What are the steps in adding dissimilar fractions?

Answer 1

1. Convert the fractions to equivalent fractions all with the same denominator
2. 1. Find a common denominator; ideally this should be the Lowest Common Denominator (LCD) but if you cannot find this, just multiplying all the denominators together will work.
   2. Divide the common denominator by the denominator of each fraction (this will be a whole number) and multiply the numerator of the fraction by this result.
3. Add the numerators
4. Simplify the result.

Example: 2/5 + 3/8 + 1/2

LCD of 5, 8, 2 is 40 so:

40 ÷ 5 = 8 → 2/5 = 2x8/5x8 = 16/40

40 ÷ 8 = 5 → 3/8 = 3x5/8x5 = 15/40

40 ÷ 2 = 20 → 1/2 = 1x20/2x20 = 20/40

→ 2/5 + 3/8 + 1/2 = 16/40 + 15/40 + 20/40

= 16+15+20/40

= 51/40

= 111/40

By multiplying the denominators together this gives 5 x 8 x 2 = 80, so:

80 ÷ 5 = 16 → 2/5 = 2x16/5x16 = 32/80

80 ÷ 8 = 10 → 3/8 = 3x10/8x10 = 30/80

80 ÷ 2 = 40 → 1/2 = 1x40/2x40 = 40/80

→ 2/5 + 3/8 + 1/2 = 32/80 + 30/80 + 40/80

= 32+30+40/80

= 102/80

= 51x2/40x2

= 111/40

Using the LCD keeps the numbers smaller.