Question

PLEASE HELP I NEED THIS NOW SO BADLY :(( Simplify: 2 1/4 x+(4 1/3 x−7 4/5 )÷2 3/5

Answer 1

Answer:

$2\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5} = \frac{47x-36}{12}$

Step-by-step explanation:

Considering the expression

$2\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5}$

Simplifying the expression

$\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{1}{4}=\frac{9}{4}$

$\frac{9}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \frac{13}{5}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 2\frac{3}{5}=\frac{13}{5}$

$\frac{9}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \frac{13}{5}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 4\frac{1}{3}=\frac{13}{3}$

$\frac{9}{4}x+\left(\frac{13}{3}x-7\frac{4}{5}\right)\div \frac{13}{5}$

$\mathrm{Convert\:mixed\:numbers\:to\:improper\:fractions}:\quad 7\frac{4}{5}=\frac{39}{5}$

$\frac{9}{4}x+\left(\frac{13}{3}x-\frac{39}{5}\right)\div \frac{13}{5}$

As

$\frac{9}{4}x=\frac{9x}{4}$

and

$\frac{\frac{13}{3}x-\frac{39}{5}}{\frac{13}{5}}=\frac{5\cdot \frac{65x-117}{15}}{13}$

So,

$\frac{9x}{4}+\frac{5\cdot \frac{65x-117}{15}}{13}$

$\mathrm{Least\:Common\:Multiplier\:of\:}4,\:13:\quad 52$

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

$\frac{117x}{52}+\frac{\frac{4\left(65x-117\right)}{3}}{52}$

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

$\mathrm{Join}\:117x+\frac{4\left(65x-117\right)}{3}:\quad \frac{611x-468}{3}$

$\frac{\frac{611x-468}{3}}{52}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

$\frac{611x-468}{3\cdot \:52}$

$\mathrm{Multiply\:the\:numbers:}\:3\cdot \:52=156$

$\frac{611x-468}{156}$

$\mathrm{Factor}\:611x-468:\quad 13\left(47x-36\right)$

$\frac{13\left(47x-36\right)}{156}$

$\mathrm{Cancel\:the\:common\:factor:}\:13$

$\frac{47x-36}{12}$

Therefore, $2\frac{1}{4}x+\left(4\frac{1}{3}x-7\frac{4}{5}\right)\div \:2\frac{3}{5} = \frac{47x-36}{12}$

Keywords: algebraic expression , simplification

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