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Lesson 10 of 17

Deepening understanding with fractions of a given amount

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

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Lesson 10 of 17
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Deepening understanding with fractions of a given amount

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

Lesson details

Key learning points

  1. To find the original amount, the result is divided by the fraction.
  2. This can be seen visually through use of a bar model.
  3. 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

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Prior knowledge starter quiz

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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

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6 Questions

Q1.
Match the following to the correct reciprocal.

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

$$1\over2$$

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

$$2\over3$$

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

$$2\over5$$

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

1.25

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

$$4\over3$$

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

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