KS3Solutions

Ratio, proportion and rates of change

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Ratio notation and simplification

  1. RPR-Q1
    Answer
    Simplify the ratio 12:18.
    Working
    1. Find the highest common factor of 12 and 18: 6.
    2. Divide both parts by 6: 126 = 2, 186 = 3.
    Answer: 2:3
  2. RPR-Q2
    Answer
    Simplify the ratio 15:20:25.
    Working
    1. Find the highest common factor of 15, 20, and 25: 5.
    2. Divide each part by 5: 155 = 3, 205 = 4, 255 = 5.
    Answer: 3:4:5

Fractions and measures

  1. RPR-Q3
    Answer
    Express 30 minutes as a fraction of 2 hours.
    Working
    1. Convert 2 hours to minutes: 2 × 60 = 120 minutes.
    2. Fraction = 30120 = 14.
    Answer: 14
  2. RPR-Q4
    Answer
    Express 2 m as a fraction of 5 m.
    Working
    1. Fraction = partwhole = 25.
    2. This is already in simplest form.
    Answer: 25

Scale and maps

  1. RPR-Q5
    Answer
    A map uses a scale of 1:10000. Two towns are 3 cm apart on the map. Find the real distance in km.
    Working
    1. Real distance = 3 × 10000 = 30000 cm.
    2. Convert to meters: 30000 ÷ 100 = 300 m.
    3. Convert to km: 300 ÷ 1000 = 0.3 km.
    Answer: 0.3 km
  2. RPR-Q6
    Answer
    A model is made to a scale of 1:50. The model length is 8 cm. Find the real length in metres.
    Working
    1. Real length = 8 × 50 = 400 cm.
    2. Convert to meters: 400 ÷ 100 = 4 m.
    Answer: 4 m

Proportion and rates

  1. RPR-Q7
    Answer
    3 packs of batteries cost 6 pounds. How much do 5 packs cost?
    Working
    1. Cost per pack = 6 ÷ 3 = 2 pounds.
    2. Cost for 5 packs = 2 × 5 = 10 pounds.
    Answer: 10 pounds
  2. RPR-Q8
    Answer
    A recipe for 2 people uses 100 g of flour. How much flour is needed for 6 people?
    Working
    1. Flour per person = 100 ÷ 2 = 50 g.
    2. For 6 people: 50 × 6 = 300 g.
    Answer: 300 g
  3. RPR-Q9
    Answer
    A car travels 90 km in 3 hours. Find the average speed in km per hour.
    Working
    1. Speed = distance ÷ time = 90 ÷ 3 = 30 km/h.
    Answer: 30 km/h

Percentage change

  1. RPR-Q10
    Answer
    Increase 200 by 10 percent, then decrease the result by 10 percent.
    Working
    1. 10% of 200 is 20, so the increase gives 200 + 20 = 220.
    2. 10% of 220 is 22, so the decrease gives 220 - 22 = 198.
    Answer: 198
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