Question

◆ calculate.
(1) $\frac{1}{2}+\frac{1}{8}+\frac{1}{12}$
$=$
(2) $\frac{1}{3}+\frac{1}{9}+\frac{1}{15}$
$=$
(3) $\frac{1}{5}+\frac{1}{10}+\frac{1}{25}$
$=$
(4) $\frac{1}{3}+\frac{1}{5}+\frac{1}{20}$
$=$
(5) $\frac{1}{6}+\frac{1}{7}+\frac{1}{21}$
$=$
(6) $\frac{1}{2}+\frac{1}{4}+\frac{1}{26}$
$=$

Explanation:

(1) Step1: Find common denominator (24)

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

(1) Step2: Sum the numerators

$\frac{12+3+2}{24} = \frac{17}{24}$

(2) Step1: Find common denominator (45)

$\frac{1}{3} + \frac{1}{9} + \frac{1}{15} = \frac{15}{45} + \frac{5}{45} + \frac{3}{45}$

(2) Step2: Sum the numerators

$\frac{15+5+3}{45} = \frac{23}{45}$

(3) Step1: Find common denominator (50)

$\frac{1}{5} + \frac{1}{10} + \frac{1}{25} = \frac{10}{50} + \frac{5}{50} + \frac{2}{50}$

(3) Step2: Sum the numerators

$\frac{10+5+2}{50} = \frac{17}{50}$

(4) Step1: Find common denominator (60)

$\frac{1}{3} + \frac{1}{5} + \frac{1}{20} = \frac{20}{60} + \frac{12}{60} + \frac{3}{60}$

(4) Step2: Sum the numerators

$\frac{20+12+3}{60} = \frac{35}{60} = \frac{7}{12}$

(5) Step1: Find common denominator (42)

$\frac{1}{6} + \frac{1}{7} + \frac{1}{21} = \frac{7}{42} + \frac{6}{42} + \frac{2}{42}$

(5) Step2: Sum the numerators

$\frac{7+6+2}{42} = \frac{15}{42} = \frac{5}{14}$

(6) Step1: Find common denominator (52)

$\frac{1}{2} + \frac{1}{4} + \frac{1}{26} = \frac{26}{52} + \frac{13}{52} + \frac{2}{52}$

(6) Step2: Sum the numerators

$\frac{26+13+2}{52} = \frac{41}{52}$

Answer:

(1) $\frac{17}{24}$
(2) $\frac{23}{45}$
(3) $\frac{17}{50}$
(4) $\frac{7}{12}$
(5) $\frac{5}{14}$
(6) $\frac{41}{52}$