Question # 1
Answer:
[tex]\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=-\frac{3}{20}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}[/tex]
[tex]=-\frac{2}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}[/tex] ∵ [tex]\frac{-2}{3}\times \frac{3}{5}=-\frac{2}{5}[/tex]
[tex]=-\frac{2}{5}+\frac{1}{4}[/tex] ∵ [tex]\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=\frac{1}{4}[/tex]
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}5,\:4:\quad 20[/tex]
[tex]=-\frac{8}{20}+\frac{5}{20}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{-8+5}{20}[/tex]
[tex]\mathrm{Add/Subtract\:the\:numbers:}\:-8+5=-3[/tex]
[tex]=\frac{-3}{20}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{3}{20}[/tex]
Therefore,
[tex]\frac{-2}{3}\times \frac{3}{5}+\frac{5}{2}\times \frac{3}{5}\times \frac{1}{6}=-\frac{3}{20}[/tex]
Question # 2
Answer:
[tex]\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=-\frac{5}{28}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}[/tex]
[tex]=-\frac{6}{35}-\frac{1}{6}\times \frac{3}{2}\times \frac{2}{5}\times \frac{1}{14}[/tex] ∵ [tex]\frac{2}{5}\times \frac{-3}{7}=-\frac{6}{35}[/tex]
[tex]=-\frac{6}{35}-\frac{1}{140}[/tex] ∵ [tex]\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=\frac{1}{140}[/tex]
[tex]\mathrm{Least\:Common\:Multiplier\:of\:}35,\:140:\quad 140[/tex]
[tex]=-\frac{24}{140}-\frac{1}{140}[/tex]
[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}[/tex]
[tex]=\frac{-24-1}{140}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:-24-1=-25[/tex]
[tex]=\frac{-25}{140}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}[/tex]
[tex]=-\frac{25}{140}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:5[/tex]
[tex]=-\frac{5}{28}[/tex]
Therefore,
[tex]\frac{2}{5}\times \frac{-3}{7}-\frac{1}{6}\times \frac{3}{2}\times \frac{1}{14}\times \frac{2}{5}=-\frac{5}{28}[/tex]
