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 $2$.

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

So $\frac{2}{3} = \frac{4}{6}$. They are equivalent!

You can multiply by any number. Multiply $\frac{2}{3}$ by $5$:

$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$

Here is a table of fractions all equal to $\frac{2}{3}$:

🔑 Key Idea: Multiplying top and bottom by the same number does NOT change how big the fraction is — only how many pieces you slice it into.

✅ 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 $8$? The answer is $2$.

So multiply BOTH numbers by $2$:

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

Answer: $\frac{3}{4} = \frac{6}{8}$ ✅

Example 2 — Fill in the missing number

$\frac{1}{5} = \frac{?}{20}$

Step 1: What times $5$ equals $20$? That is $4$.

Step 2: Do the same to the top: $1 \times 4 = 4$.

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

Answer: the missing number is $4$.

💡 Trick: Look at the denominators first. Find the number you multiply by, then use the same number on the numerator.

✍️ Your Turn — Fill in the Missing Numbers

Find the missing numerator for each equivalent fraction. Type just the number.

1. $\frac{1}{2} = \frac{?}{6}$

2. $\frac{2}{3} = \frac{?}{12}$

3. $\frac{3}{5} = \frac{?}{10}$

🎯 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.
• Measuring cups: $\frac{1}{2}$ cup of flour equals $\frac{2}{4}$ cup. Same amount!
• Money: $\frac{1}{4}$ of a dollar is one quarter, the same as $\frac{25}{100}$ of a dollar.
• Sharing: If 3 of 4 friends want pizza, that is $\frac{3}{4}$, the same as $\frac{6}{8}$.

🍰 Story: Maya cut her cake into 8 equal pieces and ate 4 of them. She ate $\frac{4}{8}$ of the cake — which is the same as eating $\frac{1}{2}$. She ate exactly half!

✍️ Word Problem Practice

Solve each problem. Type just the number.

1. A recipe needs $\frac{1}{2}$ cup of sugar. Your cup only has fourths marked on it. How many fourths of a cup do you need? Fill in: $\frac{1}{2} = \frac{?}{4}$

2. Leo ate $\frac{2}{3}$ of a chocolate bar that had 9 equal squares. How many squares did he eat? Fill in: $\frac{2}{3} = \frac{?}{9}$

3. A pizza is cut into 8 slices. Mia ate $\frac{1}{2}$ of it. How many slices did she eat? Fill in: $\frac{1}{2} = \frac{?}{8}$

🎯 Word Problem Check

📚 Review & Challenge

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

Two ways to find them

Simplest form

A fraction is in simplest form when the top and bottom share no common factor except 1.

• $\frac{3}{4}$ is in simplest form (nothing but 1 divides both 3 and 4).
• $\frac{6}{8}$ is NOT — both can be divided by 2 to get $\frac{3}{4}$.

🏆 Challenge yourself: Can you simplify $\frac{4}{8}$ all the way down? (Hint: divide top and bottom by 4 → $\frac{1}{2}$.)

🏁 Final Challenge