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