Equivalent Fractions

🍕 Equivalent Fractions

What Are Equivalent Fractions?

Equivalent fractions are fractions that look different but have the same value. They name the same amount of a whole, just cut into a different number of pieces.

Imagine a pizza:

• Cut it into 2 big slices and take 1 slice → you ate $\frac{1}{2}$.
• Cut the same pizza into 4 slices and take 2 slices → you ate $\frac{2}{4}$.

You ate exactly the same amount of pizza! So:

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

In fact, all of these name one-half:

$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}$

The top number is the numerator (how many pieces you have). The bottom number is the denominator (how many equal pieces the whole is cut into).

✖️ How to Make an Equivalent Fraction

The big secret: multiply the numerator AND the denominator by the same number.

Whatever you do to the top, you must do to the bottom. That keeps the value the same.

Worked example: Start with $\frac{2}{3}$ and multiply top and bottom by $2$.

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

✅ Concept Check

📝 Worked Examples: Building Equivalent Fractions

Let's go step by step.

Example 1 — Make $\frac{3}{4}$ into eighths

We want a denominator of $8$. Ask: what times $4$ equals $$? The answer is .

🎯 Guided Practice — Choose the Equivalent Fraction

🔽 Match the Missing Number

Pick the number that makes each pair of fractions equivalent.

🌎 Equivalent Fractions in Real Life

Equivalent fractions show up everywhere!

• Pizza & cake: $\frac{1}{2}$ of a pizza is the same as $\frac{4}{8}$ — just cut into more slices.

📚 Review & Challenge

You learned that equivalent fractions name the same value in different ways.

Two ways to find them