Understanding Equivalent Fractions

Have you ever noticed that half a pizza is the same amount of food whether it's cut into $1$ giant slice or $2$ smaller slices? This is the idea behind equivalent fractions!

Equivalent fractions are fractions that look different but show the exact same amount. "Equivalent" simply means "equal in value."

Visualizing Equivalent Fractions

Imagine you have two identical chocolate bars.

• You break the first bar into $2$ equal pieces and eat $1$ piece. You ate $\frac{1}{2}$ of the bar.
• You break the second bar into $4$ equal pieces and eat $2$ pieces. You ate $\frac{2}{4}$ of the bar.

Even though the numbers are different, you ate the exact same amount of chocolate! Therefore, we can write: $\frac{1}{2} = \frac{2}{4}$

The Golden Rule for Equivalent Fractions

To find an equivalent fraction, there is one golden rule to remember: Whatever you do to the top number (numerator), you must do the exact same thing to the bottom number (denominator).

You can find equivalent fractions by either multiplying or dividing.

Using Multiplication

Let's find a fraction equivalent to $\frac{1}{3}$. We can choose any number to multiply by, let's pick $2$:

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

So, $\frac{1}{3}$ and $\frac{2}{6}$ are equivalent fractions.

Using Division

If you have a fraction with larger numbers, like $\frac{2}{4}$, you can divide the top and bottom by the same number. Let's divide both by $2$:

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

Finding the Missing Number

Sometimes you will be asked to fill in a blank, like this: $\frac{2}{3} = \frac{\_\_}{6}$

To solve this, look at the denominators (the bottom numbers). Ask yourself: "How did the $3$ turn into a $6$?" Since $3 \times 2 = 6$, we know the bottom was multiplied by $2$.

Because of our golden rule, we must multiply the top by $2$ as well: $2 \times 2 = 4$

So, the missing number is $4$, making the equivalent fraction $\frac{4}{6}$.