Equivalent Fractions and Simplifying: Practice

Multiply both the numerator and the denominator by the same number $3$.

$\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$

So $\frac{1}{2} = \frac{3}{6}$.

Multiply the top and bottom of $\frac{1}{2}$ by the same number. Using $2$:

$\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}$

So $\frac{2}{4}$ is equivalent to $\frac{1}{2}$.

Multiply both numbers by the same $2$.

$\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$

So $\frac{2}{3} = \frac{4}{6}$.

Multiply the top and bottom of $\frac{1}{3}$ by the same number. Using $2$:

$\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$

So $\frac{2}{6}$ is equivalent to $\frac{1}{3}$.

The numerator went from $2$ to $4$, which is multiplying by $2$ since $2 \times 2 = 4$. Multiply the denominator by the same $2$.

$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$

So the missing number is $10$.

Divide the top and bottom by their greatest common factor. The GCF of $3$ and $9$ is $3$.

$\frac{3}{9} = \frac{3 \div 3}{9 \div 3} = \frac{1}{3}$

Since $1$ and $3$ share no factor above $1$, $\frac{1}{3}$ is in lowest terms.

Multiply both numbers by the same $4$.

$\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$

So $\frac{1}{5} = \frac{4}{20}$.

Each equivalent of $\frac{1}{2}$ has a denominator twice its numerator. Check each one.

$\frac{2}{4} = \frac{1}{2}, \quad \frac{3}{6} = \frac{1}{2}, \quad \frac{5}{10} = \frac{1}{2}$

But in $\frac{2}{3}$ the denominator is not twice the numerator, so $\frac{2}{3}$ is not equal to $\frac{1}{2}$.

The numerator went from $3$ to $6$, which is multiplying by $2$ since $3 \times 2 = 6$. Multiply the denominator by the same $2$.

$\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}$

So the missing number is $10$.

Multiply the top and bottom of $\frac{1}{4}$ by the same number. Using $3$:

$\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

So $\frac{3}{12}$ is equivalent to $\frac{1}{4}$.

Divide the top and bottom by their greatest common factor. The GCF of $4$ and $8$ is $4$.

$\frac{4}{8} = \frac{4 \div 4}{8 \div 4} = \frac{1}{2}$

Since $1$ and $2$ share no factor above $1$, $\frac{1}{2}$ is in lowest terms.

Divide the top and bottom by their greatest common factor. The GCF of $6$ and $8$ is $2$.

$\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$

Since $3$ and $4$ share no factor above $1$, $\frac{3}{4}$ is in lowest terms.