Question

1. $10\frac{6}{10} + \frac{2}{4} =$
2. $6\frac{6}{7} + \frac{3}{9} =$
3. $1\frac{4}{11} + \frac{2}{5} =$
4. $7\frac{3}{10} + \frac{5}{12} =$

Explanation:

Problem 7

Step1: Simplify fractions first

$10\frac{6}{10} = 10\frac{3}{5}$, $\frac{2}{4} = \frac{1}{2}$

Step2: Convert to improper fractions

$10\frac{3}{5} = \frac{53}{5}$, $\frac{1}{2} = \frac{1}{2}$

Step3: Find common denominator (10)

$\frac{53}{5} = \frac{106}{10}$, $\frac{1}{2} = \frac{5}{10}$

Step4: Add the fractions

$\frac{106}{10} + \frac{5}{10} = \frac{111}{10} = 11\frac{1}{10}$

Problem 9

Step1: Simplify the second fraction

$\frac{3}{9} = \frac{1}{3}$

Step2: Convert mixed number to improper fraction

$6\frac{6}{7} = \frac{48}{7}$

Step3: Find common denominator (21)

$\frac{48}{7} = \frac{144}{21}$, $\frac{1}{3} = \frac{7}{21}$

Step4: Add the fractions

$\frac{144}{21} + \frac{7}{21} = \frac{151}{21} = 7\frac{4}{21}$

Problem 11

Step1: Convert mixed number to improper fraction

$1\frac{4}{11} = \frac{15}{11}$

Step2: Find common denominator (55)

$\frac{15}{11} = \frac{75}{55}$, $\frac{2}{5} = \frac{22}{55}$

Step3: Add the fractions

$\frac{75}{55} + \frac{22}{55} = \frac{97}{55} = 1\frac{42}{55}$

Problem 13

Step1: Convert mixed number to improper fraction

$7\frac{3}{10} = \frac{73}{10}$

Step2: Find common denominator (60)

$\frac{73}{10} = \frac{438}{60}$, $\frac{5}{12} = \frac{25}{60}$

Step3: Add the fractions

$\frac{438}{60} + \frac{25}{60} = \frac{463}{60} = 7\frac{43}{60}$

Answer:

1. $11\frac{1}{10}$
2. $7\frac{4}{21}$
3. $1\frac{42}{55}$
4. $7\frac{43}{60}$