Question

write the letter of the exercise above it.
m $\begin{array}{r} \frac{1}{3} \\ +\frac{2}{5} \\ hline end{array}$
l $\begin{array}{r} \frac{7}{8} \\ -\frac{1}{2} \\ hline end{array}$
h $\begin{array}{r} \frac{3}{4} \\ +\frac{2}{3} \\ hline end{array}$
d $\begin{array}{r} 3\frac{5}{16} \\ +5\frac{1}{4} \\ hline end{array}$
g $\begin{array}{r} 9\frac{7}{10} \\ -4\frac{1}{5} \\ hline end{array}$

Explanation:

Step1: Find common denominator

For $\frac{1}{3} + \frac{2}{5}$, common denominator is 15.
$\frac{1\times5}{3\times5} + \frac{2\times3}{5\times3} = \frac{5}{15} + \frac{6}{15}$

Step2: Add numerators

$\frac{5+6}{15} = \frac{11}{15}$

Step3: Find common denominator

For $\frac{7}{8} - \frac{1}{2}$, common denominator is 8.
$\frac{7}{8} - \frac{1\times4}{2\times4} = \frac{7}{8} - \frac{4}{8}$

Step4: Subtract numerators

$\frac{7-4}{8} = \frac{3}{8}$

Step5: Find common denominator

For $\frac{3}{4} + \frac{2}{3}$, common denominator is 12.
$\frac{3\times3}{4\times3} + \frac{2\times4}{3\times4} = \frac{9}{12} + \frac{8}{12}$

Step6: Add numerators

$\frac{9+8}{12} = \frac{17}{12} = 1\frac{5}{12}$

Step7: Convert to improper fractions

$3\frac{5}{16} = \frac{3\times16+5}{16} = \frac{53}{16}$; $5\frac{1}{4} = \frac{5\times4+1}{4} = \frac{21}{4}$

Step8: Find common denominator, add

Common denominator is 16: $\frac{53}{16} + \frac{21\times4}{4\times4} = \frac{53}{16} + \frac{84}{16} = \frac{137}{16} = 8\frac{9}{16}$

Step9: Convert to improper fractions

$9\frac{7}{10} = \frac{9\times10+7}{10} = \frac{97}{10}$; $4\frac{1}{5} = \frac{4\times5+1}{5} = \frac{21}{5}$

Step10: Find common denominator, subtract

Common denominator is 10: $\frac{97}{10} - \frac{21\times2}{5\times2} = \frac{97}{10} - \frac{42}{10} = \frac{55}{10} = 5\frac{1}{2}$

Answer:

M: $\frac{11}{15}$
L: $\frac{3}{8}$
H: $1\frac{5}{12}$
D: $8\frac{9}{16}$
G: $5\frac{1}{2}$