Finding Equivalent Fractions

Equivalent fractions are fractions that look different because they have different numbers, but they actually represent the exact same value or amount. Imagine a pizza. If you cut it into 2 big slices and eat 1, you ate $\frac{1}{2}$ of the pizza. If your friend cuts an identical pizza into 4 smaller slices and eats 2, they ate $\frac{2}{4}$. Even though your friend has more pieces, the total amount of pizza eaten is identical! We use visual models like fraction strips or circles to prove that these areas are the same size.

You don't always need to draw a picture to find equivalent fractions. You can use the Multiplication Rule. To find a fraction equivalent to another, multiply the numerator (the top number) and the denominator (the bottom number) by the same whole number. This works because multiplying the top and bottom by the same number is like multiplying the fraction by 1. For example, multiplying by $\frac{2}{2}$ is the same as multiplying by 1, which doesn't change the value, only the way it looks!

Sometimes you will see two fractions that are equal, but one number is missing. To solve this, look at the numbers you do have. Ask yourself: 'What did I multiply the first number by to get the second number?' Once you find that 'secret multiplier,' use it on the other part of the fraction to find the missing value. This keeps the fraction in balance.