Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Aug 29, 2023

Find the sum of $\frac{1}{2}, \frac{2}{3}, \frac{1}{6}$ , simplify the answer, and express it as a mixed number.

STEP 1

Assumptions1. We are adding three fractions $\frac{1}{}$ , $\frac{}{3}$ , and $\frac{1}{6}$ . . The result should be simplified and written as a mixed number.

STEP 2

To add fractions, we need to have a common denominator. The least common multiple (LCM) of2,, and6 is6.

STEP 3

Convert each fraction to an equivalent fraction with denominator6.
$\frac{1}{2} = \frac{1 \times3}{2 \times3} = \frac{3}{6}$ $\frac{2}{3} = \frac{2 \times2}{3 \times2} = \frac{}{6}$ $\frac{1}{6} = \frac{1 \times1}{6 \times1} = \frac{1}{6}$

STEP 4

Now, add the fractions.
$\frac{3}{6} + \frac{4}{6} + \frac{1}{6} = \frac{3+4+1}{6} = \frac{8}{6}$

STEP 5

implify the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is2.
$\frac{8}{} = \frac{8 \div2}{ \div2} = \frac{4}{3}$

STEP 6

Write the fraction as a mixed number. $\frac{4}{3} =1 \frac{1}{3}$ The sum of $\frac{1}{2}$ , $\frac{2}{3}$ , and $\frac{1}{6}$ is $1 \frac{1}{3}$ .

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