New
New
Year 7

Expressing one number as a fraction of another

I can express one number as a fraction of another.

New
New
Year 7

Expressing one number as a fraction of another

I can express one number as a fraction of another.

Lesson details

Key learning points

  1. There exists a multiplier for any pair of values.
  2. The multiplier is more than just a scaling factor.
  3. The multiplier also expresses one number as a fraction of the other.

Common misconception

Only see 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.

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.

  • Terminating decimal - A terminating decimal is one that has a finite number of digits after the decimal point.. E.g. 92.2, 193.3894, non-example: $$1.\dot9$$.

Pupils get into pairs with mini-whiteboards. One writes down a statement, e.g. 18 is 2/5 of 45 and their partner writes the other fact. This will reinforce equivalences and help pupils to spot when changing the question could be beneficial.
Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
Match the following to the correct reciprocal.
Correct Answer:3,$$1\over3$$

$$1\over3$$

Correct Answer:$$5\over2$$,$$2\over5$$

$$2\over5$$

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

$$4\over5$$

Correct Answer:$$5\over20$$,4

4

Correct Answer:$$3 {1\over2}$$,$$2\over7$$

$$2\over7$$

Q2.
A shop has a sale saving you $$1\over3$$. You pay £36 for a sweatshirt. How much was it originally?
Correct Answer: £54, £54.00, 54, 54.00
Q3.
$$1\over6$$ of 150 = $$5\over6$$ of .
Correct Answer: 30, thirty
Q4.
I think of a number. $$5\over8$$ of my number is 15. What is my number?
Correct Answer: 24, twenty-four, twenty four, twentyfour
Q5.
The cost of a laptop increases by $$1\over8$$. It now costs £675. How much was it originally?
Correct Answer: £600, £600.00, 600, 600.00
Q6.
Alex's cat loses $$1\over7$$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?
Correct Answer: 4.9 kg, 4.9kg, 4.9, 4.9 kilograms, 4.9 kilograms

6 Questions

Q1.
Which of the following are terminating decimals?
Correct answer: 156.2549
Correct answer: 56.2
$$56.\dot9$$
$$1\over3$$
Correct answer: 56.0000999
Q2.
Match each calculation to the correct missing number.
Correct Answer:6 × $$\square$$ = 4,$$2\over3$$

$$2\over3$$

Correct Answer:6 × $$\square$$ = 10,$$1 {{2} \over {3}}$$

$$1 {{2} \over {3}}$$

Correct Answer:$$\square$$ × 6 = $$3\over2$$,$$1\over4$$

$$1\over4$$

Correct Answer:6 × $$\square$$ = 15,2.5

2.5

Correct Answer:$$\square$$ × 6 = $$18\over7$$,$$3\over7$$

$$3\over7$$

Q3.
A recipe requires 195 grams of chocolate chips to bake 30 cookies. What weight of chocolate chips would you need to make 130 cookies?
Correct Answer: 845 g, 845 grams, 845g, 845grams, 845
Q4.
What fraction of 300 is 45? Give your answer in its simplest form.
$$300\over45$$
$$255\over300$$
$$45\over300$$
$$17\over20$$
Correct answer: $$3\over20$$
Q5.
If 30 is $$2\over3$$ of 45, which of the following is true?
45 is $$2\over3$$ of 30
30 is $$3\over2$$ of 45
Correct answer: 45 is $$3\over2$$ of 30
45 is $$2\over2$$ of 30
Q6.
Match the following with what needs to go in the box.
Correct Answer:112 is $$\square$$ of 392,$$2\over7$$

$$2\over7$$

Correct Answer:$$\square$$ of 445 is 178,$$2\over5$$

$$2\over5$$

Correct Answer:261 is $$\square$$ of 609,$$3\over7$$

$$3\over7$$

Correct Answer:$$\square$$ of 315 is 420,$$4\over3$$

$$4\over3$$

Correct Answer:1524 is $$\square$$ of 2032,$$3\over4$$

$$3\over4$$