Ratio and proportion worksheet for Grade 6 - Free Printable

Unit Test: Ratio and Proportion

#### Class: 6
#### Total Marks: 30

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Section I: Choose the Best Answer (5 Marks)

#### 1. The equivalent ratio of 2:7 is _______
- Given ratio: 2:7
- To find an equivalent ratio, we multiply both terms of the ratio by the same number.
- Option (a): 7:2 → This is not equivalent because the order is reversed.
- Option (b): 6:14 → This is equivalent because \(2 \times 3 = 6\) and \(7 \times 3 = 14\).
- Option (c): 4:14 → This is not equivalent because \(2 \times 2 = 4\) but \(7 \times 2 \neq 14\).
- Option (d): 20:35 → This is equivalent because \(2 \times 10 = 20\) and \(7 \times 10 = 35\).

Correct Answer: b. 6:14 or d. 20:35

#### 2. The simplest form of the ratio of 12:6 is _______
- Given ratio: 12:6
- To simplify, divide both terms by their greatest common divisor (GCD), which is 6.
- \(12 ÷ 6 = 2\)
- \(6 ÷ 6 = 1\)
- Simplified ratio: 2:1

Correct Answer: d. 2:1

#### 3. The ratio of the number of sides of a triangle to the number of sides of a square is _______
- Number of sides of a triangle: 3
- Number of sides of a square: 4
- Ratio: \(3:4\)

Correct Answer: b. 3:4

#### 4. The simplest form of the ratio of 2m to 25 cm is _______
- Convert units to be consistent: 1 meter = 100 cm
- \(2 \text{ m} = 2 \times 100 = 200 \text{ cm}\)
- Given ratio: 200 cm : 25 cm
- Simplify by dividing both terms by their GCD, which is 25.
- \(200 ÷ 25 = 8\)
- \(25 ÷ 25 = 1\)
- Simplified ratio: 8:1

Correct Answer: c. 8:1

#### 5. If the cost of 3 dolls is Rs. 45, then the cost of 5 dolls is Rs. _______
- Cost of 3 dolls: Rs. 45
- Cost of 1 doll: \( \frac{45}{3} = 15 \) Rs.
- Cost of 5 dolls: \( 5 \times 15 = 75 \) Rs.

Correct Answer: a. 75

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Section II: Fill in the Blanks (5 Marks)

#### 6. 5: ____ :: 30: 18
- This is a proportion problem: \(5:x = 30:18\).
- Cross-multiply to solve for \(x\):
\[
5 \times 18 = 30 \times x
\]
\[
90 = 30x
\]
\[
x = \frac{90}{30} = 3
\]

Answer: 3

#### 7. Ratio of 5 minutes to 8 minutes is _______
- Given values: 5 minutes and 8 minutes
- Ratio: \(5:8\)

Answer: 5:8

#### 8. If Rs. 50 is divided among P and Q in the ratio 3:2, then Q’s share is Rs. _______
- Total amount: Rs. 50
- Ratio: 3:2
- Sum of parts: \(3 + 2 = 5\)
- Q’s share: \(\frac{2}{5} \times 50 = 20\) Rs.

Answer: 20

#### 9. The two quantities in a ratio should be of the ______ unit.
- For a ratio to be meaningful, the two quantities must be of the same unit.

Answer: same

#### 10. If \(a:b::c:d\), then \(ad =\) _______
- This is a proportion: \(a:b = c:d\).
- In proportions, the product of the means equals the product of the extremes:
\[
a \times d = b \times c
\]

Answer: bc

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Final Answers:

1. b. 6:14 or d. 20:35
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

Boxed Final Answer:
\[
\boxed{b, d, b, c, a, 3, 5:8, 20, \text{same}, bc}
\]