Question1. $7 \frac{2}{3}+8 \frac{5}{6}$ $\qquad$ 2. $4 \frac{3}{4}+2 \frac{2}{5}$
3. $11 \frac{9}{10}+3 \frac{1}{20}$ $\qquad$ 4. $7 \frac{6}{7}+5 \frac{2}{7}$ $\qquad$
5. $5 \frac{8}{9}+3 \frac{1}{2}$ $\qquad$ 6. $21 \frac{11}{12}+17 \frac{2}{3}$ $\qquad$

Studdy Solution
Convert $\frac{99}{6}$ to a mixed number:
$\frac{99}{6} = 16 \frac{3}{6} = 16 \frac{1}{2}$
The result for Problem 1 is:
$\boxed{16 \frac{1}{2}}$
### Problem 2: $4 \frac{3}{4} + 2 \frac{2}{5}$
STEP_1: Convert $4 \frac{3}{4}$ and $2 \frac{2}{5}$ to improper fractions.
$4 \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \frac{19}{4}$ $2 \frac{2}{5} = \frac{10}{5} + \frac{2}{5} = \frac{12}{5}$
STEP_2: Find a common denominator for $\frac{19}{4}$ and $\frac{12}{5}$.
The least common denominator (LCD) of $4$ and $5$ is $20$.
Convert $\frac{19}{4}$ and $\frac{12}{5}$ to have a denominator of $20$:
$\frac{19}{4} = \frac{19 \times 5}{4 \times 5} = \frac{95}{20}$ $\frac{12}{5} = \frac{12 \times 4}{5 \times 4} = \frac{48}{20}$
STEP_3: Add the fractions:
$\frac{95}{20} + \frac{48}{20} = \frac{95 + 48}{20} = \frac{143}{20}$
STEP_4: Convert $\frac{143}{20}$ to a mixed number:
$\frac{143}{20} = 7 \frac{3}{20}$
The result for Problem 2 is:
$\boxed{7 \frac{3}{20}}$
### Problem 3: $11 \frac{9}{10} + 3 \frac{1}{20}$
STEP_1: Convert $11 \frac{9}{10}$ and $3 \frac{1}{20}$ to improper fractions.
$11 \frac{9}{10} = \frac{110}{10} + \frac{9}{10} = \frac{119}{10}$ $3 \frac{1}{20} = \frac{60}{20} + \frac{1}{20} = \frac{61}{20}$
STEP_2: Find a common denominator for $\frac{119}{10}$ and $\frac{61}{20}$.
The least common denominator (LCD) of $10$ and $20$ is $20$.
Convert $\frac{119}{10}$ to have a denominator of $20$:
$\frac{119}{10} = \frac{119 \times 2}{10 \times 2} = \frac{238}{20}$
STEP_3: Add the fractions:
$\frac{238}{20} + \frac{61}{20} = \frac{238 + 61}{20} = \frac{299}{20}$
STEP_4: Convert $\frac{299}{20}$ to a mixed number:
$\frac{299}{20} = 14 \frac{19}{20}$
The result for Problem 3 is:
$\boxed{14 \frac{19}{20}}$
### Problem 4: $7 \frac{6}{7} + 5 \frac{2}{7}$
STEP_1: Convert $7 \frac{6}{7}$ and $5 \frac{2}{7}$ to improper fractions.
$7 \frac{6}{7} = \frac{49}{7} + \frac{6}{7} = \frac{55}{7}$ $5 \frac{2}{7} = \frac{35}{7} + \frac{2}{7} = \frac{37}{7}$
STEP_2: The fractions already have a common denominator of $7$.
STEP_3: Add the fractions:
$\frac{55}{7} + \frac{37}{7} = \frac{55 + 37}{7} = \frac{92}{7}$
STEP_4: Convert $\frac{92}{7}$ to a mixed number:
$\frac{92}{7} = 13 \frac{1}{7}$
The result for Problem 4 is:
$\boxed{13 \frac{1}{7}}$
### Problem 5: $5 \frac{8}{9} + 3 \frac{1}{2}$
STEP_1: Convert $5 \frac{8}{9}$ and $3 \frac{1}{2}$ to improper fractions.
$5 \frac{8}{9} = \frac{45}{9} + \frac{8}{9} = \frac{53}{9}$ $3 \frac{1}{2} = \frac{6}{2} + \frac{1}{2} = \frac{7}{2}$
STEP_2: Find a common denominator for $\frac{53}{9}$ and $\frac{7}{2}$.
The least common denominator (LCD) of $9$ and $2$ is $18$.
Convert $\frac{53}{9}$ and $\frac{7}{2}$ to have a denominator of $18$:
$\frac{53}{9} = \frac{53 \times 2}{9 \times 2} = \frac{106}{18}$ $\frac{7}{2} = \frac{7 \times 9}{2 \times 9} = \frac{63}{18}$
STEP_3: Add the fractions:
$\frac{106}{18} + \frac{63}{18} = \frac{106 + 63}{18} = \frac{169}{18}$
STEP_4: Convert $\frac{169}{18}$ to a mixed number:
$\frac{169}{18} = 9 \frac{7}{18}$
The result for Problem 5 is:
$\boxed{9 \frac{7}{18}}$
### Problem 6: $21 \frac{11}{12} + 17 \frac{2}{3}$
STEP_1: Convert $21 \frac{11}{12}$ and $17 \frac{2}{3}$ to improper fractions.
$21 \frac{11}{12} = \frac{252}{12} + \frac{11}{12} = \frac{263}{12}$ $17 \frac{2}{3} = \frac{51}{3} + \frac{2}{3} = \frac{53}{3}$
STEP_2: Find a common denominator for $\frac{263}{12}$ and $\frac{53}{3}$.
The least common denominator (LCD) of $12$ and $3$ is $12$.
Convert $\frac{53}{3}$ to have a denominator of $12$:
$\frac{53}{3} = \frac{53 \times 4}{3 \times 4} = \frac{212}{12}$
STEP_3: Add the fractions:
$\frac{263}{12} + \frac{212}{12} = \frac{263 + 212}{12} = \frac{475}{12}$
STEP_4: Convert $\frac{475}{12}$ to a mixed number:
$\frac{475}{12} = 39 \frac{7}{12}$
The result for Problem 6 is:
$\boxed{39 \frac{7}{12}}$