Expressing one number as a fraction of another | Maths

Starter quiz

Match the following to the correct reciprocal.

3

⇔

$1\over3$ ✓

$5\over2$

⇔

$2\over5$ ✓

1.25

⇔

$4\over5$ ✓

$5\over20$

⇔

4 ✓

$3 {1\over2}$

⇔

$2\over7$ ✓
A shop has a sale saving you $1\over3$ . You pay £36 for a sweatshirt. How much was it originally?

'£54' ✓
$1\over6$ of 150 = $5\over6$ of ______.

'30' ✓
I think of a number. $5\over8$ of my number is 15. What is my number?

'24' ✓
The cost of a laptop increases by $1\over8$ . It now costs £675. How much was it originally?

'£600' ✓
Alex's cat loses $1\over7$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?

'4.9 kg' ✓

Which of the following are terminating decimals?

156.2549 ✓

56.2 ✓

$56.\dot9$

$1\over3$

56.0000999 ✓
Match each calculation to the correct missing number.

6 × $\square$ = 4

⇔

$2\over3$ ✓

6 × $\square$ = 10

⇔

$1 {{2} \over {3}}$ ✓

$\square$ × 6 = $3\over2$

⇔

$1\over4$ ✓

6 × $\square$ = 15

⇔

2.5 ✓

$\square$ × 6 = $18\over7$

⇔

$3\over7$ ✓
A recipe requires 195 grams of chocolate chips to bake 30 cookies. What weight of chocolate chips would you need to make 130 cookies?

'845 g' ✓
What fraction of 300 is 45? Give your answer in its simplest form.

$300\over45$

$255\over300$

$45\over300$

$17\over20$

$3\over20$ ✓
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

45 is $3\over2$ of 30 ✓

45 is $2\over2$ of 30
Match the following with what needs to go in the box.

112 is $\square$ of 392

⇔

$2\over7$ ✓

$\square$ of 445 is 178

⇔

$2\over5$ ✓

261 is $\square$ of 609

⇔

$3\over7$ ✓

$\square$ of 315 is 420

⇔

$4\over3$ ✓

1524 is $\square$ of 2032

⇔

$3\over4$ ✓

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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.

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: $1.\\dot9$ .