Question

d $1\frac{2}{3}+\frac{1}{6}=$____ e $\frac{5}{10}-\frac{1}{4}=$__ f $4\frac{30}{60}+1\frac{1}{4}=$____

Explanation:

Step1: Convert mixed - number to improper fraction for d

$1\frac{2}{3}=\frac{3\times1 + 2}{3}=\frac{5}{3}$

Step2: Find a common denominator for d

The common denominator of 3 and 6 is 6. $\frac{5}{3}=\frac{5\times2}{3\times2}=\frac{10}{6}$, then $\frac{10}{6}+\frac{1}{6}=\frac{10 + 1}{6}=\frac{11}{6}=1\frac{5}{6}$

Step3: Find a common denominator for e

The common denominator of 10 and 4 is 20. $\frac{5}{10}=\frac{5\times2}{10\times2}=\frac{10}{20}$, $\frac{1}{4}=\frac{1\times5}{4\times5}=\frac{5}{20}$, then $\frac{10}{20}-\frac{5}{20}=\frac{10 - 5}{20}=\frac{5}{20}=\frac{1}{4}$

Step4: Convert mixed - number to improper fraction for f

$4\frac{30}{60}=\frac{60\times4+30}{60}=\frac{240 + 30}{60}=\frac{270}{60}$, $1\frac{1}{4}=\frac{4\times1+1}{4}=\frac{5}{4}$, the common denominator of 60 and 4 is 60. $\frac{5}{4}=\frac{5\times15}{4\times15}=\frac{75}{60}$, then $\frac{270}{60}+\frac{75}{60}=\frac{270 + 75}{60}=\frac{345}{60}=5\frac{45}{60}=5\frac{3}{4}$

Answer:

d. $1\frac{5}{6}$
e. $\frac{1}{4}$
f. $5\frac{3}{4}$