Question

I need help the second problem I don’t get this concept?

Answer 1

In general,

$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$

In our case,

$\frac{3}{4}+\frac{1}{8}=\frac{3*8+1*4}{4*8}=\frac{24+4}{32}=\frac{28}{32}$

Simplifying,

$\begin{gathered} \frac{28}{32}=\frac{4*7}{4*8}=\frac{4}{4}*\frac{7}{8}=1*\frac{7}{8}=\frac{7}{8} \\ \Rightarrow\frac{3}{4}+\frac{1}{8}=\frac{7}{8} \end{gathered}$

The simplified answer is 7/8.

a) Given

$\frac{1}{2}+\frac{2}{3}+\frac{9}{2}$

Notice that

$\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=(\frac{1}{2}+\frac{2}{3})+\frac{2}{9}$

First, calculate the term between parentheses

$\frac{1}{2}+\frac{2}{3}=\frac{1*3+2*2}{2*3}=\frac{3+4}{6}=\frac{7}{6}$

Then,

$\begin{gathered} \Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=\frac{7}{6}+\frac{2}{9}=\frac{7*9+2*6}{6*9}=\frac{63+12}{54}=\frac{75}{54} \\ \Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=\frac{75}{54} \end{gathered}$

Simplifying,

$\begin{gathered} \frac{75}{54}=\frac{3*25}{3*18}=\frac{25}{18} \\ \Rightarrow\frac{1}{2}+\frac{2}{3}+\frac{2}{9}=\frac{25}{18} \end{gathered}$

The answer to (a) is 25/18

(b)

$\begin{gathered} \frac{2}{3}*\frac{42}{5}*\frac{10}{7}=(\frac{2}{3}*\frac{42}{5})*\frac{10}{7}=(\frac{2*42}{3*5})*\frac{10}{7}=\frac{84}{15}*\frac{10}{7}=\frac{840}{105}=8 \\ \Rightarrow\frac{2}{3}*\frac{42}{5}*\frac{10}{7}=8 \end{gathered}$

The answer to part (b) is 8.