Ratio and proportion worksheet for Grade 6 - Free Printable

Let's solve each question step by step and provide explanations.

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I. CHOOSE THE BEST ANSWER (5 Marks)

#### 1. The equivalent ratio of 2:7 is ________
We need to find a ratio that is equivalent to 2:7.
An equivalent ratio means both terms are multiplied or divided by the same number.

Check options:

- a. 7:2 → Not equivalent (reversed)
- b. 6:14 → Divide both by 2 → 3:7 ≠ 2:7 ✘
- c. 4:14 → Divide both by 2 → 2:7 ✔
- d. 20:35 → Divide both 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 GCF (Greatest Common Factor), which is 6.

12 ÷ 6 = 2
6 ÷ 6 = 1
So, 12:6 = 2:1

✔ 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
- 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 meters = 200 cm
So, ratio = 200 cm : 25 cm

Now simplify:
200 ÷ 25 = 8
25 ÷ 25 = 1
So, 200:25 = 8:1

✔ 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.____
Cost of 1 doll = 45 ÷ 3 = Rs.15
Cost of 5 dolls = 15 × 5 = Rs.75

✔ Answer: a. 75

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II. FILL IN THE BLANKS (5 Marks)

#### 6. 5: ___ :: 30:18

This is a proportion:
5 : x :: 30 : 18
Which means:
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 ________

Both in same unit (minutes), so ratio is directly:

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.

For a meaningful ratio, both quantities must be in the same unit.

✔ Answer: same

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

This is the property of proportions:

If a:b :: c:d, then a/b = c/d
Cross-multiplying: a × d = b × c

So, ad = bc

✔ Answer: bc

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✔ Final Answers:

| Question | Answer |
|--------|--------|
| 1 | c. 4:14 |
| 2 | d. 2:1 |
| 3 | b. 3:4 |
| 4 | c. 8:1 |
| 5 | a. 75 |
| 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!