New

Deepening understanding with fractions of a given amount

I can find the original amount when given a fraction and the result.

Download all

View unit

Lesson 10 of 17

New

Year 7

Deepening understanding with fractions of a given amount

I can find the original amount when given a fraction and the result.

Download all

Lesson slides

Download lesson slides

Skip lesson slides

Lesson details

Key learning points

To find the original amount, the result is divided by the fraction.
This can be seen visually through use of a bar model.
A double number line can also be used.

Keywords

Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

Common misconception

Only seeing the amount, not proportion. E.g £30 from £100 is no different to £30 from £60.

Referring to the whole using bar models or fractions can emphasise the amount with respect to the whole.

After the 'think of a number' explanation. pupils get into pairs and find a fraction of 'their number', share the fraction and result and the other pupil has the work out the 'number' their partner was thinking of.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

Skip lesson video

Worksheet

Download worksheet

Skip worksheet

Prior knowledge starter quiz

Download quiz pdf

6 Questions

Q1.
Which of the following is not the reciprocal of 3?

$$12\over36$$

$$9\over27$$

Correct answer: $$2\over3$$

$$1\over3$$

Q2.
Use a bar model to calculate $$5\over8$$ of 32.

Correct Answer: 20, twenty

Q3.
Calculate 45 × $$4\over5$$.

Correct Answer: 36, thirty-six, thirty six, thirtysix

Q4.
Which of the following are equivalent calculations for $$5\over6$$ of 66?

Correct answer: 66 × $$5\over6$$

Correct answer: (66 ÷ 6) × 5

Correct answer: $$5\over6$$ × $${6\times11}\over{1}$$

(66 ÷ 5) × 6

Correct answer: $$66\over6$$ × 5

Q5.
Calculate $$3 {{3} \over {4}}$$ × $$5\over6$$, give your answer in its simplest form.

$$2{{7} \over {8}}$$

$$3 {{8} \over {24}}$$

Correct answer: $$3 {{1} \over {8}}$$

$$3 {{1} \over {4}}$$

Q6.
Find $$11 {{3} \over {4}}$$ of 32.

Correct Answer: 376

Assessment exit quiz

Download quiz pdf

6 Questions

Q1.
Match the following to the correct reciprocal.

Correct Answer:2,$$1\over2$$

Correct Answer:$$3\over2$$,$$2\over3$$

Correct Answer:2.5,$$2\over5$$

Correct Answer:$$4\over5$$,1.25

Correct Answer:$$6\over8$$,$$4\over3$$

Q2.
A shop has a sale saving you $$1\over3$$ off the original price. You pay £40 for a sweatshirt. How much was it originally?

Correct Answer: £60, 60, £60.00, 60.00

Q3.
$$1\over5$$ of 60 = $$4\over5$$ of $$\square$$.

Correct Answer: 15, fifteen

Q4.
I think of a number. $$3\over8$$ of my number is 15. What is my number?

Correct Answer: 40, forty

Q5.
The cost of a TV increases by $$1\over8$$. It now costs £450. How much was it originally?

Correct Answer: £400, £400.00, 400, 400.00

Q6.
Alex's cat loses $$1\over6$$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?

Correct Answer: 5.04 kg, 5.04kg, 5.04, 5.04 kilograms, 5.04kilograms

Lesson appears in

UnitMaths / Understanding multiplicative relationships: fractions and ratio

Maths

Show unit

Choose exam board for KS4 Biology

Choose exam board for KS4 Chemistry

Choose exam board for KS4 Combined science

Choose exam board for KS4 Computer Science (GCSE)

Choose exam board for KS4 English

Choose exam board for KS4 French

Choose exam board for KS4 Geography

Choose exam board for KS4 German

Choose exam board for KS4 History

Choose tier for KS4 Maths

Choose exam board for KS4 Music

Choose exam board for KS4 Physical education (GCSE)

Choose exam board for KS4 Physics

Choose exam board for KS4 Religious education (GCSE)

Choose exam board for KS4 Spanish

Deepening understanding with fractions of a given amount

Deepening understanding with fractions of a given amount

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which of the following is not the reciprocal of 3?

Q2.Use a bar model to calculate $$5\over8$$ of 32.

Q3.Calculate 45 × $$4\over5$$.

Q4.Which of the following are equivalent calculations for $$5\over6$$ of 66?

Q5.Calculate $$3 {{3} \over {4}}$$ × $$5\over6$$, give your answer in its simplest form.

Q6.Find $$11 {{3} \over {4}}$$ of 32.

Assessment exit quiz

6 Questions

Q1.Match the following to the correct reciprocal.

Q2.A shop has a sale saving you $$1\over3$$ off the original price. You pay £40 for a sweatshirt. How much was it originally?

Q3.$$1\over5$$ of 60 = $$4\over5$$ of $$\square$$.

Q4.I think of a number. $$3\over8$$ of my number is 15. What is my number?

Q5.The cost of a TV increases by $$1\over8$$. It now costs £450. How much was it originally?

Q6.Alex's cat loses $$1\over6$$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?

Lesson appears in

UnitMaths / Understanding multiplicative relationships: fractions and ratio

Maths

Q1.
Which of the following is not the reciprocal of 3?

Q2.
Use a bar model to calculate $$5\over8$$ of 32.

Q3.
Calculate 45 × $$4\over5$$.

Q4.
Which of the following are equivalent calculations for $$5\over6$$ of 66?

Q5.
Calculate $$3 {{3} \over {4}}$$ × $$5\over6$$, give your answer in its simplest form.

Q6.
Find $$11 {{3} \over {4}}$$ of 32.

Q1.
Match the following to the correct reciprocal.

Q2.
A shop has a sale saving you $$1\over3$$ off the original price. You pay £40 for a sweatshirt. How much was it originally?

Q3.
$$1\over5$$ of 60 = $$4\over5$$ of $$\square$$.

Q4.
I think of a number. $$3\over8$$ of my number is 15. What is my number?

Q5.
The cost of a TV increases by $$1\over8$$. It now costs £450. How much was it originally?

Q6.
Alex's cat loses $$1\over6$$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?