Percentages and ratio · Ages 13–14

Ratios and proportions worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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

1.Write 0.3 : 2.1 in its simplest whole-number form: :
Fill in each blank
Answer:
2.x : 36 = 1 : 6, x =
Answer:
3.Write 23 : 37 in its simplest whole-number form: :
Fill in each blank
Answer:
4.Write 34 : 17 in its simplest whole-number form: :
Fill in each blank
Answer:
5.If 4x = 2y, then x : y = : (simplest whole numbers).
Fill in each blank
Answer:
6.In its simplest whole-number form, 70 cm : 4 m is : .
Fill in each blank
Answer:
7.x : 5 = (x + 1) : 6, x =
Answer:
8.x : 9 = (x + 15) : 14, x =
Answer:

13.Ka-yan's dad is 1.8 m tall and Ka-yan is 150 cm. The ratio of the dad's height to Ka-yan's is : (simplest whole numbers).
Fill in each blank
Working:
Answer:
14.Solve x : 15 = 12 : 5. Put the steps in order.
- A. x15 = 125
- B. 5x = 180
- C. x = 36
- D. 5x = 15 × 12
Write the letters in the right order
Working:
Answer:
15.A drink mixes juice and water in the ratio 3 : 7. How much water goes with 450 mL of juice?
Working:
Answer:
16.Tsz-ching's and Ka-lok's money are in the ratio 3 : 2. After Tsz-ching gives Ka-lok $20, the ratio becomes 2 : 3. How much did Tsz-ching have at first?
Working:
Answer:
17.Tsz-ching's and Ka-lok's savings are in the ratio 4 : 1. Tsz-ching has $560, so Ka-lok has $, and together they have $.
Fill in each blank
Working:
Answer:
18.A photo's length and width are in the ratio 7 : 2. Enlarged, it is 56 cm long. How wide is it?
Working:
Answer:

Show the answers and working

Ratios and proportions worksheet: Answers and working

1. 1, 7
Both terms times 10 make 3 : 21; both ÷ 3 make 1 : 7.
2. 6
Cross-multiply: 6x = 36 × 1 = 36, so x = 6. Or spot the multiplier: 6 × 6 = 36, so x = 1 × 6 = 6.
3. 14, 9
Both terms times 21, the L.C.M. of the denominators, make 14 : 9. Or as a division: 23 ÷ 37 = 149.
4. 21, 4
Both terms times 28, the L.C.M. of the denominators, make 21 : 4. Or as a division: 34 ÷ 17 = 214.
5. 1, 2
Divide both sides by 4y: xy = 24, so x : y = 2 : 4 = 1 : 2. Careful with the order: 4 goes with x, yet 2 comes first.
6. 7, 40
Same units first: 4 m = 400 cm, and 70 : 400, both ÷ 10, is 7 : 40.
7. 5
Cross-multiply: 6x = 5(x + 1), 6x = 5x + 5, x = 5, x = 5.
8. 27
Cross-multiply: 14x = 9(x + 15), 14x = 9x + 135, 5x = 135, x = 27.

9. True
Simplify both, or cross-multiply: 6 × 15 = 90 and 10 × 9 = 90. Only equal products make equal ratios.
10. True
Simplify both, or cross-multiply: 6 × 14 = 84 and 21 × 4 = 84. Only equal products make equal ratios.
11. B. 12 : 5
Let x = 7k and y = 5k: x + y = 12k, so (x + y) : y = 12 : 5.
12. B. 12 : 7
Let x = 5k and y = 7k: x + y = 12k, so (x + y) : y = 12 : 7.

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

13. 6, 5
Same units first: 1.8 m = 180 cm. 180 : 150, both ÷ 30, is 6 : 5.
14. A → D → B → C
As fractions, cross-multiply, work it out, then divide both sides by 5.
15. 1050 mL
3 : 7 = 450 : x, 3x = 7 × 450, x = 1050. Or a part is 450 ÷ 3 = 150 mL, and the water is 7 parts.
16. 60 dollars
Say they had 3k and 2k dollars: (3k − 20) : (2k + 20) = 2 : 3. Cross-multiplying gives k = 20, so Tsz-ching had 3 × 20 = 60 dollars.
17. 140, 700
4 parts are 560, so a part is 140: Ka-lok has 1 × 140 = 140, 560 + 140 = 700 in all.
18. 16 cm
Enlarging keeps the ratio: 7 : 2 = 56 : x, so x = 56 × 2 ÷ 7 = 16.

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