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: $1.\\dot9$ .