Q&A for How to Add and Subtract Fractions

Think of adding or subtracting fractions as a bit like adding or subtracting apples and oranges. You can't add 1 apple to 2 oranges unless you call each of them "pieces of fruit." Then if you added them, you'd have 3 pieces of fruit. Similarly you can't add 1/4 to 1/3 unless you re-name each fraction such that they have the same denominator: 1/4 becomes 3/12, and 1/3 becomes 4/12. Adding them together simply involves adding the numerators to get 7/12. Subtracting is similar, except you subtract one numerator from the other.

First reduce fractions. The only one that will reduce is 8/12, reducing to 2/3. Next find the lowest (or least) common denominator: the LCD is 9 x 6 = 54. Then 7/9 = 42/54, 1/6 = 9/54, and 2/3 = 36/54. So 42/54 - 9/54 + 36/54 = 69/54 = 1 15/54.

Convert 5½ to 11/2 and then to 33/6. Convert 2 2/3 to 8/3 and then to 16/6. 33/6 - 16/6 = 17/6 = 2 5/6.

Change 12/3 to 24/6. 21/6 + 24/6 = 45/6 = 7 3/6 = 7½.

2 + (-¾) = 2 - ¾. 2 is the same as 8/4. 8/4 - 3/4 = 5/4 = 1¼.

First, get the LCD. The LCD of 3 and 6 is 6 why? Because 6 is a multiple of 3 and 6 is a multiple of 6. Next, To get its numerator. Whatever you multiplied with 6 to get the LCD, you also multiply it with the numerator. So it is like this, we multiplied 6 with 1 so, we multiply 1 with the number 21. 21 x 1 is 21 and for 3, we multiplied it with 2 because 2 x 3 is 6 so it is like this, 12 x 2 is 24. So, our answer is 24/6 and we should also convert that into a Mixed Number. Then, simplify if needed.

First, convert both fractions so that they have the same denominator (bottom number): 7/2 = 14/4. Then, subtract the second numerator (top number) from the first numerator: 14 - 5 = 9. This gives the solution of 9/4.

First, convert 2 4/18 to an improper fraction: 2 4/18 = ((2*18)+4)/18 = 40/18. Then add 6 to 40, giving an answer of 46. Therefore, 2 4/18 + 6/18 = 46/18. This can be simplified further 46/18 -> 23/9 or converted back into a mixed number 2 10/18, which simplifies to 2 5/9.

Whilst 9 and 6 are both factors of 18, 12 is not a factor of 18, therefore the common denominator cannot be 18. To find the common denominator, you need to find the smallest integer which all of the denominators given in the question multiply to (known as the Lowest Common Multiple [LCM] or Lowest Common Denominator [LCD]), in this case 9*4 = 36, 6*6 = 36, 12*3=36, therefore the LCD is 36.

First change the mixed numbers to improper fractions: 11/2 + 10/7 - 19/7. Now find the common denominator: (2)(7) = 14. Now change the expression so that all of the denominators are 14: 77/14 + 20/14 - 38/14. Now add and subtract: 59/14 = 4 3/14.

(8)(2) / 3 = 16/3 = 5 1/3.