How to add, subtract, multiply & divide fractions?
Answer
When adding or subtracting fractions:
The number on the top of the fraction is the numerator. The number on the bottom of the fraction is the denominator.
The fractions must have a common denominator. If each one does, add or subtract the numerators and reduce the result if necessary. Examples:
- 1/8 + 2/8 = 3/8
- 4/9 - 1/9 = 3/9 =1/3
- 1/6 + 7/6 = 8/6 = 4/3
- 6/7 - 2/7 = 4/7
If the fractions have different denominators, you may use prime factorization to find the Least Common Denominator. Example: 4/9 + 7/12 = ?
Break each number down to its prime factors (9 = 3 x 3 and 12 = 4 x 3 = 2 x 2 x 3). A prime number can only be divided by one and itself. Your LCD is 36 (36 = 2 x 2 x 3 x 3). You notice we did not use all the 3’s. It was not necessary, because 9 and 12 both fit into 36. Using the LCD, your problem will be 16/36 + 21/36 = 37/36. You notice the numerators changed to fit the new denominator. The denominator, 9, must be multiplied by 4 to become 36, so the numerator was also multiplied by 4. If the problem was 7/12 - 4/9, use the same rule and find an LCD. Your problem would be: 21/36 - 16/36 = 5/36. Always check for reductions to the answer.
When multiplying or dividing fractions, a common denominator is not necessary.
Prior to multiplying, do any reductions you can. This will make the answer easier to deal with. Just multiply the numerators and the denominators straight across as you see them. Examples:
- 2/3 x 5/7= 10/21
- 3/8 x 4/3 =1/2 (reduce across the diagonals)
If you are dividing fractions, you must invert and multiply by the second fraction in the problem. This means flipping the second fraction upside down and changing the division symbol to a multiplication symbol.
- 4/9 div. by 3/8 (the new problem will be 4/9 x 8/3 = 32/27). Check for reductions in the answer you may have missed.