. 5/4 or 1.25
  3. 60%
  4. 0.15
  5. 41.67% (approximately)
  6. 0.33 (approximately)
  7. 12.5%
  8. 11/50
  9. 2.5
  10. 45%

Feel free to practice these questions, and remember: percentages, decimals, and fractions are all different ways to show the same idea! Happy learning!