Year 9 maths lesson · Fractions

Fractions of an Amount

Find a fraction of a given amount using the divide-then-multiply strategy. Progress from concrete visual examples to abstract money problems and multi-step word problems.

  • About 3–6 minutes
  • 5 quick questions as you go
  • Then about 5 minutes of practice
Practice questions → Set for Class

Worked examples

2/3 of 15 candies

  1. Denominator is 3: divide 15 into 3 groups → 5 per group
  2. Numerator is 2: take 2 groups → 2 × 5 = 10
  3. 2/3 of 15 = 10

3/4 of 20 sweets

  1. Divide into 4 groups: 20 ÷ 4 = 5 per group
  2. Take 3 groups: 3 × 5 = 15
  3. 3/4 of 20 = 15

4/5 of $30

  1. Divide into 5 groups: $30 ÷ 5 = $6 per group
  2. Take 4 groups: 4 × $6 = $24
  3. 4/5 of $30 = $24

1/4 of 360 students are Year 9, and 2/3 of those play sport

  1. A school has 360 students. 1/4 are Year 9
  2. 360 ÷ 4 = 90 Year 9 students
  3. Of those, 2/3 play a sport: 90 ÷ 3 = 30, then 2 × 30 = 60
  4. 60 Year 9 students play sport

Before this lesson

It helps to be comfortable with:

  • Fractions
  • Division
  • Multiplication

Lesson transcript

Everything the lesson says, word for word

Let’s find two thirds of 15 candies. First, look at the denominator — it’s 3. Divide into 3 equal groups to find one third. 15 divided by 3 is 5 candies per group. Now look at the numerator — it’s 2. We want 2 of those groups. 2 times 5 is 10. So two thirds of 15 is 10.

Now let’s find three quarters of 20 sweets. First, look at the denominator — it’s 4. Divide into 4 equal groups to find one quarter. 20 divided by 4 is 5 sweets per group. Now look at the numerator — it’s 3. We want 3 of those groups. 3 times 5 is 15. Three quarters of 20 is 15.

Let’s try one without a picture. Find four fifths of $30. First, look at the denominator — it’s 5. Divide into 5 equal groups to find one fifth. $30 divided by 5 is $6 per group. Now look at the numerator — it’s 4. We want 4 groups. 4 times $6 is $24.

Here’s a word problem. A school has 360 students. One quarter are in Year 9. Of the Year 9 students, two thirds play a sport. How many Year 9 students play sport? Step 1: find one quarter of 360. 360 divided by 4 is 90 Year 9 students. Step 2: find two thirds of 90. 90 divided by 3 is 30. 2 times 30 is 60. So 60 Year 9 students play sport.

More Fractions lessons

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