Get the answer to "Evaluate each expression. Express your answer as a..."

defazajx

Answered question

2021-10-29

Evaluate each expression. Express your answer as a fraction in lowest terms.
a)

\frac{5}{6} + \frac{2}{3}

\frac{5}{6} - \frac{2}{3}

\frac{7}{10} - \frac{11}{15}

\frac{7}{10} + \frac{11}{15}

Answer & Explanation

stuth1

Skilled2021-10-30Added 97 answers

Step 1
a) The lowest common multiple of 6 and 3 is 6.
$\frac{5}{6} + \frac{2}{3} = \frac{5 \times 1}{6 \times 1} + \frac{2 \times 2}{3 \times 2}$
$= \frac{5}{6} + \frac{4}{6}$
$= \frac{9}{6}$
$= \frac{3 \times 3}{2 \times 3}$
$= \frac{3}{2}$
Therefore, the resultant fraction is $\frac{3}{2}$
Step 2
b) The lowest common multiple of 6 and 3 is 6.
$\frac{5}{6} - \frac{2}{3} = \frac{5 \times 1}{6 \times 1} - \frac{2 \times 2}{3 \times 2}$
$= \frac{5}{6} - \frac{4}{6}$
$= \frac{5 - 4}{6}$
$= \frac{1}{6}$
Therefore, the resultant fraction is $\frac{1}{6}$
Step 3
c) The lowest common multiple of 10 and 15 is 30.
$\frac{7}{10} - \frac{11}{15} = \frac{7 \times 3}{10 \times 3} - \frac{11 \times 2}{15 \times 2}$
$= \frac{21}{30} - \frac{22}{30}$
$= \frac{21 - 21}{30}$
$= - \frac{1}{30}$
Therefore, the resultant fraction is $- \frac{1}{30}$
Step 4
d) The lowest common multiple of 10 and 15 is 30.
$\frac{7}{10} + \frac{11}{15} = \frac{7 \times 3}{10 \times 3} + \frac{11 \times 2}{15 \times 2}$
$= \frac{21}{30} + \frac{22}{30}$
$= \frac{21 + 22}{30}$
$= \frac{43}{30}$
Therefore, the resultant fraction is $\frac{43}{30}$

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