Equivalent Fractions Worksheets | Math fractions worksheets ... - Free Printable

Problem Explanation:

The task involves finding equivalent fractions for given fractions. Equivalent fractions are fractions that have the same value but are expressed with different numerators and denominators. To find equivalent fractions, you multiply or divide both the numerator and the denominator of a fraction by the same non-zero number.

Solution:

#### 1)
Given: $\frac{1}{5} = \frac{2}{10} = \frac{4}{20} = \frac{6}{30}$

- To find $\frac{1}{5} = \frac{?}{15}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{5 \times 3} = \frac{3}{15}$.

- To find $\frac{1}{5} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{5 \times 4} = \frac{4}{20}$.

- To find $\frac{1}{5} = \frac{6}{?}$:
Multiply numerator and denominator by 6: $\frac{1 \times 6}{5 \times 6} = \frac{6}{30}$.

- To find $\frac{1}{5} = \frac{?}{35}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{5 \times 7} = \frac{7}{35}$.

So, the completed row is:
$$
\frac{1}{5} = \frac{2}{10} = \frac{3}{15} = \frac{4}{20} = \frac{6}{30} = \frac{7}{35}
$$

#### 2)
Given: $\frac{3}{7} = \frac{6}{14} = \frac{9}{21}$

- To find $\frac{3}{7} = \frac{?}{14}$:
Multiply numerator and denominator by 2: $\frac{3 \times 2}{7 \times 2} = \frac{6}{14}$.

- To find $\frac{3}{7} = \frac{9}{?}$:
Multiply numerator and denominator by 3: $\frac{3 \times 3}{7 \times 3} = \frac{9}{21}$.

- To find $\frac{3}{7} = \frac{12}{?}$:
Multiply numerator and denominator by 4: $\frac{3 \times 4}{7 \times 4} = \frac{12}{28}$.

- To find $\frac{3}{7} = \frac{15}{?}$:
Multiply numerator and denominator by 5: $\frac{3 \times 5}{7 \times 5} = \frac{15}{35}$.

- To find $\frac{3}{7} = \frac{21}{?}$:
Multiply numerator and denominator by 7: $\frac{3 \times 7}{7 \times 7} = \frac{21}{49}$.

So, the completed row is:
$$
\frac{3}{7} = \frac{6}{14} = \frac{9}{21} = \frac{12}{28} = \frac{15}{35} = \frac{21}{49}
$$

#### 3)
Given: $\frac{1}{4} = \frac{2}{8} = \frac{3}{12}$

- To find $\frac{1}{4} = \frac{?}{8}$:
Multiply numerator and denominator by 2: $\frac{1 \times 2}{4 \times 2} = \frac{2}{8}$.

- To find $\frac{1}{4} = \frac{3}{?}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{4 \times 3} = \frac{3}{12}$.

- To find $\frac{1}{4} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{4 \times 4} = \frac{4}{16}$.

- To find $\frac{1}{4} = \frac{5}{?}$:
Multiply numerator and denominator by 5: $\frac{1 \times 5}{4 \times 5} = \frac{5}{20}$.

- To find $\frac{1}{4} = \frac{7}{?}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{4 \times 7} = \frac{7}{28}$.

So, the completed row is:
$$
\frac{1}{4} = \frac{2}{8} = \frac{3}{12} = \frac{4}{16} = \frac{5}{20} = \frac{7}{28}
$$

#### 4)
Given: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$

- To find $\frac{1}{2} = \frac{?}{4}$:
Multiply numerator and denominator by 2: $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.

- To find $\frac{1}{2} = \frac{3}{?}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.

- To find $\frac{1}{2} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$.

- To find $\frac{1}{2} = \frac{5}{?}$:
Multiply numerator and denominator by 5: $\frac{1 \times 5}{2 \times 5} = \frac{5}{10}$.

- To find $\frac{1}{2} = \frac{7}{?}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{2 \times 7} = \frac{7}{14}$.

So, the completed row is:
$$
\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{7}{14}
$$

#### 5)
Given: $\frac{1}{7} = \frac{2}{14} = \frac{3}{21}$

- To find $\frac{1}{7} = \frac{?}{14}$:
Multiply numerator and denominator by 2: $\frac{1 \times 2}{7 \times 2} = \frac{2}{14}$.

- To find $\frac{1}{7} = \frac{3}{?}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{7 \times 3} = \frac{3}{21}$.

- To find $\frac{1}{7} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{7 \times 4} = \frac{4}{28}$.

- To find $\frac{1}{7} = \frac{5}{?}$:
Multiply numerator and denominator by 5: $\frac{1 \times 5}{7 \times 5} = \frac{5}{35}$.

- To find $\frac{1}{7} = \frac{7}{?}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{7 \times 7} = \frac{7}{49}$.

So, the completed row is:
$$
\frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{7}{49}
$$

#### 6)
Given: $\frac{1}{1} = \frac{2}{2} = \frac{3}{3}$

- To find $\frac{1}{1} = \frac{?}{3}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{1 \times 3} = \frac{3}{3}$.

- To find $\frac{1}{1} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{1 \times 4} = \frac{4}{4}$.

- To find $\frac{1}{1} = \frac{5}{?}$:
Multiply numerator and denominator by 5: $\frac{1 \times 5}{1 \times 5} = \frac{5}{5}$.

- To find $\frac{1}{1} = \frac{6}{?}$:
Multiply numerator and denominator by 6: $\frac{1 \times 6}{1 \times 6} = \frac{6}{6}$.

- To find $\frac{1}{1} = \frac{7}{?}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{1 \times 7} = \frac{7}{7}$.

So, the completed row is:
$$
\frac{1}{1} = \frac{2}{2} = \frac{3}{3} = \frac{4}{4} = \frac{5}{5} = \frac{6}{6} = \frac{7}{7}
$$

#### 7)
Given: $\frac{1}{2} = \frac{2}{4} = \frac{3}{6}$

- To find $\frac{1}{2} = \frac{?}{6}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{2 \times 3} = \frac{3}{6}$.

- To find $\frac{1}{2} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{2 \times 4} = \frac{4}{8}$.

- To find $\frac{1}{2} = \frac{5}{?}$:
Multiply numerator and denominator by 5: $\frac{1 \times 5}{2 \times 5} = \frac{5}{10}$.

- To find $\frac{1}{2} = \frac{6}{?}$:
Multiply numerator and denominator by 6: $\frac{1 \times 6}{2 \times 6} = \frac{6}{12}$.

- To find $\frac{1}{2} = \frac{7}{?}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{2 \times 7} = \frac{7}{14}$.

So, the completed row is:
$$
\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12} = \frac{7}{14}
$$

#### 8)
Given: $\frac{3}{8} = \frac{6}{16} = \frac{9}{24}$

- To find $\frac{3}{8} = \frac{?}{16}$:
Multiply numerator and denominator by 2: $\frac{3 \times 2}{8 \times 2} = \frac{6}{16}$.

- To find $\frac{3}{8} = \frac{9}{?}$:
Multiply numerator and denominator by 3: $\frac{3 \times 3}{8 \times 3} = \frac{9}{24}$.

- To find $\frac{3}{8} = \frac{12}{?}$:
Multiply numerator and denominator by 4: $\frac{3 \times 4}{8 \times 4} = \frac{12}{32}$.

- To find $\frac{3}{8} = \frac{18}{?}$:
Multiply numerator and denominator by 6: $\frac{3 \times 6}{8 \times 6} = \frac{18}{48}$.

- To find $\frac{3}{8} = \frac{21}{?}$:
Multiply numerator and denominator by 7: $\frac{3 \times 7}{8 \times 7} = \frac{21}{56}$.

So, the completed row is:
$$
\frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{18}{48} = \frac{21}{56}
$$

#### 9)
Given: $\frac{1}{3} = \frac{2}{6} = \frac{3}{9}$

- To find $\frac{1}{3} = \frac{?}{6}$:
Multiply numerator and denominator by 2: $\frac{1 \times 2}{3 \times 2} = \frac{2}{6}$.

- To find $\frac{1}{3} = \frac{3}{?}$:
Multiply numerator and denominator by 3: $\frac{1 \times 3}{3 \times 3} = \frac{3}{9}$.

- To find $\frac{1}{3} = \frac{4}{?}$:
Multiply numerator and denominator by 4: $\frac{1 \times 4}{3 \times 4} = \frac{4}{12}$.

- To find $\frac{1}{3} = \frac{5}{?}$:
Multiply numerator and denominator by 5: $\frac{1 \times 5}{3 \times 5} = \frac{5}{15}$.

- To find $\frac{1}{3} = \frac{6}{?}$:
Multiply numerator and denominator by 6: $\frac{1 \times 6}{3 \times 6} = \frac{6}{18}$.

- To find $\frac{1}{3} = \frac{7}{?}$:
Multiply numerator and denominator by 7: $\frac{1 \times 7}{3 \times 7} = \frac{7}{21}$.

So, the completed row is:
$$
\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18} = \frac{7}{21}
$$

#### 10)
Given: $\frac{7}{10} = \frac{14}{20} = \frac{21}{30}$

- To find $\frac{7}{10} = \frac{?}{20}$:
Multiply numerator and denominator by 2: $\frac{7 \times 2}{10 \times 2} = \frac{14}{20}$.

- To find $\frac{7}{10} = \frac{21}{?}$:
Multiply numerator and denominator by 3: $\frac{7 \times 3}{10 \times 3} = \frac{21}{30}$.

- To find $\frac{7}{10} = \frac{28}{?}$:
Multiply numerator and denominator by 4: $\frac{7 \times 4}{10 \times 4} = \frac{28}{40}$.

- To find $\frac{7}{10} = \frac{35}{?}$:
Multiply numerator and denominator by 5: $\frac{7 \times 5}{10 \times 5} = \frac{35}{50}$.

- To find $\frac{7}{10} = \frac{42}{?}$:
Multiply numerator and denominator by 6: $\frac{7 \times 6}{10 \times 6} = \frac{42}{60}$.

- To find $\frac{7}{10} = \frac{49}{?}$:
Multiply numerator and denominator by 7: $\frac{7 \times 7}{10 \times 7} = \frac{49}{70}$.

So, the completed row is:
$$
\frac{7}{10} = \frac{14}{20} = \frac{21}{30} = \frac{28}{40} = \frac{35}{50} = \frac{42}{60} = \frac{49}{70}
$$

Final Answer:

$$
\boxed{
\begin{array}{l}
1) \frac{1}{5} = \frac{2}{10} = \frac{3}{15} = \frac{4}{20} = \frac{6}{30} = \frac{7}{35} \\
2) \frac{3}{7} = \frac{6}{14} = \frac{9}{21} = \frac{12}{28} = \frac{15}{35} = \frac{21}{49} \\
3) \frac{1}{4} = \frac{2}{8} = \frac{3}{12} = \frac{4}{16} = \frac{5}{20} = \frac{7}{28} \\
4) \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{7}{14} \\
5) \frac{1}{7} = \frac{2}{14} = \frac{3}{21} = \frac{4}{28} = \frac{5}{35} = \frac{7}{49} \\
6) \frac{1}{1} = \frac{2}{2} = \frac{3}{3} = \frac{4}{4} = \frac{5}{5} = \frac{6}{6} = \frac{7}{7} \\
7) \frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{6}{12} = \frac{7}{14} \\
8) \frac{3}{8} = \frac{6}{16} = \frac{9}{24} = \frac{12}{32} = \frac{18}{48} = \frac{21}{56} \\
9) \frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{6}{18} = \frac{7}{21} \\
10) \frac{7}{10} = \frac{14}{20} = \frac{21}{30} = \frac{28}{40} = \frac{35}{50} = \frac{42}{60} = \frac{49}{70}
\end{array}
}
$$