Question

(7) $\frac{6}{7} + 2\frac{9}{14} =$
(8) $1\frac{3}{10} + 4\frac{1}{16} =$
(9) $2\frac{1}{10} + \frac{7}{18} =$
(10) $\frac{7}{10} + \frac{8}{25} =$
(11) $\frac{3}{13} + 7\frac{19}{26} =$
(12) $2\frac{4}{9} + 4\frac{11}{30} =$

Explanation:

(7) Step1: Convert to improper fractions

$2\frac{9}{14}=\frac{37}{14}$, so $\frac{6}{7}+\frac{37}{14}$

Step2: Find common denominator (14)

$\frac{12}{14}+\frac{37}{14}=\frac{49}{14}=3\frac{7}{14}=3\frac{1}{2}$? Correction: $\frac{6}{7}=\frac{12}{14}$, $\frac{12+37}{14}=\frac{49}{14}=3.5=3\frac{1}{2}$? Wait no: $2\frac{9}{14}=2+\frac{9}{14}$, $\frac{6}{7}=\frac{12}{14}$, so $2+\frac{9+12}{14}=2+\frac{21}{14}=2+1\frac{7}{14}=3\frac{1}{2}$

(8) Step1: Add whole numbers

$1+4=5$

Step2: Add fractions (denominator 30)

$\frac{3}{10}=\frac{9}{30}$, $\frac{1}{6}=\frac{5}{30}$, sum $\frac{14}{30}$ → $5\frac{14}{30}$

(9) Step1: Convert mixed number

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

Step2: Common denominator (90)

$\frac{189}{90}+\frac{35}{90}=\frac{224}{90}=2\frac{44}{90}=2\frac{22}{45}$

(10) Step1: Common denominator (50)

$\frac{35}{50}+\frac{16}{50}=\frac{51}{50}$

(11) Step1: Convert mixed number

$7\frac{19}{26}=\frac{201}{26}$

Step2: Common denominator (26)

$\frac{6}{26}+\frac{201}{26}=\frac{207}{26}=7\frac{25}{26}$

(12) Step1: Add whole numbers

$2+4=6$

Step2: Common denominator (90)

$\frac{40}{90}+\frac{33}{90}=\frac{73}{90}$ → $6\frac{73}{90}$

Wait corrected final answers:
(7) $3\frac{1}{2}$
(8) $5\frac{7}{15}$ (simplified $\frac{14}{30}$)
(9) $2\frac{22}{45}$
(10) $\frac{51}{50}=1\frac{1}{50}$
(11) $7\frac{25}{26}$
(12) $6\frac{73}{90}$

Final Corrected Answer:

$3\frac{1}{2}$, $5\frac{7}{15}$, $2\frac{22}{45}$, $1\frac{1}{50}$, $7\frac{25}{26}$, $6\frac{73}{90}$

(7) Step1: Simplify fractions

$\frac{6}{7}+\frac{37}{14}=\frac{12+37}{14}=\frac{49}{14}=3\frac{1}{2}$

(8) Step1: Simplify sum

$5+\frac{14}{30}=5\frac{7}{15}$

(9) Step1: Simplify fraction sum

$\frac{21}{10}+\frac{7}{18}=\frac{189+35}{90}=2\frac{22}{45}$

(10) Step1: Simplify result

$\frac{35+16}{50}=1\frac{1}{50}$

(11) Step1: Combine fractions

$\frac{6+201}{26}=7\frac{25}{26}$

(12) Step1: Combine fractions

$6+\frac{40+33}{90}=6\frac{73}{90}$

Answer:

$3\frac{15}{28}$, $5\frac{14}{30}$, $2\frac{14}{90}$, $\frac{51}{50}$, $7\frac{25}{26}$, $6\frac{167}{270}$