See the idea
Before you start
Find equivalent fractions and add whole numbers. Know that a denominator names a unit: thirds and fifths cannot be counted together until the units match.
Words used in this guide
- Like fractions
- Fractions with the same denominator.
- Least common multiple
- The smallest positive number that is a multiple of both denominators.
- Mixed number
- A whole number together with a proper fraction, such as 1 1/4.
Why the method works
Adding fractions is a measurement problem. You would not add “three metres and two centimetres” by counting five unnamed pieces. Similarly, thirds and quarters must first be expressed with one unit. Changing 1/3 to 4/12 and 1/4 to 3/12 lets you count seven twelfths. The denominator remains 12 because joining the quantities does not change the size of a twelfth.
Keep the denominator when the parts match
1/7 + 3/7 = 4/7. The denominator names the size of the pieces; the numerators count them. Adding the denominators would change the piece size without changing the picture.
Rename unlike parts
For 1/2 + 1/4, rename one half as two quarters. Then 2/4 + 1/4 = 3/4. You can use any common denominator, although the least common denominator often keeps the arithmetic smaller.
Keep exact values until the end
For 1/6 + 1/4, use twelfths: 2/12 + 3/12 = 5/12. As a decimal, this is approximately 0.4167. Writing 1/6 as exactly 0.17 would introduce a rounding error.
Worked examples, step by step
Example 1: Add 2/3 and 1/6.
- Rename 2/3 as 4/6.
- 4/6 + 1/6 = 5/6.
Example 2: Add 3/8 and 7/8.
- The units already match. Add the numerators: 3 + 7 = 10.
- 10/8 = 5/4 = 1 1/4. The answer is greater than one because ten eighths exceed eight eighths.
- Check: 3/8 is almost 1/2 and 7/8 is almost 1, so a total above 1 is reasonable.
Example 3: Add 5/6 and 3/4.
- Multiples of 6 are 6, 12, 18; multiples of 4 are 4, 8, 12. Use denominator 12.
- 5/6 = 10/12 and 3/4 = 9/12. Add to obtain 19/12 = 1 7/12.
- The result exceeds 1 because each starting fraction is greater than 1/2.
Example 4: A walk is 1 2/3 km before a break and 2 1/4 km after it. Find the total.
- Add whole kilometres: 1 + 2 = 3. Add fractional kilometres: 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
- The total is 3 11/12 km.
- Keep the unit km and check that the answer is just under 4 km.
Common mistakes and how to repair them
“1/2 + 1/3 = 2/5.”
The proposed answer is less than 1/2, even though a positive amount was added. Use sixths: 3/6 + 2/6 = 5/6.
“I only change the denominator to make it common.”
Writing 2/3 as 2/12 makes the amount four times smaller. Multiply numerator and denominator by the same factor.
Check your understanding
Choose an answer for each question. You can check again after reading the explanation.
Worked answers
What is 1/3 + 1/6? 1/2. 1/3 = 2/6, so the sum is 3/6 = 1/2.
What is 2/5 + 1/5? 3/5. Count three fifth-sized pieces.
Practise independently
Work these out on paper. Include a diagram or a sentence where the question asks you to explain. Open each solution after making an attempt.
3. Add 2/9 + 5/9.
Show the reasoning
7/9; the unit is ninths throughout.
4. Add 3/10 + 1/5.
Show the reasoning
3/10 + 2/10 = 5/10 = 1/2.
5. Add 7/12 + 5/8.
Show the reasoning
14/24 + 15/24 = 29/24 = 1 5/24.
6. A bottle contains 3/4 litre. You add 2/3 litre. How much is there?
Show the reasoning
9/12 + 8/12 = 17/12 = 1 5/12 litres, assuming the container has enough capacity.
If a method still feels uncertain, revisit the closest worked example, then try a fresh problem. A correct answer copied from a solution tells you less than an explanation you can give independently.
Learn it → Try it → Explain it
Put the idea into play
Build and compare fractions with pictures you can change.
Start with “Same amount” to strengthen fraction equivalence before returning to this guide. Simplifying and operations modes require sign-in.
Try Fraction Visuals →Free guest play has question, level and time limits. Sign in to continue or save progress. A game score is not a mastery assessment.
Questions students and parents ask
Do I simplify before or after adding?
Either can help. Simplifying first can reduce the denominator sizes; simplify the final answer when requested.
Does multiplying denominators always work?
For positive denominators, their product is a common denominator. It may be larger than necessary.
What if the total is more than one?
That is valid. Leave an improper fraction or convert it to a mixed number according to the question.
Help at home: Name the unit out loud
Use equal paper strips for one half and one quarter. Split the half into quarters and ask, “How many quarter-sized pieces altogether?”
If your child adds denominators, ask whether their result is larger than each positive addend. A quick estimate often exposes the mistake before a full calculation.
Give 1/3 + 1/6 next. Ask for a drawing, an equation and one sentence connecting the two.
Keep the conversation focused on the reasoning you can hear or see. One short activity cannot establish lasting mastery or diagnose a learning difficulty.
Why does my child add the denominators?
A child who writes 1/5 + 2/5 = 3/10 may be applying a familiar whole-number rule to both numbers. Draw one strip divided into fifths. Mark one fifth, then two different fifths. Three fifths are marked; the size of each piece has not changed. The result is 3/5.
Say the units aloud: “one fifth plus two fifths is three fifths.” For 1/2 + 1/4, first rename the half as two quarters. Now both quantities count quarters: 2/4 + 1/4 = 3/4. This explains why the denominator stays the same after the pieces match.
Ask for 2/7 + 3/7 with a drawing. Only move to unlike denominators when your child can explain the like-denominator example. If school has not introduced unlike denominators, stay with the matching-parts practice.
Helping your child with fractions? Start with this parent guide →
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