How to add, subtract, multiply and divide fractions
Here it is with your numbers:
- Make the bottom numbers the same. The smallest number that both 3 and 4 go into is 12, so 2/3 becomes 8/12 and 5/4 becomes 15/12.
- Add the top numbers: 8 + 15 = 23, so the answer is 23/12.
- 23/12 can't be simplified any further.
- Write it as a mixed number: 23/12 is 1 11/12.
It means 2/3 + 5/4 is 23/12, which is 1 11/12, or 1.9167 as a decimal. The decimal never ends, so it is rounded to 4 decimal places.
Every answer is simplified, and written as a mixed number when it is bigger than 1. Dividing is the same as multiplying by the flipped fraction, and a fraction is also a division: 3/4 means 3 ÷ 4.
Source Common Core State Standards · Grade 5, add and subtract fractions (5.NF.A.1) ↗Common Core State Standards · Grade 5, multiply fractions (5.NF.B.4.a) ↗Common Core State Standards · Grade 6, divide fractions by fractions (6.NS.A.1) ↗Common Core State Standards · Grade 5, a fraction is a division (5.NF.B.3) ↗
Common fractions as decimals and percents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.3333 | 33.33% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.6667 | 66.67% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
A decimal that never ends is rounded to 4 places, and the percent is worked out from that decimal, so the two always agree.
Fraction examples
Source Common Core State Standards · Grade 5, divide by a unit fraction (5.NF.B.7.b) ↗
FAQs
How do you multiply fractions?
Multiply the top numbers together and the bottom numbers together. For example, 2/3 × 4/5 is (2 × 4) over (3 × 5), which is 8/15. Simplify the answer if you can.
Source Common Core State Standards · Grade 5, multiply fractions (5.NF.B.4.a) ↗
How do you divide fractions?
Flip the second fraction and multiply. In general, a/b ÷ c/d = ad/bc, so 2/3 ÷ 3/4 is (2 × 4) over (3 × 3), which is 8/9. Dividing by a whole number works the same way: 4 ÷ 1/5 is 20.
Source Common Core State Standards · Grade 6, divide fractions by fractions (6.NS.A.1) ↗
How do you add fractions?
Give both fractions the same bottom number, then add the top numbers. For 2/3 + 5/4, use 12 on the bottom: 8/12 + 15/12 is 23/12, which is 1 11/12.
Source Common Core State Standards · Grade 5, add and subtract fractions (5.NF.A.1) ↗
How do you simplify fractions?
Find the biggest number that goes into both the top and the bottom and divide each by it. 18/24 divides by 6 and becomes 3/4. The value stays the same; only the numbers get smaller.
Source Common Core State Standards · Grade 5, equivalent fractions (5.NF.B.5.b) ↗
How do you subtract fractions?
Do the same as for adding: make the bottom numbers match, then subtract the top numbers. For 3/4 − 1/2, use 4 on the bottom: 3/4 − 2/4 is 1/4.
Source Common Core State Standards · Grade 5, add and subtract fractions (5.NF.A.1) ↗
Sources
- Common Core State Standards: Grade 5, add and subtract fractions (5.NF.A.1)
- Common Core State Standards: Grade 5, multiply fractions (5.NF.B.4.a)
- Common Core State Standards: Grade 6, divide fractions by fractions (6.NS.A.1)
- Common Core State Standards: Grade 5, equivalent fractions (5.NF.B.5.b)