Equivalent Fractions Worksheets - Math Monks - Free Printable

To solve the problem of completing the equivalent fractions, we need to find the missing numerators or denominators in each fraction so that the fractions remain equivalent. Two fractions are equivalent if they represent the same value when simplified.

Step-by-Step Solution:

#### 1) $\frac{5}{10} = \frac{\square}{90}$
- Simplify $\frac{5}{10}$: $\frac{5}{10} = \frac{1}{2}$.
- To make the denominator 90, we need to multiply both the numerator and the denominator of $\frac{1}{2}$ by 45 (since $2 \times 45 = 90$).
- $\frac{1}{2} = \frac{1 \times 45}{2 \times 45} = \frac{45}{90}$.
- So, the missing numerator is 45.

#### 2) $\frac{2}{4} = \frac{\square}{20}$
- Simplify $\frac{2}{4}$: $\frac{2}{4} = \frac{1}{2}$.
- To make the denominator 20, we need to multiply both the numerator and the denominator of $\frac{1}{2}$ by 10 (since $2 \times 10 = 20$).
- $\frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20}$.
- So, the missing numerator is 10.

#### 3) $\frac{3}{7} = \frac{\square}{28}$
- To make the denominator 28, we need to multiply both the numerator and the denominator of $\frac{3}{7}$ by 4 (since $7 \times 4 = 28$).
- $\frac{3}{7} = \frac{3 \times 4}{7 \times 4} = \frac{12}{28}$.
- So, the missing numerator is 12.

#### 4) $\frac{\square}{15} = \frac{8}{3}$
- To make the denominator 15, we need to multiply both the numerator and the denominator of $\frac{8}{3}$ by 5 (since $3 \times 5 = 15$).
- $\frac{8}{3} = \frac{8 \times 5}{3 \times 5} = \frac{40}{15}$.
- So, the missing numerator is 40.

#### 5) $\frac{9}{2} = \frac{\square}{40}$
- To make the denominator 40, we need to multiply both the numerator and the denominator of $\frac{9}{2}$ by 20 (since $2 \times 20 = 40$).
- $\frac{9}{2} = \frac{9 \times 20}{2 \times 20} = \frac{180}{40}$.
- So, the missing numerator is 180.

#### 6) $\frac{6}{\square} = \frac{30}{45}$
- Simplify $\frac{30}{45}$: $\frac{30}{45} = \frac{2}{3}$.
- To make the numerator 6, we need to multiply both the numerator and the denominator of $\frac{2}{3}$ by 3 (since $2 \times 3 = 6$).
- $\frac{2}{3} = \frac{2 \times 3}{3 \times 3} = \frac{6}{9}$.
- So, the missing denominator is 9.

#### 7) $\frac{\square}{27} = \frac{7}{9}$
- To make the denominator 27, we need to multiply both the numerator and the denominator of $\frac{7}{9}$ by 3 (since $9 \times 3 = 27$).
- $\frac{7}{9} = \frac{7 \times 3}{9 \times 3} = \frac{21}{27}$.
- So, the missing numerator is 21.

#### 8) $\frac{39}{12} = \frac{13}{\square}$
- Simplify $\frac{39}{12}$: $\frac{39}{12} = \frac{13}{4}$.
- To make the numerator 13, we need to multiply both the numerator and the denominator of $\frac{13}{4}$ by 1 (since it is already in simplest form).
- $\frac{13}{4} = \frac{13 \times 1}{4 \times 1} = \frac{13}{4}$.
- So, the missing denominator is 4.

#### 9) $\frac{10}{3} = \frac{\square}{27}$
- To make the denominator 27, we need to multiply both the numerator and the denominator of $\frac{10}{3}$ by 9 (since $3 \times 9 = 27$).
- $\frac{10}{3} = \frac{10 \times 9}{3 \times 9} = \frac{90}{27}$.
- So, the missing numerator is 90.

#### 10) $\frac{1}{6} = \frac{\square}{54}$
- To make the denominator 54, we need to multiply both the numerator and the denominator of $\frac{1}{6}$ by 9 (since $6 \times 9 = 54$).
- $\frac{1}{6} = \frac{1 \times 9}{6 \times 9} = \frac{9}{54}$.
- So, the missing numerator is 9.

#### 11) $\frac{4}{4} = \frac{\square}{12}$
- Simplify $\frac{4}{4}$: $\frac{4}{4} = 1$.
- To make the denominator 12, we need to multiply both the numerator and the denominator of $\frac{1}{1}$ by 12 (since $1 \times 12 = 12$).
- $\frac{1}{1} = \frac{1 \times 12}{1 \times 12} = \frac{12}{12}$.
- So, the missing numerator is 12.

#### 12) $\frac{1}{2} = \frac{5}{\square}$
- To make the numerator 5, we need to multiply both the numerator and the denominator of $\frac{1}{2}$ by 5 (since $1 \times 5 = 5$).
- $\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}$.
- So, the missing denominator is 10.

#### 13) $\frac{4}{12} = \frac{\square}{6}$
- Simplify $\frac{4}{12}$: $\frac{4}{12} = \frac{1}{3}$.
- To make the denominator 6, we need to multiply both the numerator and the denominator of $\frac{1}{3}$ by 2 (since $3 \times 2 = 6$).
- $\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$.
- So, the missing numerator is 2.

#### 14) $\frac{1}{4} = \frac{\square}{48}$
- To make the denominator 48, we need to multiply both the numerator and the denominator of $\frac{1}{4}$ by 12 (since $4 \times 12 = 48$).
- $\frac{1}{4} = \frac{1 \times 12}{4 \times 12} = \frac{12}{48}$.
- So, the missing numerator is 12.

#### 15) $\frac{1}{7} = \frac{\square}{28}$
- To make the denominator 28, we need to multiply both the numerator and the denominator of $\frac{1}{7}$ by 4 (since $7 \times 4 = 28$).
- $\frac{1}{7} = \frac{1 \times 4}{7 \times 4} = \frac{4}{28}$.
- So, the missing numerator is 4.

Final Answer:

$$
\boxed{
\begin{array}{lll}
1) & 45 & 2) & 10 & 3) & 12 \\
4) & 40 & 5) & 180 & 6) & 9 \\
7) & 21 & 8) & 4 & 9) & 90 \\
10) & 9 & 11) & 12 & 12) & 10 \\
13) & 2 & 14) & 12 & 15) & 4 \\
\end{array}
}
$$