A girl and her grandfather smiling at a pizza dinner

Fractions Are Made of Unit Pieces

Marisol takes 5 slices at a pizza party. Each slice is 1/4 of a whole pizza. How much pizza did she take?

4th Grade Math

Step 1: Find the Unit Piece

Each pizza is cut into 4 equal parts. Look at the one shaded part. What fraction of the whole is one slice?

One slice out of 4 equal parts is 1/4. A fraction with a numerator of 1 is called a unit fraction. It is our building block!

Step 2: Count the Copies

Marisol takes 5 slices. Count the shaded parts across both bars. How many fourths did she take in all?

Count them: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5 fourths. That is the fraction 5/4. It is 5 copies of the unit piece 1/4.

Step 3: Write It as a Product

5 copies of 1/4 can be written as multiplication. What number fills the blank?

5/4 = ? × (1/4)

5/4 = 5 × (1/4). The product of 5 and 1/4 is 5/4, because 5/4 is a multiple of 1/4.

Let's Remember

          Every Fraction Is Built From Unit Fractions
        
          The numerator
          tells you how many copies.

          The denominator
          tells you the size of each piece.

          So a/b = a × (1/b). Example: 5/4 = 5 × (1/4).

Marisol A fraction is like a stack of matching blocks. 5/4 is just five 1/4 blocks stacked together!

Watch Out!

          A Common Mistake
        
          Some students write 5 × (1/4) = 5/20. That is wrong!

          Only the numerator counts the copies: 5 × (1/4) = 5/4.

          The denominator names the piece size. It does not change.

Five quarter-slices are still quarter-slices. The pieces do not shrink just because you have more of them.

Jump the Number Line

0

1/4

2/4

3/4

4/4

5/4

6/4

Start at 0. Take 3 jumps of 1/4 each. Where do you land?

3 jumps of 1/4 land on 3/4, so 3 × (1/4) = 3/4. The jumps count fourths; the piece size stays the same.

Solve It!

7/10 = ? × (1/10)

7/10 = 7 × (1/10). The numerator 7 tells how many copies of the unit fraction 1/10 you need.

Word Problem

Deshawn fills a 1/3-cup scoop with water. He pours it into a bowl 4 times. How much water is in the bowl?

4 × (1/3) = 4/3 cups. Four copies of 1/3 make 4 thirds. The pieces are still thirds, so the denominator stays 3.

Match the Model

Which equation matches this fraction model?

The bar shows 3 shaded eighths, so 3/8 = 3 × (1/8). Three copies of the unit piece 1/8 are shaded.

What Goes in the Blank?

6 × (1/5) = ?

6 × (1/5) = 6/5. Six copies of 1/5 make 6 fifths. The denominator 5 stays the same because the pieces are still fifths.

Challenge!

A recipe needs 1/8 teaspoon of salt per batch. Ava bakes 11 batches. How much salt does she use, and is it more than 1 whole teaspoon?

11 × (1/8) = 11/8. Since 8/8 makes 1 whole teaspoon, 11/8 is 3 eighths more than 1 whole.

Compare and contrast: How is 5 × (1/4) like 5 × 4? How is it different? Explain your thinking to someone near you.

Great Work!

0/8

correct

fraction numerator denominator multiple product