Question

add.
(1) $4\frac{5}{6}+\frac{2}{9}=$

(2) $\frac{3}{8}+2\frac{1}{10}=$

(3) $\frac{7}{9}+\frac{5}{12}=$

(4) $2\frac{3}{4}+1\frac{3}{14}=$

(5) $\frac{1}{3}+4\frac{11}{18}=$

(6) $3\frac{1}{8}+\frac{3}{20}=$

Explanation:

(1)

Step1: Convert the mixed number to an improper fraction

$4\frac{5}{6}=\frac{4\times6 + 5}{6}=\frac{29}{6}$

Step2: Find a common denominator (18) and add the fractions

$\frac{29}{6}+\frac{2}{9}=\frac{29\times3}{6\times3}+\frac{2\times2}{9\times2}=\frac{87}{18}+\frac{4}{18}=\frac{91}{18}=5\frac{1}{18}$

Step1: Convert the mixed number to an improper fraction

$2\frac{1}{10}=\frac{2\times10 + 1}{10}=\frac{21}{10}$

Step2: Find a common denominator (40) and add the fractions

$\frac{3}{8}+\frac{21}{10}=\frac{3\times5}{8\times5}+\frac{21\times4}{10\times4}=\frac{15}{40}+\frac{84}{40}=\frac{99}{40}=2\frac{19}{40}$

Step1: Find a common denominator (36)

$\frac{7}{9}+\frac{5}{12}=\frac{7\times4}{9\times4}+\frac{5\times3}{12\times3}=\frac{28}{36}+\frac{15}{36}$

Step2: Add the fractions

$\frac{28 + 15}{36}=\frac{43}{36}=1\frac{7}{36}$

Answer:

$5\frac{1}{18}$

(2)