Calculator fraction addition
Adding fractions only works once both parts are cut the same way. Enter two fractions above and the answer appears reduced; below is how to do it on paper, and where it usually goes wrong.
12 × 12 = 144
Adding 12 to itself 12 times gives the same answer.
Add the pieces, not the labels
A denominator says how many pieces the whole was cut into, so it is not a quantity to be added. Halves and quarters cannot be combined until both are written in the same size of piece. That is the whole method: make the denominators match, add the numerators, then reduce.
The three steps, worked
Take 2/3 + 1/4.
- Common denominator. 3 and 4 share no factor, so the smallest common denominator is 3 × 4 = 12.
- Rewrite both. 2/3 becomes 8/12 (multiply top and bottom by 4). 1/4 becomes 3/12 (multiply top and bottom by 3).
- Add the numerators. 8 + 3 = 11, so the answer is 11/12. The denominator does not change.
Where the denominators do share a factor, the smallest common denominator is smaller than their product. For 1/6 + 1/4 the product is 24, but 12 works, because 12 is the lowest number both 6 and 4 divide into.
The two mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. A sanity check catches it: 2/5 is less than a half, and the answer must be more than a half because you added something to one.
- Forgetting to reduce. 2/8 is correct but unfinished. Divide both parts by their highest common factor to get 1/4. Our highest common factor page covers finding that number.
Mixed numbers
Add the whole parts separately, add the fractions, then carry. 1½ + 2¾ is 3 whole plus 1/2 + 3/4, which is 3 + 5/4, which is 4¼. Converting to improper fractions first works too and is harder to get wrong under time pressure.
Turning the answer into a decimal or a percentage
Divide the numerator by the denominator: 11/12 is 0.9166…, which rounds to 91.7 per cent. The decimal to percentage page covers the direction of that conversion, including where the decimal point actually moves.