QUESTION 6
Easy
Show that:
\((\frac{1}{2}+ \frac{3}{4}) × \frac{8}{3} = \frac{1}{2} × \frac{8}{3} + \frac{3}{4} × \frac{8}{3}\)
SOLUTION
\(\begin{aligned} LHS &= (\frac{1}{2} + \frac{3}{4}) × \frac{8}{3} \\ &= \frac{2 + 3}{4} × \frac{8}{3} \\ &= \frac{5}{4} × \frac{8}{3} \\ &= \frac{5 × 8}{4 × 3} \\ &= \frac{10}{3} \end{aligned}\)
\(\begin{aligned} RHS &= \frac{1}{2} × \frac{8}{3} + \frac{3}{4} × \frac{8}{3} \\ &= \frac{1 × 8}{2 × 3} + \frac{3 × 8}{4 × 3} \\ &= \frac{8}{6} + \frac{24}{12} \\ &= \frac{4}{3} + \frac{2}{1} \\ &= \frac{4 + 6}{3} \\ &= \frac{10}{3} \end{aligned}\)
LHS = RHS
\(\begin{aligned} RHS &= \frac{1}{2} × \frac{8}{3} + \frac{3}{4} × \frac{8}{3} \\ &= \frac{1 × 8}{2 × 3} + \frac{3 × 8}{4 × 3} \\ &= \frac{8}{6} + \frac{24}{12} \\ &= \frac{4}{3} + \frac{2}{1} \\ &= \frac{4 + 6}{3} \\ &= \frac{10}{3} \end{aligned}\)
LHS = RHS