A girl in an apron stirring batter next to a honey jar

Multiply Fractions by Whole Numbers

Riya's muffin recipe needs 2/5 cup of honey for each batch. She wants to bake 3 batches. How much honey does she need?

4th Grade Math

Step 1: Look Inside the Fraction

This bar shows the fraction 2/5. Each shaded piece is one fifth. How many pieces of 1/5 are shaded?

2/5 is made of 2 pieces of 1/5. The numerator counts the pieces. So 2/5 = 2 × 1/5.

Step 2: Count the Fifths in 3 Batches

Each bar is one batch. Each batch has 2 shaded fifths. How many shaded fifths are there in all 3 bars?

3 groups of 2 fifths is 3 × 2 = 6 fifths. That means 3 × (2/5) is the same as 6 × (1/5).

Step 3: Write the Product

3 × 2/5 = ?

We counted 6 fifths in all. Write that amount as a single fraction.

6 fifths = 6/5. The product is 6/5, which is more than 1 whole cup! Riya needs 6/5 cups of honey.

Let's Remember

          The Multiplying Rule
        
          Step 1: Multiply the whole number by the
          numerator.

          Step 2: Keep the
          denominator the same.

          n × a/b = (n × a)/b

Do you see the pattern? A multiple of 2/5 is just a multiple of 1/5, counted in groups of 2.

Watch Out!

          A Common Mistake
        
          Some kids write 3 × 2/5 = 6/15. That is wrong!

          They multiplied the denominator too.

Riya says: The denominator only names the size of each piece. Fifths stay fifths, no matter how many you count. Only the top number grows!

Solve It!

5 × 1/4 = ?

Multiply the numerator: 5 × 1 = 5. Keep the denominator: fourths stay fourths. So 5 × 1/4 = 5/4.

Read the Model

Each bar shows 3/8. There are 2 bars. What is 2 × 3/8?

Count the shaded eighths: 3 + 3 = 6. 2 × 3/8 = (2 × 3)/8 = 6/8.

Word Problem

Marco feeds his 4 dogs every morning. Each dog gets 2/3 cup of food. How many cups does Marco scoop in all?

4 × 2/3 = (4 × 2)/3 = 8/3 cups. The thirds stay thirds. That is more than 2 whole cups!

What Goes in the Blank?

? × 3/10 = 12/10

Which whole-number factor makes this equation true?

Think: ? × 3 = 12 on top. Since 4 × 3 = 12, the missing factor is 4. Check: 4 × 3/10 = 12/10.

Jump the Number Line

0

1/3

2/3

3/3

4/3

5/3

6/3

Start at 0. Make 5 jumps of 1/3 each. Where do you land?

5 jumps of 1/3 is 5 × 1/3 = 5/3. Count the ticks: 1/3, 2/3, 3/3, 4/3, 5/3. The thirds never change size.

Challenge!

Jade runs 3/4 mile every day for 6 days. How many miles does she run in all? Write your answer as a mixed number.

Step 1: 6 × 3/4 = 18/4. Step 2: 18/4 = 16/4 + 2/4 = 4 wholes and 2/4. Since 2/4 = 1/2, the answer is 4 1/2 miles.

When might you multiply a fraction by a whole number in real life? Think about recipes, running, or sharing snacks. Why does the denominator stay the same every time?

Great Work!

0/9

correct

fraction numerator denominator product multiple pattern