Fractions · Ages 11–12

Equivalent ratios and simplest form worksheet

Part of: Ratio and rate

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Fractions · Ages 11–12

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

1.9 : 7 = 72 :
Answer:
2.Write 30 : 5 in its simplest form: :
Fill in each blank
Answer:
3.4 : 7 = 36 :
Answer:
4.Write 12 : 3 in its simplest form: :
Fill in each blank
Answer:
5.1 m = 100 cm. Write 20 cm : 1 m in its simplest form: :
Fill in each blank
Answer:
6.Write 6 : 24 : 48 in its simplest form: : :
Fill in each blank
Answer:
7.1 m = 100 cm. Write 20 cm : 2 m in its simplest form: :
Fill in each blank
Answer:
8.Write 30 : 5 : 10 in its simplest form: : :
Fill in each blank
Answer:

13.Workers mix sand, cement and stones in the ratio 2 : 2 : 3. They use 16 buckets of sand. How many buckets of stones do they need?
Working:
Answer:
14.1 m = 100 cm. A long rope is 2 m long and a short rope is 65 cm long. In simplest form, the ratio of the long rope's length to the short rope's is : .
Fill in each blank
Working:
Answer:
15.In the morning a cha chaan teng sells 6 milk teas, 12 coffees and 6 lemon teas. In simplest form, the ratio of milk teas to coffees to lemon teas is : : .
Fill in each blank
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16.Ka-lok has 11 stickers and Ka-yee has 66. In simplest form, the ratio of Ka-lok's stickers to Ka-yee's is : .
Fill in each blank
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Answer:
17.For pineapple buns, the ratio of flour to sugar by weight is 6 : 1. The baker uses 180 g of flour. How many grams of sugar are needed?
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18.For pineapple buns, the ratio of flour to sugar by weight is 5 : 4. The baker uses 150 g of flour. How many grams of sugar are needed?
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Answer:

Show the answers and working

Equivalent ratios and simplest form worksheet: Answers and working

1. 56
9 became 72: what was it multiplied by? 7 must be multiplied by the same.
9 × 8 = 72, so 7 must be multiplied by 8 too: 7 × 8 = 56.
2. 6, 1
Find the H.C.F. of 30 and 5, then divide both terms by it.
The H.C.F. of 30 and 5 is 5; divide both terms by 5: 6 : 1.
3. 63
4 became 36: what was it multiplied by? 7 must be multiplied by the same.
4 × 9 = 36, so 7 must be multiplied by 9 too: 7 × 9 = 63.
4. 4, 1
Find the H.C.F. of 12 and 3, then divide both terms by it.
The H.C.F. of 12 and 3 is 3; divide both terms by 3: 4 : 1.
5. 1, 5
The units must match. Change 1 m into centimetres first, then simplify.
Same units first: 1 m = 100 cm. The H.C.F. of 20 and 100 is 20: 1 : 5.
6. 1, 4, 8
Find the H.C.F. of 6, 24 and 48, then divide all three by it.
The H.C.F. of all three terms is 6; divide all three by 6: 1 : 4 : 8.
7. 1, 10
The units must match. Change 2 m into centimetres first, then simplify.
Same units first: 2 m = 200 cm. The H.C.F. of 20 and 200 is 20: 1 : 10.
8. 6, 1, 2
Find the H.C.F. of 30, 5 and 10, then divide all three by it.
The H.C.F. of all three terms is 5; divide all three by 5: 6 : 1 : 2.

9. True
Find the H.C.F. of 40 and 8, then see whether 5 : 1 can be simplified any further.
The H.C.F. of 40 and 8 is 8; dividing by 8 gives 5 : 1. Dividing by a smaller common factor doesn't reach the simplest form.
10. B. 48 : 54
Equal ratios multiply or divide both terms by the same number. Check each choice for that.
Multiply both terms by 6: 8 × 6 = 48 and 9 × 6 = 54, so 48 : 54 equals 8 : 9.
11. True
Find the H.C.F. of 24 and 32, then see whether 3 : 4 can be simplified any further.
The H.C.F. of 24 and 32 is 8; dividing by 8 gives 3 : 4. Dividing by a smaller common factor doesn't reach the simplest form.
12. C. 4 : 16
Equal ratios multiply or divide both terms by the same number. Check each choice for that.
Multiply both terms by 4: 1 × 4 = 4 and 4 × 4 = 16, so 4 : 16 equals 1 : 4.

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

13. 24 buckets
Sand is 2 parts, 16 buckets. Find one part first.
Sand is 2 parts, 16 buckets, so a part is 8; stones are 3 parts: 3 × 8 = 24.
14. 40, 13
The units must match. Change 2 m into centimetres, then simplify; the long rope comes first.
Same units first: 2 m = 200 cm. The H.C.F. of 200 and 65 is 5: 40 : 13.
15. 1, 2, 1
Find the H.C.F. of 6, 12 and 6, then divide all three by it.
The H.C.F. of the three is 6; divide them all by 6: 1 : 2 : 1.
16. 1, 6
Find the H.C.F. of 11 and 66, then divide both terms by it.
The H.C.F. of 11 and 66 is 11: 1 : 6.
17. 30 g
Flour is 6 parts, 180 g. Find one part first.
180 ÷ 6 = 30, so a part is 30 g; sugar: 1 × 30 = 30 g.
18. 120 g
Flour is 5 parts, 150 g. Find one part first.
150 ÷ 5 = 30, so a part is 30 g; sugar: 4 × 30 = 120 g.

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