Deepening understanding with fractions of a given amount | Maths

Starter quiz

Which of the following is not the reciprocal of 3?
- $12\over36$
- $9\over27$
- $2\over3$ ✓
- $1\over3$
Use a bar model to calculate $5\over8$ of 32.
- '20' ✓
Calculate 45 × $4\over5$ .
- '36' ✓
Which of the following are equivalent calculations for $5\over6$ of 66?
- 66 × $5\over6$ ✓
- (66 ÷ 6) × 5 ✓
- $5\over6$ × ${6\times11}\over{1}$ ✓
- (66 ÷ 5) × 6
- $66\over6$ × 5 ✓
Calculate $3 {{3} \over {4}}$ × $5\over6$ , give your answer in its simplest form.
- $2{{7} \over {8}}$
- $3 {{8} \over {24}}$
- $3 {{1} \over {8}}$ ✓
- $3 {{1} \over {4}}$
Find $11 {{3} \over {4}}$ of 32.
- '376' ✓

Match the following to the correct reciprocal.
- 2
  
  ⇔
  
  $1\over2$ ✓
- $3\over2$
  
  ⇔
  
  $2\over3$ ✓
- 2.5
  
  ⇔
  
  $2\over5$ ✓
- $4\over5$
  
  ⇔
  
  1.25 ✓
- $6\over8$
  
  ⇔
  
  $4\over3$ ✓
A shop has a sale saving you $1\over3$ off the original price. You pay £40 for a sweatshirt. How much was it originally?
- '£60' ✓
$1\over5$ of 60 = $4\over5$ of $\square$ .
- '15' ✓
I think of a number. $3\over8$ of my number is 15. What is my number?
- '40' ✓
The cost of a TV increases by $1\over8$ . It now costs £450. How much was it originally?
- '£400' ✓
Alex's cat loses $1\over6$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?
- '5.04 kg' ✓

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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.

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