   SEARCH HOME Math Central Quandaries & Queries  Question from bradley, a student: 1) Perform the indicated operation on the mixed numbers below; write answer in simplest form: 8 1/3 – 2 ¼ 2) Perform the indicated operations on the mixed numbers below; write answer in simplest form; note;: "•" denotes multiplication: 2 1/2 • 3 2/3 • 5 3 1. When adding and subtracting quantities involving fractions, the easiest thing to do is this: Convert all mixed numbers to improper fractions. For example, 2 &frac34; equals (2x4 + 3) / 4 = 11/4. Then make the two fractions you are adding or subtracting have a common denominator. For example           11/4 - 4/3 = (11x3)/(4x3) - (4x4)/(3x4) = 33/12 - 16/12.
Then subtract the numerators, leaving the common denominator alone:
33/12 - 16/12 = (33-16) / 12 = 17/12.
Next, convert it back to a mixed number if the numerator is larger than the denominator:
17/12 = (1x12 + 5) / 12 = 1 5/12.
Last, put the fraction part in lowest terms. For example, 6/8 would reduce to 3/4.

2. When multiplying mixed numbers, you again start by converting each mixed number to an improper fraction. Then you multiply the numerators and you multiply the denominators (no need to worry about making a common denominator; this is why multiplying fractions is easier than adding them). For example:
21/2 x 5/7 = 105/14.
Then convert to a mixed fraction again:
105/14 = (7x14 + 7)/14 = 7 7/14.
Then put the fraction in lowest terms (reduce it).
7 7/14 = 7 ½.
When multiplying three numbers together, just do it step by step, but you can save yourself time if you leave things in improper fraction form until you have finished all your multiplications.

Cheers,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.