Children at a kitchen table excited about a pizza box

The Pizza Fraction Mystery

Mia and Leo each get the same size pizza. Mia says her share is bigger. Leo disagrees. Who is right?

4th Grade Math

Step 1: Name Mia's Fraction

Mia's pizza bar

Mia's pizza is cut into 2 equal parts. She eats 1 part, shown in blue. What fraction of the pizza did Mia eat?

Mia ate 1/2. The top number is the numerator: 1 part eaten. The bottom number is the denominator: 2 equal parts in all.

Step 2: Compare the Bars

Mia: 1/2

Leo: 2/4

Leo's pizza is cut into 4 parts. He eats 2. Look at the shaded amounts. Who ate more?

The shaded amounts are the same size! 1/2 and 2/4 are equivalent fractions. Leo's parts are smaller, but he has more of them.

The Multiplication Rule

How to Generate Equivalent Fractions

          To generate an equivalent fraction, multiply the top AND the bottom by the same factor.

1/2 × 2/2 = 2/4

Multiplying by 2/2 is like multiplying by 1. The parts get smaller, but you get more of them. The total amount stays exactly the same.

Step 3: Use the Rule

1/2

Sixths

1/2 = ?/6

The denominator changed from 2 to 6. Since 2 × 3 = 6, the factor is 3. What is the missing numerator?

Multiply the numerator by the same factor: 1 × 3 = 3. So 1/2 = 3/6. The bars prove it!

Watch Out!

1/2

1/4 -- NOT the same!

A Common Mistake

          Jade multiplied only the bottom: 1/2 became 1/4. The bars show these are NOT equal. Always multiply the top and bottom by the same factor.

Solve It!

2/3

Ninths

2/3 = ?/9

The factor is 3 because 3 × 3 = 9. Multiply the numerator too: 2 × 3 = 6. So 2/3 = 6/9.

Word Problem

Nadia bakes bread. Her recipe needs 3/4 cup of oats. Her measuring cup only marks eighths. Which fraction of a cup should she measure?

The factor is 2 because 4 × 2 = 8. Then 3 × 2 = 6. So 3/4 = 6/8 cup.

What Goes in the Blank?

2/5

Tenths

2/5 = 4/?

The numerator changed from 2 to 4, so the factor is 2. Multiply the denominator: 5 × 2 = 10. So 2/5 = 4/10.

Find the Factor

3/5 × ?/? = 12/20

These fractions are equivalent. Which factor was used to multiply the top and the bottom?

The factor is 4. Check both parts: 3 × 4 = 12 and 5 × 4 = 20. The same factor must work for top and bottom.

Generate One Yourself

Which fraction is equivalent to 3/7?

Multiply top and bottom by 2: 3 × 2 = 6 and 7 × 2 = 14. So 3/7 = 6/14. Doubling only the top or only the bottom changes the amount.

Challenge!

5/6 of the trail

A hiking trail map splits the trail into 24 equal sections. Sam has hiked 5/6 of the trail. How many sections is that?

5/6 = ?/24

First find the factor: 6 × 4 = 24. Then multiply the numerator: 5 × 4 = 20. So 5/6 = 20/24 sections.

Where could equivalent fractions help you in real life? Think about cooking, measuring, or sharing food fairly.

Great Work!

0/8

correct

equivalent fraction numerator denominator factor generate