Mathematics
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Fluency · Pack A

7.4 Decimals & Measurement

Answer each question. Show working where needed.

Bronze

  1. Write three different decimals between 0.3 and 0.4. Justify that each one lies in that range.

  2. Round 4.372 to 1 decimal place and name the digit that decided the rounding. Justify.

  3. The sum 4.37 + 2.85 should equal 7.22. A student writes 6.122. What error did they make? Give the correct answer.

  4. A pencil is 18 cm long. Express its length in mm AND in m, then explain the relationship between the units.

  5. A recipe needs 3.67 g of flour. The cook has 8.52 g. How much flour is left over? Show your calculation with decimal points aligned.

  6. Find 2.4 × 3 in two different ways: (i) directly, (ii) by treating 2.4 as a whole number, then adjusting. Show both methods give the same answer.

  7. Without fully dividing, decide: will 8.4 ÷ 4 be greater or less than 2? Then calculate to check.

  8. Convert 4.7 cm to mm AND state what operation you performed and why.

  9. Convert 3500 g to kg AND explain why you divide (not multiply) to convert g to kg.

  10. A rectangle has perimeter 9.4 cm. Give two different pairs of whole-number or one-decimal-place side lengths that could produce this perimeter. Justify each.

Silver

  1. Round 5.6847 to 2 decimal places.

  2. Calculate 12.47 + 8.65 + 3.28.

  3. Calculate 20.30 − 8.67.

  4. Calculate 3.4 × 2.5.

  5. Calculate 15.6 ÷ 1.2.

  6. Convert 2.35 m into (a) cm and (b) mm.

  7. A rectangle has area 22.4 cm² and width 3.2 cm. Find its length.

  8. A journey starts at 9:45 am and takes 2 hours and 35 minutes. What time does it finish?

  9. Convert 2.45 kg to g.

  10. Shop A sells juice at £1.20 per bottle. Shop B sells the same juice in packs of 3 for £3.24. Which is better value? Show your working.

Gold

  1. Substitute $x = 1.4$ into $3x + 2$.

  2. Estimate $4.87 \times 3.2$ by rounding each factor to 1 decimal place, then calculate the exact answer.

  3. A road is 2.4 km long. A second road is 850 m long. What is the total length in metres?

  4. A rectangle has perimeter 24.6 cm. Its width is 3.4 cm. Find its length.

  5. Work out $(1.5)^2 + 3.2 \times 4$.

  6. Work out −3.5 + 7.2.

  7. Solve $5x = 8.5$.

  8. A train journey takes 1 hours and 45 minutes. How many seconds is that in total?

  9. A rectangle has length 8.5 cm and width 4.2 cm. Find its area and its perimeter.

  10. A square has side 4.5 cm. Find its area. Then evaluate $\sqrt{\text{area}}$ and comment on the result.

Platinum

  1. A rectangle has perimeter 20.4 cm. Its length is $(2x + 0.6)$ cm and its width is $x$ cm. Find $x$ and calculate the area.

  2. Substitute $t = 3.0$ into $\dfrac{t^2 - 1}{t + 2}$. Give your answer as a decimal.

  3. The temperature rises from −6.4°C to 2.8°C over 4 hours. Find the rise and the rate of change in °C per hour.

  4. Write 196 as a product of prime factors in index form, then find $\sqrt{196}$.

  5. Simplify $5x + 3.2 - 2x + 1.7$, then evaluate it for $x = 0.5$.

  6. How many pieces of ribbon each 0.35 m long can be cut from a roll of 5.0 m? How much is left over? Give the leftover in cm.

  7. The HCF of two numbers is 6 and their LCM is 90. One number is 18. Find the other.

  8. Work out $\dfrac{3.6 \times (10 - 2^2)}{4}$. Give your answer as a decimal.

  9. A tank holds 18.0 litres. Water drains at 2.5 litres/min and is added at 1.0 litres/min simultaneously. How long until the tank is empty?

  10. A farmer's field is a rectangle. Its perimeter is 960 m. The length is 3 times the width. Find the area in m², then convert to hectares (1 ha = 10 000 m²).