A fraction calculator that shows the working.
1/2 + 1/3 is 5/6 (about 0.8333 as a decimal)
1/2 plus 1/3.
The working
- Find the lowest common denominator (LCD): the smallest number that 2 and 3 both divide intoLCD of 2 and 3= 6
- Multiply the top and bottom by 3, so the bottom is 61 × 3/2 × 3= 3/6
- Multiply the top and bottom by 2, so the bottom is 61 × 2/3 × 2= 2/6
- Add the tops and keep the bottom3/6 + 2/6= 5/6
1/2 + 1/3 is 5/6 (about 0.8333 as a decimal)
Type two fractions and the answer appears with every step of the working, so you can check it by hand. Fill in the whole-number box for a mixed number, or use it alone for a whole number. It all happens in your browser; nothing you type is sent anywhere.
How do you add or subtract fractions?
Rewrite both fractions over the lowest common denominator, then add or subtract the tops and keep the bottom. Fractions can only be added or subtracted when their bottoms (denominators) match. The lowest common denominator is the smallest number both bottoms divide into, and a fraction is rewritten over it by multiplying its top and bottom by the same number.
For 1/2 + 1/3, the lowest common denominator of 2 and 3 is 6. 1/2 = 3/6 and 1/3 = 2/6, so 3/6 + 2/6 = 5/6.
Subtracting works the same way, and the answer is negative when the second fraction is the bigger one. For 1/3 − 1/2: 2/6 − 3/6 = −1/6.
How do you multiply fractions?
Multiply the tops together and the bottoms together, then simplify. For 2/3 × 3/4: 2 × 3 = 6 on top and 3 × 4 = 12 on the bottom gives 6/12, which simplifies to 1/2.
How do you divide fractions?
Flip the second fraction and multiply. For 1/2 ÷ 3/4, flip 3/4 to 4/3: 1/2 × 4/3 = 4/6, which simplifies to 2/3.
How do you simplify a fraction?
Divide the top and bottom by the largest number that goes into both. For 6/12 that number is 6, giving 1/2. A top-heavy answer is then written as a mixed number: 13/6 is 2 1/6, because 6 goes into 13 twice with 1 left over.
How do you work with mixed numbers?
A mixed number is turned into a top-heavy fraction first: multiply the whole number by the bottom and add the top. 1 1/2 becomes 3/2, because 1 × 2 + 1 = 3.