This mental maths quiz features a variety of questions ranging from basic division to complex word problems involving currency and measurement.

Let's solve each question in the Mental Maths Quiz 5:6 step by step and explain the reasoning.

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1) 540 ÷ 6

Divide 540 by 6:

$$
540 ÷ 6 = 90
$$

✔ Answer: 90

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2) Write down a multiple of 7 between 40 and 50.

List multiples of 7:
- 7, 14, 21, 28, 35, 42, 49, 56...

Between 40 and 50: 42 and 49

✔ Answer: 42 or 49 (either is acceptable)

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3) 28.6 × 100

Multiplying by 100 moves the decimal point two places to the right:

$$
28.6 × 100 = 2860
$$

✔ Answer: 2860

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4) The radius of a circle is 6.5 cm. What is the diameter?

Diameter = 2 × Radius

$$
2 × 6.5 = 13 \text{ cm}
$$

✔ Answer: 13 cm

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5) In a spelling test, the scores are 15, 8, 11, 16, 10, 5 and 10. What is the range?

Range = Highest score − Lowest score

- Highest: 16
- Lowest: 5

$$
16 - 5 = 11
$$

✔ Answer: 11

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6) What is this part of the circle called?

*(Image shows a slice of a circle with a central angle)*

The shaded region is bounded by two radii and an arc → This is a sector.

Options: chord, radius, circumference, sector

✔ Answer: sector

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7) Add up ⅜, ¾₁₀, and ½. Give your answer as a mixed number.

First, clarify fractions:
- ⅜
- ¾₁₀ = 3/10
- ½

Find a common denominator. LCM of 8, 10, 2 is 40.

Convert:
- ⅜ = (3×5)/(8×5) = 15/40
- 3/10 = (3×4)/(10×4) = 12/40
- ½ = 20/40

Add:
$$
15/40 + 12/40 + 20/40 = 47/40
$$

Convert to mixed number:
$$
47 ÷ 40 = 1 \text{ remainder } 7 → 1\frac{7}{40}
$$

✔ Answer: $1\frac{7}{40}$

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8) Which two numbers have a sum of 11 and a product of 28?

Let the numbers be x and y.

We know:
- x + y = 11
- x × y = 28

Try factor pairs of 28:
- 1 & 28 → sum = 29 ✘
- 2 & 14 → sum = 16 ✘
- 4 & 7 → sum = 11 ✔

So, the numbers are 4 and 7

✔ Answer: 4 and 7

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9) Which fraction is equivalent to ⅓?

Given options:
⅛, ⅜, ⁴⁄₁₀, ²⁄₇, ³⁄₉

Check each:
- ⅛ ≠ ⅓
- ⅜ ≈ 0.375; ⅓ ≈ 0.333 → no
- ⁴⁄₁₀ = 0.4 → no
- ²⁄₇ ≈ 0.286 → no
- ³⁄₉ = 1/3 → yes!

✔ Answer: ³⁄₉

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10) 578 ÷ 10

Dividing by 10 moves decimal one place left:

$$
578 ÷ 10 = 57.8
$$

✔ Answer: 57.8

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11) Write down 7:20pm as a 24-hour clock time.

7:20 PM = 19:20 (add 12 hours)

✔ Answer: 19:20

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12) Milly and Molly’s ages add up to 19 years. Milly is 3 years older than Molly. How old are they?

Let Molly’s age = x
Then Milly’s age = x + 3

Total:
x + (x + 3) = 19
2x + 3 = 19
2x = 16
x = 8

So:
- Molly = 8 years
- Milly = 11 years

✔ Answer: Milly is 11, Molly is 8

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13) (12 inches = 1 foot) Mandy is 67 inches tall. She is ___ ft ___ inches tall.

Divide 67 by 12:

- 12 × 5 = 60 → 5 feet
- Remainder: 67 − 60 = 7 inches

✔ Answer: 5 ft 7 inches

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**14) Frazer buys a 6 multi-pack bag of crisps for £2.40.

Quadra buys 6 single packs of crisps for 45p each.
How much more did Quadra spend on her crisps?**

Frazer: £2.40

Quadra: 6 × 45p = 270p = £2.70

Difference: £2.70 − £2.40 = £0.30

✔ Answer: £0.30 (or 30p)

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15) In a competition, Tyger throws the ball 3.58m and Frazer throws it 380cm. Who throws furthest? By how many much?

Convert both to same unit. Let's use meters.

- Tyger: 3.58 m
- Frazer: 380 cm = 3.80 m (since 100 cm = 1 m)

Compare:
- 3.80 > 3.58 → Frazer threw further

Difference: 3.80 − 3.58 = 0.22 m

✔ Answer: Frazer threw further by 0.22 m (or 22 cm)

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16) A third of a number is 21. What is the number?

Let the number be x.

$$
\frac{1}{3}x = 21
$$

Multiply both sides by 3:

$$
x = 21 × 3 = 63
$$

✔ Answer: 63

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✔ Final Answers Summary:

| Q | Answer |
|---|--------|
| 1 | 90 |
| 2 | 42 or 49 |
| 3 | 2860 |
| 4 | 13 cm |
| 5 | 11 |
| 6 | sector |
| 7 | $1\frac{7}{40}$ |
| 8 | 4 and 7 |
| 9 | ³⁄₉ |
| 10 | 57.8 |
| 11 | 19:20 |
| 12 | Milly: 11, Molly: 8 |
| 13 | 5 ft 7 inches |
| 14 | £0.30 |
| 15 | Frazer by 0.22 m (or 22 cm) |
| 16 | 63 |

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