44. add and simplify:\na. $\frac{1}{4}+\frac{2}{5}$\nb. $\frac{1}{5}+\frac{7}{15}$\nc. $\frac{5}{12}+\frac{7}…

planation:

Step1: Find common denominator for a

For $\frac{1}{4}+\frac{2}{5}$, the common denominator of 4 and 5 is $4\times5 = 20$. $\frac{1}{4}\times\frac{5}{5}=\frac{5}{20}$ and $\frac{2}{5}\times\frac{4}{4}=\frac{8}{20}$.

Step2: Add fractions for a

$\frac{5}{20}+\frac{8}{20}=\frac{5 + 8}{20}=\frac{13}{20}$.

Step3: Find common denominator for b

For $\frac{1}{5}+\frac{7}{15}$, the common denominator of 5 and 15 is 15. $\frac{1}{5}\times\frac{3}{3}=\frac{3}{15}$.

Step4: Add fractions for b

$\frac{3}{15}+\frac{7}{15}=\frac{3+7}{15}=\frac{10}{15}=\frac{2}{3}$.

Step5: Find common denominator for c

For $\frac{5}{12}+\frac{7}{16}$, the least - common multiple of 12 and 16 is 48. $\frac{5}{12}\times\frac{4}{4}=\frac{20}{48}$ and $\frac{7}{16}\times\frac{3}{3}=\frac{21}{48}$.

Step6: Add fractions for c

$\frac{20}{48}+\frac{21}{48}=\frac{20 + 21}{48}=\frac{41}{48}$.

Answer:

a. $\frac{13}{20}$ b. $\frac{2}{3}$ c. $\frac{41}{48}$