B. Number · Operations: Numbers to 100 000, Decimals, Fractions, Ratios and Rates

Adding and Subtracting Fractions with Like Denominators

B2.5 A1About 40 minutes

Learning goals

I can add fractions that have the same denominator.
I can subtract fractions that have the same denominator, including from 1 whole.
I can show adding and subtracting fractions with fraction strips, drawings and number lines.
I can write an answer greater than 1 as a mixed number.

Words to know

numerator
The top number in a fraction. It tells how many parts we have.

denominator
The bottom number in a fraction. It tells how many equal parts make one whole, so it tells the size of the parts.

like denominators
Fractions with the same denominator, like 3/8 and 4/8.

improper fraction
A fraction where the numerator is bigger than or equal to the denominator, like 7/4.

mixed number
A whole number and a fraction together, like 1 3/4.

Remember from Grade 4

In Grade 4 you added unit fractions over and over, like 1/4 + 1/4 + 1/4 = 3 × 1/4 = 3/4, and wrote answers greater than 1 as mixed numbers. In Grade 5 you'll add and subtract any fractions that have the same denominator, like 2/8 + 3/8.

Let's start with pizza

A pizza is cut into 8 equal slices. Ana eats 2 slices and Ben eats 3 slices. What fraction of the pizza did they eat together?

Each slice is 1/8 of the pizza. Ana ate 2/8 and Ben ate 3/8.

2 eighths + 3 eighths = 5 eighths. So 2/8 + 3/8 = 5/8.

A strip cut into 8 equal parts. 2 parts are green (Ana's 2/8) and 3 parts are yellow (Ben's 3/8). Together 5 of the 8 parts are shaded: 5/8.

The rule

When the denominators are the same:

Add or subtract the numerators (how many pieces).
Keep the denominator (what size the pieces are).

Why does the denominator stay the same? Because the size of the pieces doesn't change. Two eighths plus three eighths is five eighths, just like 2 apples plus 3 apples is 5 apples.

2/8 + 3/8 is NOT 5/16. Sixteenths are much smaller pieces!

Worked example

Example 1: Subtract

A chocolate bar has 6 equal pieces. 5/6 of the bar is left. Mila eats 2/6. How much is left now?

Same denominator, so subtract the numerators: 5 − 2 = 3.
Keep the denominator: sixths.

5/6 − 2/6 = 3/6 of the bar is left. (That's the same as half the bar!)

A bar of 6 equal pieces. 5 pieces are shaded, and 2 of them are crossed out (eaten). 3 shaded pieces are left: 5/6 − 2/6 = 3/6.

Worked example

Example 2: An answer greater than 1

Solve 3/4 + 3/4.

Same denominator: add the numerators. 3 + 3 = 6. So the sum is 6/4.
4 fourths make 1 whole. 6 fourths is 4 fourths + 2 fourths.
So 6/4 = 1 2/4 (one and two fourths).

3/4 + 3/4 = 6/4 = 1 2/4

A number line in fourths from 0 to 2. Six jumps of 1/4 land on 6/4, which is between 1 and 2. 3/4 + 3/4 = 6/4 = 1 2/4.

Worked example

Example 3: Subtract from 1 whole

Sami has 1 cup of maple syrup for a recipe. He uses 2/5 of a cup. How much is left?

Write 1 whole as fifths: 1 = 5/5.
5/5 − 2/5 = 3/5.

3/5 of a cup is left.

Fraction tips

Check that the denominators are the same before you add or subtract.
Only the numerators change.
To subtract from a whole number, rewrite the whole with the same denominator: 1 = 4/4, 1 = 8/8, 2 = 16/8.
Drawing a strip or number line is a great way to check.

Just for fun

Silly what if: If 2/8 + 3/8 really made 5/16, then every time two friends shared a pizza, the slices would shrink. Keep the denominator, and keep your pizza!

Hands-on activity

Fraction strips and measuring cups

Part 1: Fraction strips. You need: 3 strips of paper the same length, scissors (a grown-up can help) and a pencil.

Fold one strip in half, then in half again, then in half again. Unfold it: 8 equal parts. Label each part 1/8.
Colour 3/8 in one colour and 4/8 in another. What fraction is coloured? (7/8)
Fold another strip into 4 equal parts. Show 3/4 − 1/4.

Part 2: In the kitchen. You need: a 1/4 measuring cup and a bigger measuring cup or bowl, plus water or dry rice. With a grown-up, pour 3/4 cup (three scoops) and then 2/4 cup (two scoops) into a bowl. How many fourths is that? (5/4 = 1 1/4 cups)

Math talk: "Why didn't the pieces get smaller when we added?"

Your turn

1/5 + 2/5 = ?

3/8 + 4/8 = ?

5/6 − 1/6 = ?

9/10 − 4/10 = ?

2/3 + 2/3 = ? Write it as a mixed number too.

1 − 3/4 = ?

Ana ate 2/8 of a pizza and Ben ate 3/8. How much did they eat? How much is left?

More practice: warm-up

1/4 + 1/4 = ?

2/7 + 3/7 = ?

4/5 − 1/5 = ?

6/9 − 6/9 = ?

1/3 + 1/3 + 1/3 = ?

More practice: on your own

7/12 + 4/12 = ?

11/12 − 5/12 = ?

5/8 + 6/8 = ? Write it as a mixed number.

Liam walked 3/10 km in the morning and 6/10 km in the afternoon. How far did he walk?

Jo says 2/5 + 1/5 = 3/10. Explain her mistake.

Challenge

1 3/4 + 3/4 = ?

2 − 5/8 = ?

Find two fractions with denominator 6 that add to 1 whole, where one fraction is 2 sixths bigger than the other.

Check your understanding

Quiz

What is 3/7 + 2/7?

What is 7/9 − 4/9?

What is 1 − 2/6?

What is 3/5 + 4/5?

Why does the denominator stay the same when you add 2/8 + 3/8?

5/8 of a pizza is left. Dad eats 2/8. How much is left now?

For parents and teachers

Big idea: The Grade 5 curriculum (B2.5) asks students to add and subtract fractions with like denominators in various contexts. The key idea is that the denominator names the size of the pieces, so it stays the same; only the number of pieces (the numerator) changes.

Common difficulties:

Adding the denominators (2/8 + 3/8 = 5/16). Ask "Did the slices get smaller?" and draw it.
Subtracting from 1 whole (1 − 3/4). Show that 1 = 4/4 with a folded strip.
Answers greater than 1. 7/5 is correct, and so is 1 2/5; both are fine.

How to help: Use food (pizza, chocolate bars, pies) and measuring cups. Ask questions like "We have 3/4 of a cup of milk and use 1/4. How much is left?" Encourage your child to draw a quick strip to check. Explaining why the denominator stays the same builds the reasoning skills in A1.