Question

1. calculate.

(1) $\frac{1}{4}+\frac{1}{5}+\frac{1}{6}$
$=$
(2) $\frac{1}{4}+\frac{1}{5}+\frac{1}{8}$
$=$
(3) $\frac{1}{4}+\frac{1}{5}+\frac{1}{10}$
$=$
(4) $\frac{1}{4}+\frac{1}{6}+\frac{1}{10}$
$=$
(5) $\frac{1}{4}+\frac{1}{6}+\frac{1}{24}$
$=$
(6) $\frac{1}{4}+\frac{1}{7}+\frac{1}{14}$
$=$

Explanation:

(1) Step1: Find common denominator (60)

$\frac{1}{4}+\frac{1}{5}+\frac{1}{6} = \frac{15}{60}+\frac{12}{60}+\frac{10}{60}$

(1) Step2: Sum the numerators

$\frac{15+12+10}{60} = \frac{37}{60}$

(2) Step1: Find common denominator (40)

$\frac{1}{4}+\frac{1}{5}+\frac{1}{8} = \frac{10}{40}+\frac{8}{40}+\frac{5}{40}$

(2) Step2: Sum the numerators

$\frac{10+8+5}{40} = \frac{23}{40}$

(3) Step1: Find common denominator (20)

$\frac{1}{4}+\frac{1}{5}+\frac{1}{10} = \frac{5}{20}+\frac{4}{20}+\frac{2}{20}$

(3) Step2: Sum the numerators

$\frac{5+4+2}{20} = \frac{11}{20}$

(4) Step1: Find common denominator (60)

$\frac{1}{4}+\frac{1}{6}+\frac{1}{10} = \frac{15}{60}+\frac{10}{60}+\frac{6}{60}$

(4) Step2: Sum the numerators

$\frac{15+10+6}{60} = \frac{31}{60}$

(5) Step1: Find common denominator (24)

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

(5) Step2: Sum the numerators

$\frac{6+4+1}{24} = \frac{11}{24}$

(6) Step1: Find common denominator (28)

$\frac{1}{4}+\frac{1}{7}+\frac{1}{14} = \frac{7}{28}+\frac{4}{28}+\frac{2}{28}$

(6) Step2: Sum the numerators

$\frac{7+4+2}{28} = \frac{13}{28}$

Answer:

(1) $\frac{37}{60}$
(2) $\frac{23}{40}$
(3) $\frac{11}{20}$
(4) $\frac{31}{60}$
(5) $\frac{11}{24}$
(6) $\frac{13}{28}$