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Fractions course overview
Section 03 · Addition and Subtraction · F08

Adding fractions with like denominators

I can add fractions with the same denominator by combining equal-sized parts.

Builds on: F02 Non-unit fractions and fractions greater than one

Learn

You walk 2/5 of a mile to the park and 2/5 of a mile further to the library. How far did you walk?

When denominators match, the parts are the same size, so you just count how many parts you have altogether.

Add the numerators and keep the denominator: 2/7 + 3/7 = 5/7. The parts are still sevenths.

If the total is more than one whole, you can write it as an improper fraction or a mixed number: 4/5 + 3/5 = 7/5 = 1 2/5.

Simplify the answer when you can: 1/6 + 3/6 = 4/6 = 2/3.

Worked examples

2/7 + 3/7

1/71/71/71/71/71/71/7
  1. Both are sevenths.
  2. 2 sevenths + 3 sevenths = 5 sevenths.
  3. 2/7 + 3/7 = 5/7.

4/5 + 3/5

1/51/51/51/51/51/51/51/51/51/5
  1. 4 + 3 = 7 fifths.
  2. 5 fifths fill one whole, with 2 fifths left.
  3. 7/5 = 1 2/5.

Explore

Start at 2/5 and press the numerator + button twice more. You are adding 2/5 one fifth at a time — the denominator never changes.

1/51/51/51/51/5
Fraction bar showing 2 fifths: 1 whole bar, each split into 5 equal parts, with 2 shaded.
Numerator2
Denominator5

Guided practice

Use the hints as much as you like. You can try each question as many times as you need.

0 of 2 solved

1

2/7 + 3/7 = ?

Type a fraction with a slash, a mixed number with a space, or a whole number.
2

3/8 + 5/8 = ?

Type a fraction with a slash, a mixed number with a space, or a whole number.

Independent practice

Answers are checked exactly — equivalent fractions count unless a question asks for a particular form.

0 of 4 solved

1

4/5 + 3/5 = ? (any equivalent form)

Type a fraction with a slash, a mixed number with a space, or a whole number.
2

1/6 + 3/6 in simplest form.

Type a fraction with a slash, a mixed number with a space, or a whole number.
3

Sam ate 2/9 of a pie and Lea ate 5/9. How much did they eat together?

Type a fraction with a slash, a mixed number with a space, or a whole number.
4

1 1/4 + 2/4 = ? Write it as a mixed number.

Type a fraction with a slash, a mixed number with a space, or a whole number.

Common mistakes

Adding the denominators: 2/7 + 3/7 = 5/14.

Why it happens: The size of each part does not change when you combine them.

What to do: Say the unit out loud: “2 sevenths plus 3 sevenths is 5 sevenths”.

Leaving 7/5 without noticing it is more than a whole.

Why it happens: An improper fraction is correct, but a mixed number can show the size more clearly.

What to do: Check whether the numerator is at least the denominator.

Lesson check

Three practice questions to check your understanding. Hints and retries are allowed, so this counts as practice — not mastery.

0 of 3 solved

1

5/12 + 4/12 in simplest form.

Type a fraction with a slash, a mixed number with a space, or a whole number.
2

3/10 + 6/10 = ?

Type a fraction with a slash, a mixed number with a space, or a whole number.
3

5/6 + 5/6 = ? (any form)

Type a fraction with a slash, a mixed number with a space, or a whole number.

Show mastery on your own

Ready? Answer 4 new questions with no hints and one try each. This is the only way a lesson is marked as mastered.

Start mastery check
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