Operations with Mixed Numbers

A mixed number is a number such as $\mathbf{3}\frac{\mathbf{1}}{\mathbf{2}}$ that consists of an integer followed by a fraction. It is an abbreviation for the sum of the integer and the fraction; so, $\mathbf{3}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{=}\mathbf{3}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}$.

TACTIC B3 To do arithmetic with mixed numbers, just enter them into your calculator as sums written in parentheses.

EXAMPLE 9: How you evaluate $1\frac{2}{3}\times 3\frac{1}{4}$ depends on your calculator. If you use a scientific calculator with a fraction button, you can enter $\left(1+\frac{2}{3}\right)\left(3+\frac{1}{4}\right)$. If you use a graphing calculator, you would probably enter it as (1 + 2 ÷ 3)(3 + 1 ÷ 4). Either way, you should get $\frac{65}{12}$ or $5\frac{5}{12}$ or $5.41\overline{6666}$, which you can convert to the fraction $\frac{65}{12}$.