Ratio and proportion worksheet for Grade 6 - Free Printable

Let's solve each question step by step and explain the reasoning.

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I. CHOOSE THE BEST ANSWER (5 Marks)

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1. The equivalent ratio of 2:7 is ________

We need to find a ratio that is equivalent to 2:7, meaning both numbers are multiplied by the same factor.

Let’s check each option:

- a. 7:2 → This is the reverse, not equivalent.
- b. 6:14 → Divide both by 2 → 3:7 ≠ 2:7 ✘
- c. 4:14 → Divide by 2 → 2:7 ✔ Yes! Equivalent.
- d. 20:35 → Divide by 5 → 4:7 ≠ 2:7 ✘

✔ Answer: c. 4:14

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2. The simplest form of the ratio of 12:6 is ________

Simplify 12:6 by dividing both by their GCD (which is 6):

12 ÷ 6 = 2
6 ÷ 6 = 1
So, 12:6 = 2:1

Now check options:

- a. 6:3 → simplifies to 2:1, but it's not simplest form yet
- b. 6:12 → simplifies to 1:2
- c. 1:2 → wrong direction
- d. 2:1 → ✔ Correct and simplest form

✔ Answer: d. 2:1

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3. The ratio of the number of sides of a triangle to the number of sides of a square is ________

- Triangle has 3 sides
- Square has 4 sides

So ratio = 3:4

✔ Answer: b. 3:4

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4. The simplest form of the ratio of 2m to 25 cm is ________

First, convert units to be the same.

2 m = 200 cm

So ratio = 200 cm : 25 cm

Now simplify:

Divide both by 25 → 200 ÷ 25 = 8, 25 ÷ 25 = 1

So, 8:1

Check options:

- a. 2:25 ✘
- b. 200:25 → not simplified
- c. 8:1 ✔
- d. 1:8 ✘

✔ Answer: c. 8:1

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5. If the cost of 3 dolls is Rs.45, then the cost of 5 dolls is Rs.____

Find cost per doll:

45 ÷ 3 = Rs.15 per doll

Then, 5 dolls = 5 × 15 = Rs.75

✔ Answer: a. 75

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II. FILL IN THE BLANKS (5 Marks)

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6. 5:___ :: 30:18

This is a proportion:
5 : x = 30 : 18

Cross-multiply:

5 × 18 = 30 × x
90 = 30x
x = 90 ÷ 30 = 3

✔ Answer: 3

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7. Ratio of 5 minutes to 8 minutes is ______

Since both are in same unit (minutes), ratio = 5:8

✔ Answer: 5:8

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8. If Rs.50 is divided among P and Q in the ratio 3:2, then Q’s share is Rs.____

Total parts = 3 + 2 = 5

Each part = 50 ÷ 5 = Rs.10

Q gets 2 parts → 2 × 10 = Rs.20

✔ Answer: 20

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9. The two quantities in a ratio should be of the _____ unit.

In ratios, both quantities must be in the same unit for comparison.

✔ Answer: same

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10. If a:b :: c:d, then ad = ______

This is the property of proportion:

If a:b = c:d, then a × d = b × c (product of means = product of extremes)

So, ad = bc

✔ Answer: bc

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✔ Final Answers:

I. Choose the best answer:
1. c. 4:14
2. d. 2:1
3. b. 3:4
4. c. 8:1
5. a. 75

II. Fill in the blanks:
6. 3
7. 5:8
8. 20
9. same
10. bc

Let me know if you'd like this formatted as a printable answer sheet!