Generating Equivalent Fractions

Equivalent fractions are fractions that look different but represent the exact same value. For example, half of a pizza is the same whether you cut it into $2$ pieces ($\frac{1}{2}$) or $4$ pieces ($\frac{2}{4}$).

How to Make Equivalent Fractions

To create an equivalent fraction, you can multiply both the numerator (the top number) and the denominator (the bottom number) by the same nonzero number.

Let's find three equivalent fractions for $\frac{2}{5}$:

• Multiply by $2$: $\frac{2 \times 2}{5 \times 2} = \frac{4}{10}$
• Multiply by $3$: $\frac{2 \times 3}{5 \times 3} = \frac{6}{15}$
• Multiply by $4$: $\frac{2 \times 4}{5 \times 4} = \frac{8}{20}$

So, $\frac{2}{5} = \frac{4}{10} = \frac{6}{15} = \frac{8}{20}$.

Finding Missing Numbers

Sometimes you need to find a missing number to make two fractions equivalent, like this: $\frac{3}{4} = \frac{?}{20}$

1. Look at the denominators: How do you get from $4$ to $20$? You multiply by $5$ because $4 \times 5 = 20$.
2. Do the exact same thing to the numerator: Multiply $3$ by $5$. $3 \times 5 = 15$

So, the missing number is $15$, making the equivalent fraction $\frac{15}{20}$.

Simplifying Fractions (Lowest Terms)

You can also make equivalent fractions by dividing. When you divide the top and bottom by the same number to make the fraction as simple as possible, it is called writing the fraction in its lowest terms.

Let's simplify $\frac{8}{12}$:

1. Find a number that divides evenly into both $8$ and $12$. Both can be divided by $4$.
2. Divide the numerator and the denominator by $4$: $\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

Since $2$ and $3$ cannot be divided evenly by any other number besides $1$, $\frac{2}{3}$ is in its lowest terms!