Adding and Subtracting Fractions
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Adding and Subtracting Fractions
When you add or subtract fractions, the pieces being combined must be the same size. That means they need the same denominator before you can add or subtract the numerators.
Same denominator? Just add or subtract the numerators.
If two fractions already have the same denominator, keep the denominator the same and add or subtract the numerators. For example, 4/9 + 2/9 = 6/9, because you now have 6 ninths altogether. The denominator never gets added or subtracted — it just tells you the size of the pieces.
Related denominators? Rename one fraction first.
Denominators are "related" when one is a multiple of the other, like 3 and 6, or 4 and 8. Rename the fraction with the smaller denominator so both fractions have the same denominator. For example, to work out 1/3 + 1/6, rename 1/3 as 2/6. Now you can add: 2/6 + 1/6 = 3/6, which simplifies to 1/2.
When the answer is more than one whole
Sometimes the numerators add up to more than the denominator. When this happens, convert the improper fraction to a mixed numeral. For example, 7/8 + 5/8 = 12/8, and 12/8 = 1 4/8, which simplifies to 1 1/2.
Subtracting from a whole number
To subtract a fraction from a whole number, rename the whole number as a fraction with the same denominator first. For example, 2 = 1 5/5, so 2 − 3/5 = 1 5/5 − 3/5 = 1 2/5.
Worked Example
On a hike, Priya walks 5/6 of a kilometre before morning tea, then walks another 2/3 of a kilometre after morning tea. How far does she walk in total? Give your answer as a mixed numeral in simplest form. Step 1: Check the denominators. 6 and 3 are related, because 3 × 2 = 6. Rewrite 2/3 in sixths. 2/3 = 4/6 Step 2: Add the numerators and keep the denominator. 5/6 + 4/6 = 9/6 Step 3: Convert the improper fraction to a mixed numeral, then simplify. 9/6 = 1 3/6 = 1 1/2 Step 4: State the answer. Priya walks 1 1/2 km in total.
Practice
3/8 + 2/8 = ?
Flashcards
How do you add or subtract fractions that already have the same denominator?
Keep the denominator the same and add or subtract the numerators only.
What does it mean for two denominators to be 'related'?
One denominator is a multiple of the other, like 3 and 6, or 4 and 8.
How do you add or subtract fractions with related denominators?
Rename the fraction with the smaller denominator so both fractions have the same denominator, then add or subtract the numerators.
What should you do if the numerators add up to more than the denominator?
Convert the improper fraction into a mixed numeral, for example 12/8 = 1 4/8 = 1 1/2.
How do you subtract a fraction from a whole number?
Rename the whole number as a fraction with the same denominator first, then subtract the numerators.
Why can't you just add the denominators together?
The denominator shows the size of the pieces, not a quantity to combine — only the numerators are added or subtracted once the pieces are the same size.
All 15 practice questions
3/8 + 2/8 = ?
- 5/16
- 1/8
- 5/8
- 6/8
Show the answer to question 1
Answer: 5/8
Same denominator, so add the numerators: 3/8 + 2/8 = 5/8, so 5/8.
7/9 − 4/9 = ? Give your answer in simplest form.
- 11/9
- 1/3
- 4/9
- 3/9
Show the answer to question 2
Answer: 1/3
7/9 − 4/9 = 3/9 = 1/3, so 1/3.
1/3 + 1/6 = ? Give your answer in simplest form.
- 1/2
- 2/3
- 3/6
- 2/9
Show the answer to question 3
Answer: 1/2
1/3 = 2/6, so 2/6 + 1/6 = 3/6 = 1/2, so 1/2.
5/6 − 1/3 = ? Give your answer in simplest form.
- 3/6
- 1/2
- 4/3
- 2/3
Show the answer to question 4
Answer: 1/2
1/3 = 2/6, so 5/6 − 2/6 = 3/6 = 1/2, so 1/2.
2 1/5 + 1 2/5 = ?
- 3 3/10
- 4 3/5
- 3 3/5
- 3/5
Show the answer to question 5
Answer: 3 3/5
2 + 1 = 3 wholes, and 1/5 + 2/5 = 3/5, so 3 3/5.
1 3/4 + 2 1/2 = ? Give your answer as a mixed numeral, with the fraction part simplified.
- 3 1/4
- 3 4/6
- 4 1/4
- 3 5/4
Show the answer to question 6
Answer: 4 1/4
3/4 + 2/4 = 5/4 = 1 1/4; add the wholes: 1 + 2 + 1 = 4, so 4 1/4.
3 − 2/5 = ?
- 1 3/5
- 2 2/5
- 2 3/5
- 3 3/5
Show the answer to question 7
Answer: 2 3/5
3 = 2 5/5, so 2 5/5 − 2/5 = 2 3/5, so 2 3/5.
A recipe uses 2/5 cup of flour for the base and 1/5 cup for the topping. How much flour in total, in simplest form?
- 3/10
- 3/5
- 2/5
- 1/5
Show the answer to question 8
Answer: 3/5
2/5 + 1/5 = 3/5, so 3/5 cup of flour in total.
Maya had 3/4 of a pizza. She ate 1/2 of the pizza. How much pizza is left, in simplest form?
- 1/3
- 5/4
- 1/2
- 1/4
Show the answer to question 9
Answer: 1/4
1/2 = 2/4, so 3/4 − 2/4 = 1/4, so 1/4 of the pizza is left.
9/10 − 3/10 = ? Give your answer in simplest form.
- 3/5
- 2/5
- 6/10
- 12/10
Show the answer to question 10
Answer: 3/5
9/10 − 3/10 = 6/10 = 3/5, so 3/5.
3/4 + 5/8 = ? Give your answer as a mixed numeral in simplest form.
- 2/3
- 1 1/8
- 11/8
- 1 3/8
Show the answer to question 11
Answer: 1 3/8
3/4 = 6/8, so 6/8 + 5/8 = 11/8 = 1 3/8, so 1 3/8.
1 1/2 − 3/4 = ? Give your answer in simplest form.
- 3/2
- 3/4
- 1/4
- 1 1/4
Show the answer to question 12
Answer: 3/4
1 1/2 = 6/4, so 6/4 − 3/4 = 3/4, so 3/4.
Tom jogged 5/6 km on Monday and 1/6 km on Tuesday. How far did he jog in total, in simplest form?
- 1/2
- 2/3
- 1
- 6/6
Show the answer to question 13
Answer: 1
5/6 + 1/6 = 6/6 = 1, so Tom jogged 1 km in total.
Which pair of denominators are 'related', meaning one is a multiple of the other?
- 3 and 5
- 6 and 7
- 4 and 8
- 2 and 9
Show the answer to question 14
Answer: 4 and 8
8 is a multiple of 4 (4 × 2 = 8), so 4 and 8 are related denominators.
A ribbon is 7/9 m long. Zara cuts off 5/9 m to use for a bow. How much ribbon is left, in simplest form?
- 2/9
- 12/9
- 5/9
- 3/9
Show the answer to question 15
Answer: 2/9
7/9 − 5/9 = 2/9, so 2/9 m of ribbon is left.
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