Grade 4 Fractions worksheets I Maths - key2practice Workbooks - Free Printable

Problem: Equivalent Fractions Worksheet

The task is to complete the equivalent fractions for each given pair. This involves finding the missing numerator or denominator in each fraction so that it is equivalent to the given fraction.

Solution Approach:

To solve these problems, we use the concept of equivalent fractions. Two fractions are equivalent if they represent the same value. This can be achieved by multiplying or dividing both the numerator and the denominator of a fraction by the same non-zero number.

#### General Steps:
1. Identify the relationship between the given numerator/denominator and the target numerator/denominator.
2. Use multiplication or division to find the missing value.
3. Ensure that the resulting fraction is equivalent to the original fraction.

Detailed Solutions:

#### 1. $\frac{1}{6} = \frac{\square}{24}$
- The denominator changes from 6 to 24. To find the multiplier:
$$
24 \div 6 = 4
$$
- Multiply the numerator (1) by 4:
$$
1 \times 4 = 4
$$
- Answer: $\frac{1}{6} = \frac{4}{24}$

#### 2. $\frac{42}{9} = \frac{\square}{53}$
- This problem seems incorrect because the denominators (9 and 53) are not related by a simple multiplication or division. Let's assume it should be $\frac{42}{9} = \frac{\square}{27}$ (a common mistake in copying).
- The denominator changes from 9 to 27. To find the multiplier:
$$
27 \div 9 = 3
$$
- Multiply the numerator (42) by 3:
$$
42 \times 3 = 126
$$
- Corrected Answer: $\frac{42}{9} = \frac{126}{27}$

#### 3. $\frac{4}{8} = \frac{\square}{24}$
- The denominator changes from 8 to 24. To find the multiplier:
$$
24 \div 8 = 3
$$
- Multiply the numerator (4) by 3:
$$
4 \times 3 = 12
$$
- Answer: $\frac{4}{8} = \frac{12}{24}$

#### 4. $\frac{18}{25} = \frac{126}{\square}$
- The numerator changes from 18 to 126. To find the multiplier:
$$
126 \div 18 = 7
$$
- Multiply the denominator (25) by 7:
$$
25 \times 7 = 175
$$
- Answer: $\frac{18}{25} = \frac{126}{175}$

#### 5. $\frac{12}{4} = \frac{\square}{24}$
- The denominator changes from 4 to 24. To find the multiplier:
$$
24 \div 4 = 6
$$
- Multiply the numerator (12) by 6:
$$
12 \times 6 = 72
$$
- Answer: $\frac{12}{4} = \frac{72}{24}$

#### 6. $\frac{9}{12} = \frac{54}{\square}$
- The numerator changes from 9 to 54. To find the multiplier:
$$
54 \div 9 = 6
$$
- Multiply the denominator (12) by 6:
$$
12 \times 6 = 72
$$
- Answer: $\frac{9}{12} = \frac{54}{72}$

#### 7. $\frac{6}{7} = \frac{\square}{56}$
- The denominator changes from 7 to 56. To find the multiplier:
$$
56 \div 7 = 8
$$
- Multiply the numerator (6) by 8:
$$
6 \times 8 = 48
$$
- Answer: $\frac{6}{7} = \frac{48}{56}$

#### 8. $\frac{5}{10} = \frac{\square}{90}$
- The denominator changes from 10 to 90. To find the multiplier:
$$
90 \div 10 = 9
$$
- Multiply the numerator (5) by 9:
$$
5 \times 9 = 45
$$
- Answer: $\frac{5}{10} = \frac{45}{90}$

#### 9. $\frac{1}{2} = \frac{\square}{10}$
- The denominator changes from 2 to 10. To find the multiplier:
$$
10 \div 2 = 5
$$
- Multiply the numerator (1) by 5:
$$
1 \times 5 = 5
$$
- Answer: $\frac{1}{2} = \frac{5}{10}$

#### 10. $\frac{2}{3} = \frac{12}{\square}$
- The numerator changes from 2 to 12. To find the multiplier:
$$
12 \div 2 = 6
$$
- Multiply the denominator (3) by 6:
$$
3 \times 6 = 18
$$
- Answer: $\frac{2}{3} = \frac{12}{18}$

#### 11. $\frac{\square}{5} = \frac{30}{50}$
- Simplify $\frac{30}{50}$:
$$
\frac{30 \div 10}{50 \div 10} = \frac{3}{5}
$$
- The numerator of the simplified fraction is 3.
- Answer: $\frac{3}{5} = \frac{30}{50}$

#### 12. $\frac{4}{\square} = \frac{40}{100}$
- Simplify $\frac{40}{100}$:
$$
\frac{40 \div 20}{100 \div 20} = \frac{2}{5}
$$
- The denominator of the simplified fraction is 5.
- Answer: $\frac{4}{5} = \frac{40}{100}$

#### 13. $\frac{1}{3} = \frac{10}{\square}$
- The numerator changes from 1 to 10. To find the multiplier:
$$
10 \div 1 = 10
$$
- Multiply the denominator (3) by 10:
$$
3 \times 10 = 30
$$
- Answer: $\frac{1}{3} = \frac{10}{30}$

#### 14. $\frac{3}{7} = \frac{\square}{28}$
- The denominator changes from 7 to 28. To find the multiplier:
$$
28 \div 7 = 4
$$
- Multiply the numerator (3) by 4:
$$
3 \times 4 = 12
$$
- Answer: $\frac{3}{7} = \frac{12}{28}$

#### 15. $\frac{6}{\square} = \frac{6}{12}$
- Simplify $\frac{6}{12}$:
$$
\frac{6 \div 6}{12 \div 6} = \frac{1}{2}
$$
- The denominator of the simplified fraction is 2.
- Answer: $\frac{6}{2} = \frac{6}{12}$

#### 16. $\frac{4}{5} = \frac{\square}{10}$
- The denominator changes from 5 to 10. To find the multiplier:
$$
10 \div 5 = 2
$$
- Multiply the numerator (4) by 2:
$$
4 \times 2 = 8
$$
- Answer: $\frac{4}{5} = \frac{8}{10}$

#### 17. $\frac{12}{6} = \frac{\square}{36}$
- Simplify $\frac{12}{6}$:
$$
\frac{12 \div 6}{6 \div 6} = \frac{2}{1}
$$
- The numerator of the simplified fraction is 2.
- Answer: $\frac{2}{1} = \frac{72}{36}$

#### 18. $\frac{2}{4} = \frac{\square}{16}$
- Simplify $\frac{2}{4}$:
$$
\frac{2 \div 2}{4 \div 2} = \frac{1}{2}
$$
- The numerator of the simplified fraction is 1.
- Answer: $\frac{1}{2} = \frac{8}{16}$

Final Answers:

$$
\boxed{
\begin{aligned}
1. & \quad \frac{1}{6} = \frac{4}{24} \\
2. & \quad \frac{42}{9} = \frac{126}{27} \\
3. & \quad \frac{4}{8} = \frac{12}{24} \\
4. & \quad \frac{18}{25} = \frac{126}{175} \\
5. & \quad \frac{12}{4} = \frac{72}{24} \\
6. & \quad \frac{9}{12} = \frac{54}{72} \\
7. & \quad \frac{6}{7} = \frac{48}{56} \\
8. & \quad \frac{5}{10} = \frac{45}{90} \\
9. & \quad \frac{1}{2} = \frac{5}{10} \\
10. & \quad \frac{2}{3} = \frac{12}{18} \\
11. & \quad \frac{3}{5} = \frac{30}{50} \\
12. & \quad \frac{4}{5} = \frac{40}{100} \\
13. & \quad \frac{1}{3} = \frac{10}{30} \\
14. & \quad \frac{3}{7} = \frac{12}{28} \\
15. & \quad \frac{6}{2} = \frac{6}{12} \\
16. & \quad \frac{4}{5} = \frac{8}{10} \\
17. & \quad \frac{2}{1} = \frac{72}{36} \\
18. & \quad \frac{1}{2} = \frac{8}{16}
\end{aligned}
}
$$