Introduction

Hello, Year 6! Today, we are going to learn how to find a fraction of an amount using a method called cancelling. This might sound tricky at first, but with a little practice, you’ll be great at it!

What Does It Mean to Find a Fraction of an Amount?

Finding a fraction of an amount means you want to take a part of that amount, based on the fraction given. For example, if you want to find $\frac{1}{2}$ of 8, you are looking for half of 8, which is 4.

What is Cancelling?

Cancelling is a way to simplify fractions before you do the calculations. It helps make your numbers smaller and easier to work with.

Step-by-Step Guide to Finding a Fraction of an Amount by Cancelling

  1. Write Down the Fraction: Start with the fraction you need to find. For example, $\frac{2}{3}$.
  2. Multiply by the Amount: Next, multiply this fraction by the total amount you have. For example, if you want to find $\frac{2}{3}$ of 12, you write:\frac{2}{3} \times 12
  3. Change the Whole Number to a Fraction: Remember that any whole number can be turned into a fraction by putting it over 1. So, 12 becomes $\frac{12}{1}$:\frac{2}{3} \times \frac{12}{1}
  4. Multiply the Numerators and Denominators: Now, multiply the top numbers (numerators) and the bottom numbers (denominators):\frac{2 \times 12}{3 \times 1} = \frac{24}{3}
  5. Cancelling: Before you multiply, see if you can simplify (or cancel) the fraction. Look for common numbers in the numerator and denominator. In our example, we can see that 24 and 3 have a common factor of 3:\frac{24 \div 3}{3 \div 3} = \frac{8}{1} = 8
  6. Conclusion: So, $\frac{2}{3}$ of 12 is 8.

Key Rules to Remember

  • Always simplify fractions if you can before multiplying.
  • Remember that cancelling can make your calculations easier.
  • Check if the numbers have any common factors.

Tips and Tricks

  • Look for easy numbers to cancel, like 2, 3, or 5.
  • Practise with different fractions and amounts to build your confidence.
  • Use visual aids like fraction circles or bars to help you understand.

Questions

Easy Level

  1. Find $\frac{1}{2}$ of 10.
  2. Find $\frac{3}{4}$ of 8.
  3. Find $\frac{2}{5}$ of 20.
  4. Find $\frac{1}{3}$ of 9.
  5. Find $\frac{1}{4}$ of 16.
  6. Find $\frac{3}{5}$ of 15.
  7. Find $\frac{2}{3}$ of 30.
  8. Find $\frac{1}{2}$ of 14.
  9. Find $\frac{1}{5}$ of 25.
  10. Find $\frac{3}{6}$ of 12.

Medium Level

  1. Find $\frac{2}{7}$ of 21.
  2. Find $\frac{5}{8}$ of 32.
  3. Find $\frac{3}{10}$ of 50.
  4. Find $\frac{4}{9}$ of 36.
  5. Find $\frac{3}{5}$ of 25.
  6. Find $\frac{2}{6}$ of 18.
  7. Find $\frac{3}{4}$ of 28.
  8. Find $\frac{1}{3}$ of 15.
  9. Find $\frac{5}{6}$ of 48.
  10. Find $\frac{7}{8}$ of 64.

Hard Level

  1. Find $\frac{9}{10}$ of 70.
  2. Find $\frac{3}{11}$ of 121.
  3. Find $\frac{8}{15}$ of 75.
  4. Find $\frac{5}{12}$ of 48.
  5. Find $\frac{7}{9}$ of 81.
  6. Find $\frac{11}{13}$ of 65.
  7. Find $\frac{4}{5}$ of 100.
  8. Find $\frac{6}{11}$ of 110.
  9. Find $\frac{9}{14}$ of 84.
  10. Find $\frac{8}{9}$ of 72.

Answers

Easy Level Answers

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

Medium Level Answers

  1. 6
  2. 20
  3. 15
  4. 16
  5. 15
  6. 6
  7. 21
  8. 5
  9. 40
  10. 56

Hard Level Answers

  1. 63
  2. 33
  3. 40
  4. 20
  5. 63
  6. 55
  7. 80
  8. 60
  9. 54
  10. 64

Now you are ready to tackle fractions of amounts by cancelling! Keep practicing, and soon you’ll be a fraction expert!