Printable ratio and Proportion worksheets for grade 5 and 6 math - Free Printable

Let's solve each question step by step:

---

Q.1: Fill in the box:

$$
\frac{14}{21} = \frac{\square}{3} = \frac{6}{\square}
$$

#### Step 1: Solve for the first blank ($\square$ in $\frac{\square}{3}$)
We know:
$$
\frac{14}{21} = \frac{\square}{3}
$$
Simplify $\frac{14}{21}$:
$$
\frac{14}{21} = \frac{2}{3}
$$
So:
$$
\frac{2}{3} = \frac{\square}{3}
$$
By comparing, we see that $\square = 2$.

#### Step 2: Solve for the second blank ($\square$ in $\frac{6}{\square}$)
We know:
$$
\frac{14}{21} = \frac{6}{\square}
$$
Again, simplify $\frac{14}{21}$:
$$
\frac{14}{21} = \frac{2}{3}
$$
So:
$$
\frac{2}{3} = \frac{6}{\square}
$$
Cross-multiply to solve for $\square$:
$$
2 \cdot \square = 3 \cdot 6
$$
$$
2 \cdot \square = 18
$$
$$
\square = \frac{18}{2} = 9
$$

#### Final Answer for Q.1:
$$
\boxed{2, 9}
$$

---

Q.2: Find the ratio of the following:

#### (i) 21 hours to 49 hours
The ratio is:
$$
\frac{21}{49} = \frac{3}{7}
$$
So the ratio is:
$$
3:7
$$

#### (ii) 75 cm to 3 m
Convert 3 m to cm:
$$
3 \text{ m} = 300 \text{ cm}
$$
The ratio is:
$$
\frac{75}{300} = \frac{1}{4}
$$
So the ratio is:
$$
1:4
$$

#### (iii) A dozen to a score
A dozen = 12, and a score = 20.
The ratio is:
$$
\frac{12}{20} = \frac{3}{5}
$$
So the ratio is:
$$
3:5
$$

#### (iv) 1 hour to 20 minutes
Convert 1 hour to minutes:
$$
1 \text{ hour} = 60 \text{ minutes}
$$
The ratio is:
$$
\frac{60}{20} = \frac{3}{1}
$$
So the ratio is:
$$
3:1
$$

#### (v) A dozen to a gross
A dozen = 12, and a gross = 144.
The ratio is:
$$
\frac{12}{144} = \frac{1}{12}
$$
So the ratio is:
$$
1:12
$$

#### Final Answers for Q.2:
$$
\boxed{3:7, 1:4, 3:5, 3:1, 1:12}
$$

---

Q.3: Write True or False:

#### (i) $2 : 8 :: 4 : 16$
Check if the ratios are equal:
$$
\frac{2}{8} = \frac{1}{4} \quad \text{and} \quad \frac{4}{16} = \frac{1}{4}
$$
Since both are equal, the statement is True.

#### (ii) $500 : 200 :: 150 : 60$
Check if the ratios are equal:
$$
\frac{500}{200} = \frac{5}{2} \quad \text{and} \quad \frac{150}{60} = \frac{5}{2}
$$
Since both are equal, the statement is True.

#### (iii) $50 : 45 :: 30 : 20$
Check if the ratios are equal:
$$
\frac{50}{45} = \frac{10}{9} \quad \text{and} \quad \frac{30}{20} = \frac{3}{2}
$$
Since $\frac{10}{9} \neq \frac{3}{2}$, the statement is False.

#### Final Answers for Q.3:
$$
\boxed{\text{True, True, False}}
$$

---

Q.4: Fill in the blanks so that the numbers are in proportion:

#### (i) $20, 18, 40, \ldots$
For the numbers to be in proportion:
$$
\frac{20}{18} = \frac{40}{x}
$$
Cross-multiply:
$$
20x = 18 \cdot 40
$$
$$
20x = 720
$$
$$
x = \frac{720}{20} = 36
$$

#### (ii) $\ldots, 35, 3, 15$
Let the missing number be $x$. For the numbers to be in proportion:
$$
\frac{x}{35} = \frac{3}{15}
$$
Simplify $\frac{3}{15}$:
$$
\frac{3}{15} = \frac{1}{5}
$$
So:
$$
\frac{x}{35} = \frac{1}{5}
$$
Cross-multiply:
$$
5x = 35
$$
$$
x = \frac{35}{5} = 7
$$

#### (iii) $25, 100, \ldots, 160$
Let the missing number be $x$. For the numbers to be in proportion:
$$
\frac{25}{100} = \frac{x}{160}
$$
Simplify $\frac{25}{100}$:
$$
\frac{25}{100} = \frac{1}{4}
$$
So:
$$
\frac{1}{4} = \frac{x}{160}
$$
Cross-multiply:
$$
4x = 160
$$
$$
x = \frac{160}{4} = 40
$$

#### (iv) $32, \ldots, 6, 12$
Let the missing number be $x$. For the numbers to be in proportion:
$$
\frac{32}{x} = \frac{6}{12}
$$
Simplify $\frac{6}{12}$:
$$
\frac{6}{12} = \frac{1}{2}
$$
So:
$$
\frac{32}{x} = \frac{1}{2}
$$
Cross-multiply:
$$
x = 32 \cdot 2 = 64
$$

#### Final Answers for Q.4:
$$
\boxed{36, 7, 40, 64}
$$

---

Q.5: Find $x$, if the numbers are in proportion:

#### (i) $3, 9, 9, x$
For the numbers to be in proportion:
$$
\frac{3}{9} = \frac{9}{x}
$$
Simplify $\frac{3}{9}$:
$$
\frac{3}{9} = \frac{1}{3}
$$
So:
$$
\frac{1}{3} = \frac{9}{x}
$$
Cross-multiply:
$$
x = 9 \cdot 3 = 27
$$

#### (ii) $25, x, 1, 4$
For the numbers to be in proportion:
$$
\frac{25}{x} = \frac{1}{4}
$$
Cross-multiply:
$$
25 \cdot 4 = x \cdot 1
$$
$$
x = 100
$$

#### Final Answers for Q.5:
$$
\boxed{27, 100}
$$

---

Q.6: Divide ₹60 in the ratio 1:2 between Bulbul and Kanika:

The total ratio is:
$$
1 + 2 = 3
$$
Bulbul's share:
$$
\text{Bulbul's share} = \frac{1}{3} \times 60 = 20
$$
Kanika's share:
$$
\text{Kanika's share} = \frac{2}{3} \times 60 = 40
$$

#### Final Answers for Q.6:
$$
\boxed{20, 40}
$$

---

Q.7: Give two equivalent ratios of $6 : 4$:

Simplify $6 : 4$:
$$
6 : 4 = \frac{6}{4} = \frac{3}{2} = 3 : 2
$$
Two equivalent ratios can be obtained by multiplying $3 : 2$ by any non-zero number. For example:
$$
3 : 2 = 6 : 4 \quad \text{(already given)}
$$
Multiply by 2:
$$
3 : 2 = 6 : 4 = 12 : 8
$$
Multiply by 3:
$$
3 : 2 = 6 : 4 = 9 : 6
$$

#### Final Answers for Q.7:
$$
\boxed{12 : 8, 9 : 6}
$$

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Q.8: Weight of 80 books is 160 kg. What is the weight of 25 books?

First, find the weight of one book:
$$
\text{Weight of one book} = \frac{160 \text{ kg}}{80} = 2 \text{ kg}
$$
Now, find the weight of 25 books:
$$
\text{Weight of 25 books} = 25 \times 2 = 50 \text{ kg}
$$

#### Final Answer for Q.8:
$$
\boxed{50}
$$

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Final Boxed Answers:

1. $\boxed{2, 9}$
2. $\boxed{3:7, 1:4, 3:5, 3:1, 1:12}$
3. $\boxed{\text{True, True, False}}$
4. $\boxed{36, 7, 40, 64}$
5. $\boxed{27, 100}$
6. $\boxed{20, 40}$
7. $\boxed{12 : 8, 9 : 6}$
8. $\boxed{50}$