Question

1. calculate.

(1) $\frac{1}{3}+\frac{1}{6}+\frac{1}{8}$
$=$
(2) $\frac{1}{3}+\frac{1}{6}+\frac{1}{10}$
$=$
(3) $\frac{1}{3}+\frac{1}{7}+\frac{1}{14}$
$=$
(4) $\frac{1}{3}+\frac{1}{8}+\frac{1}{12}$
$=$
(5) $\frac{1}{3}+\frac{1}{8}+\frac{1}{16}$
$=$
(6) $\frac{1}{3}+\frac{1}{9}+\frac{1}{18}$
$=$

Explanation:

(1) Step1: Find common denominator (24)

$\frac{1}{3} + \frac{1}{6} + \frac{1}{8} = \frac{8}{24} + \frac{4}{24} + \frac{3}{24}$

(1) Step2: Sum the numerators

$\frac{8+4+3}{24} = \frac{15}{24}$

(1) Step3: Simplify the fraction

$\frac{15\div3}{24\div3} = \frac{5}{8}$

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(2) Step1: Find common denominator (30)

$\frac{1}{3} + \frac{1}{6} + \frac{1}{10} = \frac{10}{30} + \frac{5}{30} + \frac{3}{30}$

(2) Step2: Sum the numerators

$\frac{10+5+3}{30} = \frac{18}{30}$

(2) Step3: Simplify the fraction

$\frac{18\div6}{30\div6} = \frac{3}{5}$

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(3) Step1: Find common denominator (42)

$\frac{1}{3} + \frac{1}{7} + \frac{1}{14} = \frac{14}{42} + \frac{6}{42} + \frac{3}{42}$

(3) Step2: Sum the numerators

$\frac{14+6+3}{42} = \frac{23}{42}$

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(4) Step1: Find common denominator (24)

$\frac{1}{3} + \frac{1}{8} + \frac{1}{12} = \frac{8}{24} + \frac{3}{24} + \frac{2}{24}$

(4) Step2: Sum the numerators

$\frac{8+3+2}{24} = \frac{13}{24}$

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(5) Step1: Find common denominator (48)

$\frac{1}{3} + \frac{1}{8} + \frac{1}{16} = \frac{16}{48} + \frac{6}{48} + \frac{3}{48}$

(5) Step2: Sum the numerators

$\frac{16+6+3}{48} = \frac{25}{48}$

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(6) Step1: Find common denominator (18)

$\frac{1}{3} + \frac{1}{9} + \frac{1}{18} = \frac{6}{18} + \frac{2}{18} + \frac{1}{18}$

(6) Step2: Sum the numerators

$\frac{6+2+1}{18} = \frac{9}{18}$

(6) Step3: Simplify the fraction

$\frac{9\div9}{18\div9} = \frac{1}{2}$

Answer:

(1) $\frac{5}{8}$
(2) $\frac{3}{5}$
(3) $\frac{23}{42}$
(4) $\frac{13}{24}$
(5) $\frac{25}{48}$
(6) $\frac{1}{2}$