Question

Number one please answer the question

Answer 1

Answer:

$\displaystyle\left|\frac{5}{7}-\frac{2}{3}\right|+\left|\frac{3}{14}-\frac{5}{7}\right|=\frac{23}{42}\quad \left(\mathrm{Decimal:\quad }\:0.54761\dots \right)$

Step-by-step explanation:

$\displaystyle\left|\frac{5}{7}-\frac{2}{3}\right|+\left|\frac{3}{14}-\frac{5}{7}\right|$

$\displaystyle\black{\left|\frac{5}{7}-\frac{2}{3}\right|}$

$\displaystyle\pink{\mathrm{Join~}\frac{5}{7}-\frac{2}{3}:}$

$\displaystyle\frac{5}{7}-\frac{2}{3}$

$\gray{\mathrm{Least\:Common\:Multiplier\:of\:}7,\:3:\quad 21}$

$\gray{\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}}$

$\displaystyle=\frac{15}{21}-\frac{14}{21}$

$\displaystyle\gray{\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}$

$\displaystyle=\frac{15-14}{21}$

$\gray{\mathrm{Subtract\:the\:numbers:}\:15-14=1}$

$\displaystyle=\frac{1}{21}$

$\displaystyle=\left|\frac{1}{21}\right|$

$\gray{\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0}$

$\displaystyle\gray{\left|\frac{1}{21}\right|=\frac{1}{21}}$

$\displaystyle=\frac{1}{21}$

$\displaystyle\black{\left|\frac{3}{14}-\frac{5}{7}\right|}$

$\displaystyle\pink{\mathrm{Join~}\frac{3}{14}-\frac{5}{7}:}$

$\displaystyle \frac{3}{14}-\frac{5}{7}$

$\gray{\mathrm{Least\:Common\:Multiplier\:of\:}14,\:7:\quad 14}$

$\gray{\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}}$

$\displaystyle =\frac{3}{14}-\frac{10}{14}$

$\displaystyle\gray{\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}$

$\displaystyle=\frac{3-10}{14}$

$\gray{\mathrm{Subtract\:the\:numbers:}\:3-10=-7}$

$\displaystyle=\frac{-7}{14}$

$\displaystyle\gray{\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}}$

$\displaystyle=-\frac{7}{14}$

$\gray{\mathrm{Cancel\:the\:common\:factor:}\:7}$

$\displaystyle=-\frac{1}{2}$

$\displaystyle=\left|-\frac{1}{2}\right|$

$\gray{\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a}$

$\displaystyle\gray{\left|-\frac{1}{2}\right|=\frac{1}{2}}$

$\displaystyle=\frac{1}{2}$

$\displaystyle=\frac{1}{21}+\frac{1}{2}$

$\black{\mathrm{Simplify}}$

$\displaystyle\frac{1}{21}+\frac{1}{2}$

$\gray{\mathrm{Least\:Common\:Multiplier\:of\:}21,\:2:\quad 42}$

$\gray{\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}}$

$\displaystyle=\frac{2}{42}+\frac{21}{42}$

$\displaystyle\gray{\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}}$

$\displaystyle=\frac{2+21}{42}$

$\gray{\mathrm{Add\:the\:numbers:}\:2+21=23}$

$\displaystyle=\frac{23}{42}$