Mathematics
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Fluency · Pack B

7.4 Decimals & Measurement

Answer each question. Show working where needed.

Bronze

  1. Write three different decimals between 1.5 and 1.6. Justify that each one lies in that range.

  2. Round 7.849 to 1 decimal place and name the digit that decided the rounding. Justify.

  3. The sum 6.48 + 3.76 should equal 10.24. A student writes 9.124. What error did they make? Give the correct answer.

  4. A pencil is 24.5 cm long. Express its length in mm AND in m, then explain the relationship between the units.

  5. A recipe needs 2.39 g of flour. The cook has 7.04 g. How much flour is left over? Show your calculation with decimal points aligned.

  6. Find 3.5 × 4 in two different ways: (i) directly, (ii) by treating 3.5 as a whole number, then adjusting. Show both methods give the same answer.

  7. Without fully dividing, decide: will 7.5 ÷ 5 be greater or less than 2? Then calculate to check.

  8. Convert 3.8 cm to mm AND state what operation you performed and why.

  9. Convert 6250 g to kg AND explain why you divide (not multiply) to convert g to kg.

  10. A rectangle has perimeter 13.8 cm. Give two different pairs of whole-number or one-decimal-place side lengths that could produce this perimeter. Justify each.

Silver

  1. Round 3.4251 to 2 decimal places.

  2. Calculate 15.36 + 7.48 + 4.19.

  3. Calculate 30.50 − 14.78.

  4. Calculate 4.2 × 3.5.

  5. Calculate 22.4 ÷ 1.6.

  6. Convert 4.08 m into (a) cm and (b) mm.

  7. A rectangle has area 28.8 cm² and width 4.5 cm. Find its length.

  8. A journey starts at 11:20 am and takes 3 hours and 55 minutes. What time does it finish?

  9. Convert 3.072 kg to g.

  10. Shop A sells juice at £0.85 per bottle. Shop B sells the same juice in packs of 4 for £3.08. Which is better value? Show your working.

Gold

  1. Substitute $x = 2.5$ into $3x + 2$.

  2. Estimate $6.94 \times 2.8$ by rounding each factor to 1 decimal place, then calculate the exact answer.

  3. A road is 1.7 km long. A second road is 640 m long. What is the total length in metres?

  4. A rectangle has perimeter 31.2 cm. Its width is 4.8 cm. Find its length.

  5. Work out $(2.4)^2 + 1.8 \times 3$.

  6. Work out −8.4 + 5.6.

  7. Solve $5x = 7.2$.

  8. A train journey takes 2 hours and 20 minutes. How many seconds is that in total?

  9. A rectangle has length 7.6 cm and width 3.8 cm. Find its area and its perimeter.

  10. A square has side 6.3 cm. Find its area. Then evaluate $\sqrt{\text{area}}$ and comment on the result.

Platinum

  1. A rectangle has perimeter 25.2 cm. Its length is $(2x + 1.2)$ cm and its width is $x$ cm. Find $x$ and calculate the area.

  2. Substitute $t = 4.0$ into $\dfrac{t^2 - 4}{t + 1}$. Give your answer as a decimal.

  3. The temperature rises from −3.5°C to 5.5°C over 5 hours. Find the rise and the rate of change in °C per hour.

  4. Write 225 as a product of prime factors in index form, then find $\sqrt{225}$.

  5. Simplify $7x + 4.8 - 3x + 2.4$, then evaluate it for $x = 1.5$.

  6. How many pieces of ribbon each 0.45 m long can be cut from a roll of 7.2 m? How much is left over? Give the leftover in cm.

  7. The HCF of two numbers is 4 and their LCM is 60. One number is 12. Find the other.

  8. Work out $\dfrac{5.4 \times (15 - 3^2)}{6}$. Give your answer as a decimal.

  9. A tank holds 24.0 litres. Water drains at 3.2 litres/min and is added at 0.8 litres/min simultaneously. How long until the tank is empty?

  10. A farmer's field is a rectangle. Its perimeter is 720 m. The length is 2 times the width. Find the area in m², then convert to hectares (1 ha = 10 000 m²).