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Percentages and ratio · Ages 13–14

Rates, ratios & proportions worksheet

Covers: Rates, Density, pressure and exchange rates, Ratios and proportions, Three-term ratios and sharing, Direct proportion, Inverse proportion, Average speed and mixtures, Scales on maps and plans

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Rates, ratios & proportions worksheet

Percentages and ratio · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

Part A: Working out and filling in (2 marks each)

  1. 1.2 ballpoint pens cost $50: $ each, and 7 of them cost $.

    Fill in each blank

    Answer:

  2. 2.An empty tank is a cuboid 60 cm long, 60 cm wide and 60 cm high. A hose lets in 2 L of water a minute. How many minutes does it take to fill?

    Answer:

  3. 3.If 2x = 6y, then x : y = : (simplest whole numbers).

    Fill in each blank

    Answer:

  4. 4.Three numbers are in the ratio 2 : 2 : 1, and the largest is 9 more than the smallest. Their sum =

    Answer:

  5. 5.y is in direct proportion to x, and y = 12 when x = 2. In y = kx, k = ; when x = 12, y = .

    Fill in each blank

    Answer:

  6. 6.At 100 km/h the trip takes 3 hours. To cover the same distance in 2 hours, the speed must be km/h

    Answer:

  7. 7.The first half of a trip is driven at 30 km/h. At what speed must the second half go for the average over the whole trip to be 50 km/h?

    Answer:

Part B: Choose, or true or false (2 marks each)

  1. 8.How many m/s is 108 km/h?

    • A. 30 m/s
    • B. 388.8 m/s
    • C. 108000 m/s
    • D. 1800 m/s

    Choose the right answer

    Answer:

  2. 9.One day, 1 pound buys 10.2 Hong Kong dollars. How many Hong Kong dollars do 280 pounds buy?

    • A. 285.6 Hong Kong dollars
    • B. 290.2 Hong Kong dollars
    • C. 2856 Hong Kong dollars
    • D. About 274.5 Hong Kong dollars

    Choose the right answer

    Answer:

  3. 10.If x : y = 4 : 5, what is (x + y) : y?

    • A. 5 : 9
    • B. 9 : 5
    • C. 9 : 4
    • D. 4 : 9

    Choose the right answer

    Answer:

  4. 11.a : b : c = 5 : 4 : 8, so a : c = 5 : 8.

    True or false?

    Answer:

  5. 12.On a plan with scale 1 : 5000, what real length in metres do 3 cm stand for?

    • A. 15 m
    • B. 15000 m
    • C. 150 m
    • D. 1500 m

    Choose the right answer

    Answer:

Part C: Word problems (4 marks each)

  1. 13.Turn 72 km/h into m/s. Put the steps in order.

    • A. 1 hour = 3600 seconds
    • B. 72 km = 72000 m
    • C. 72000 ÷ 3600 = 20

    Write the letters in the right order

    Working:

    Answer:

  2. 14.A crown has a mass of 636.9 g. Lowered into a container full to the brim, it spills 37 cm³ of water: that is its volume. Pure gold has a density of 19.3 g/cm³. Were the crown pure gold, its volume would be cm³; it is cm³ more, so it isn't pure gold.

    Fill in each blank

    Working:

    Answer:

  3. 15.Ka-yan's dad is 1.9 m tall and Ka-yan is 125 cm. The ratio of the dad's height to Ka-yan's is : (simplest whole numbers).

    Fill in each blank

    Working:

    Answer:

  4. 16.Tsz-hin's, Chi-keung's and Ka-yee's money are in the ratio 1 : 3 : 3. After Ka-yee gives Tsz-hin $35, Tsz-hin and Ka-yee have the same. How much do the three have together?

    Working:

    Answer:

  5. 17.40 L of petrol cost $800. Petrol costs $ a litre; $400 buys L.

    Fill in each blank

    Working:

    Answer:

  6. 18.On a 1 : 1000 map, a patch of 16 cm² stands for a real 1600 m².

    True or false?

    Working:

    Answer:

Show the answers and working

Rates, ratios & proportions worksheet: Answers and working

Part A: Working out and filling in

  1. 1. 25, 175

    The unit rate first: 50 ÷ 2 = 25; then 25 × 7 = 175.

  2. 2. 108 minutes

    Capacity = 60 × 60 × 60 = 216000 cm³ = 216 L (1 L = 1000 cm³); time = 216 ÷ 2 = 108 minutes.

  3. 3. 3, 1

    Divide both sides by 2y: xy = 62, so x : y = 6 : 2 = 3 : 1. Careful with the order: 2 goes with x, yet 6 comes first.

  4. 4. 45

    The largest and smallest are 2 − 1 = 1 parts apart, which is 9, so a part is 9; 5 parts make 5 × 9 = 45.

  5. 5. 6, 72

    k = y ÷ x = 12 ÷ 2 = 6; y = 6 × 12 = 72.

  6. 6. 150

    Over the same distance, speed and time are inversely proportional: 100 × 3 = 300 km, and 300 ÷ 2 = 150 km/h.

  7. 7. 150 km/h

    Say each half is d km: 2d ÷ (d30 + dx) = 50, so 1x = 250 − 130, and x = 150. Not 2 × 50 − 30.

Part B: Choose, or true or false

  1. 8. A. 30 m/s

    108 × 1000 ÷ 3600 = 30: 1000 ÷ 3600 is 1 ÷ 3.6.

  2. 9. C. 2856 Hong Kong dollars

    Each pound buys 10.2 Hong Kong dollars, so 280 pounds buy 280 × 10.2 = 2856.

  3. 10. B. 9 : 5

    Let x = 4k and y = 5k: x + y = 9k, so (x + y) : y = 9 : 5.

  4. 11. True

    a is 5 parts and c is 8: a : c = 5 : 8 = 5 : 8. Keep the order a, then c.

  5. 12. C. 150 m

    Real length = 3 × 5000 = 15000 cm = 150 m.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

  1. 13. B → A → C

    km into m, then hours into seconds, then divide: 72 km/h = 20 m/s.

  2. 14. 33, 4

    Volume = mass ÷ density = 636.9 ÷ 19.3 = 33 cm³; 37 − 33 = 4 cm³. The same mass in a bigger volume is less dense: a lighter metal is mixed in.

  3. 15. 38, 25

    Same units first: 1.9 m = 190 cm. 190 : 125, both ÷ 5, is 38 : 25.

  4. 16. 245 dollars

    Ka-yee has 3 − 1 parts more than Tsz-hin; giving 35 evens them, so the gap is 2 × 35: a part = 2 × 35 ÷ (3 − 1) = 35, and (1 + 3 + 3) × 35 = 245 dollars in all.

  5. 17. 20, 20

    Price is in direct proportion to litres: 800 ÷ 40 = 20 a litre; 400 ÷ 20 = 20 L.

  6. 18. True

    1 cm stands for 10 m, so 1 cm² for 10 × 10 m²: 16 × 10 × 10 = 1600 m². Multiplying by 10 once is wrong.

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