Mental Maths Practise Year 5 Worksheets - Free Printable

Let's go through each question and explain the solution step by step.

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1. \( \frac{5}{8} - \frac{1}{4} \)

- To subtract fractions, we need a common denominator.
- The denominators are 8 and 4. The least common denominator (LCD) is 8.
- Convert \( \frac{1}{4} \) to an equivalent fraction with denominator 8:
\[
\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}
\]
- Now subtract:
\[
\frac{5}{8} - \frac{2}{8} = \frac{5 - 2}{8} = \frac{3}{8}
\]
- Answer: \( \frac{3}{8} \)

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2. \( 8 \frac{1}{4} \text{ kg} = \_\_\_\_ \text{g} \)

- Convert the mixed number \( 8 \frac{1}{4} \) to an improper fraction:
\[
8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{32 + 1}{4} = \frac{33}{4}
\]
- Convert kilograms to grams (1 kg = 1000 g):
\[
\frac{33}{4} \text{ kg} = \frac{33}{4} \times 1000 \text{ g} = \frac{33 \times 1000}{4} = \frac{33000}{4} = 8250 \text{ g}
\]
- Answer: \( 8250 \text{ g} \)

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3. Which is longer?

- Compare the following lengths: \( 1 \text{ m} \), \( 200 \text{ cm} \), \( 3 \text{ ft} \), \( 700 \text{ mm} \), \( 1 \text{ yard} \).
- Convert all lengths to the same unit (cm):
- \( 1 \text{ m} = 100 \text{ cm} \)
- \( 200 \text{ cm} = 200 \text{ cm} \)
- \( 3 \text{ ft} = 3 \times 30.48 \text{ cm} = 91.44 \text{ cm} \)
- \( 700 \text{ mm} = 700 \div 10 = 70 \text{ cm} \)
- \( 1 \text{ yard} = 3 \text{ ft} = 91.44 \text{ cm} \)
- The longest length is \( 200 \text{ cm} \).
- Answer: \( 200 \text{ cm} \)

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4. Work out the value of \( 7(x - 2) \) if \( x = 5 \)

- Substitute \( x = 5 \) into the expression:
\[
7(x - 2) = 7(5 - 2) = 7 \times 3 = 21
\]
- Answer: \( 21 \)

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5. The scores in a times table test are 17, 21, 29, 14, 23, 26. What is the range?

- The range is the difference between the highest and lowest values.
- Highest score: \( 29 \)
- Lowest score: \( 14 \)
- Range:
\[
29 - 14 = 15
\]
- Answer: \( 29 - 14 = 15 \)

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6. What mixed fraction does the number line show?

- The number line shows a point between 1 and 2, closer to 1 but not exactly halfway.
- The point is at \( 1 \frac{2}{3} \).
- Answer: \( 1 \frac{2}{3} \)

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7. What is the next number? \( 7.4, 7.1, 6.8, 6.5, 6.2, \_\_\_ \)

- The sequence decreases by 0.3 each time:
\[
7.4 - 0.3 = 7.1, \quad 7.1 - 0.3 = 6.8, \quad 6.8 - 0.3 = 6.5, \quad 6.5 - 0.3 = 6.2
\]
- Next number:
\[
6.2 - 0.3 = 5.9
\]
- Answer: \( 5.9 \)

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8. Work out \( 6 + 7 \times 3 \) (think about the order of operations!)

- Follow the order of operations (PEMDAS/BODMAS): multiplication before addition.
- First, multiply:
\[
7 \times 3 = 21
\]
- Then add:
\[
6 + 21 = 27
\]
- Answer: \( 27 \)

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9. Which is more: \( \frac{5}{8} \) of 40 or \( \frac{3}{4} \) of 32?

- Calculate \( \frac{5}{8} \) of 40:
\[
\frac{5}{8} \times 40 = \frac{5 \times 40}{8} = \frac{200}{8} = 25
\]
- Calculate \( \frac{3}{4} \) of 32:
\[
\frac{3}{4} \times 32 = \frac{3 \times 32}{4} = \frac{96}{4} = 24
\]
- Compare:
\[
25 > 24
\]
- Answer: \( \frac{5}{8} \) of 40

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10. Which of these quadrilaterals is a rhombus?

- A rhombus is a quadrilateral with all sides of equal length.
- Option B is the only shape where all sides appear to be equal.
- Answer: B

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11. A raffle ticket costs £1.50. How many tickets would I need to sell to make my target of £150?

- Total target: £150
- Cost per ticket: £1.50
- Number of tickets needed:
\[
\frac{150}{1.50} = 100
\]
- Answer: 100

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12. I set off on a 15-mile cycle ride at a speed of 10 miles per hour. How long does the ride take?

- Distance: 15 miles
- Speed: 10 miles per hour
- Time:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{15}{10} = 1.5 \text{ hours}
\]
- Convert 1.5 hours to minutes:
\[
1.5 \text{ hours} = 1 \text{ hour} + 0.5 \text{ hours} = 1 \text{ hour} + 30 \text{ minutes} = 1 \frac{1}{2} \text{ hours}
\]
- Answer: \( 1 \frac{1}{2} \text{ hours} \) (or 90 min)

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13. Tyger and Frazer weigh a total of 23 kg. Tyger is 7 kg heavier than Frazer. How much do they each weigh?

- Let Frazer's weight be \( x \) kg.
- Tyger's weight is \( x + 7 \) kg.
- Total weight:
\[
x + (x + 7) = 23
\]
- Simplify:
\[
2x + 7 = 23
\]
- Solve for \( x \):
\[
2x = 23 - 7 = 16 \implies x = \frac{16}{2} = 8
\]
- Frazer weighs 8 kg, and Tyger weighs:
\[
x + 7 = 8 + 7 = 15 \text{ kg}
\]
- Answer: Tyger 15 kg, Frazer 8 kg

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14. A rectangle has an area of \( 24 \text{ cm}^2 \) and one side of length 6 cm. What is the length of the other side?

- Area of a rectangle: \( \text{Area} = \text{length} \times \text{width} \)
- Given:
\[
\text{Area} = 24 \text{ cm}^2, \quad \text{length} = 6 \text{ cm}
\]
- Width:
\[
\text{Width} = \frac{\text{Area}}{\text{Length}} = \frac{24}{6} = 4 \text{ cm}
\]
- Answer: 4 cm

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15. A milkshake costs £0.99. How much are 5 milkshakes?

- Cost of one milkshake: £0.99
- Cost of 5 milkshakes:
\[
5 \times 0.99 = 4.95
\]
- Answer: £4.95

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16. A mile is 1609 m. How many meters in 2 miles?

- 1 mile = 1609 m
- 2 miles:
\[
2 \times 1609 = 3218 \text{ m}
\]
- Answer: 3218 m

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Final Answer

\[
\boxed{3218}
\]