Question

◆ calculate.
(1) $\frac{1}{4}+\frac{1}{8}+\frac{1}{12}$
$= \frac{11}{24}$
(2) $\frac{1}{4}+\frac{1}{8}+\frac{1}{16}$
$= \frac{6}{16}=\frac{3}{8}$
(3) $\frac{1}{4}+\frac{1}{8}+\frac{1}{20}$
$= \frac{17}{40}$
(4) $\frac{1}{5}+\frac{1}{6}+\frac{1}{9}$
$= $
(5) $\frac{1}{5}+\frac{1}{6}+\frac{1}{10}$
$= \frac{14}{30}=\frac{7}{15}$
(6) $\frac{1}{6}+\frac{1}{8}+\frac{1}{16}$
$= $

Explanation:

Step1: Find common denominator (4,8,16)

The least common denominator (LCD) of 4, 8, 16 is 16.
Convert each fraction:
$\frac{1}{4} = \frac{4}{16}$, $\frac{1}{8} = \frac{2}{16}$, $\frac{1}{16} = \frac{1}{16}$

Step2: Sum the numerators

$\frac{4}{16} + \frac{2}{16} + \frac{1}{16} = \frac{4+2+1}{16} = \frac{7}{16}$

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Step1: Find common denominator (4,8,20)

The LCD of 4, 8, 20 is 40.
Convert each fraction:
$\frac{1}{4} = \frac{10}{40}$, $\frac{1}{8} = \frac{5}{40}$, $\frac{1}{20} = \frac{2}{40}$

Step2: Sum the numerators

$\frac{10}{40} + \frac{5}{40} + \frac{2}{40} = \frac{10+5+2}{40} = \frac{17}{40}$

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Step1: Find common denominator (5,6,9)

The LCD of 5, 6, 9 is 90.
Convert each fraction:
$\frac{1}{5} = \frac{18}{90}$, $\frac{1}{6} = \frac{15}{90}$, $\frac{1}{9} = \frac{10}{90}$

Step2: Sum the numerators

$\frac{18}{90} + \frac{15}{90} + \frac{10}{90} = \frac{18+15+10}{90} = \frac{43}{90}$

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Step1: Find common denominator (6,8,16)

The LCD of 6, 8, 16 is 48.
Convert each fraction:
$\frac{1}{6} = \frac{8}{48}$, $\frac{1}{8} = \frac{6}{48}$, $\frac{1}{16} = \frac{3}{48}$

Step2: Sum the numerators

$\frac{8}{48} + \frac{6}{48} + \frac{3}{48} = \frac{8+6+3}{48} = \frac{17}{48}$

Answer:

(2) $\frac{7}{16}$
(3) $\frac{17}{40}$
(4) $\frac{43}{90}$
(6) $\frac{17}{48}$