Question

solve using properties
pls help me with this sum​

Answer 1

Answer:

$\dfrac{2}{5}\times \dfrac{-3}{7}-\dfrac{1}{14}-\dfrac{3}{7}\times \dfrac{3}{5}=-\dfrac{1}{2}\quad \left(\mathrm{Decimal:\quad }\:-0.5\right)$

Step-by-step explanation:

$\dfrac{2}{5}\times \dfrac{-3}{7}-\dfrac{1}{14}-\dfrac{3}{7}\times \dfrac{3}{5}$

$\dfrac{2}{5}\times \dfrac{-3}{7}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{-a}{b}=-\dfrac{a}{b}$

$=\dfrac{2}{5}\left(-\dfrac{3}{7}\right)$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=-\dfrac{2}{5}\times \dfrac{3}{7}$

$\mathrm{Multiply\:fractions}:\quad \dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\:\times \:c}{b\:\times \:d}$

$=-\dfrac{2\times \:3}{5\times \:7}$

$\mathrm{Multiply\:the\:numbers:}\:2\times \:3=6$

$=-\dfrac{6}{5\times \:7}$

$\mathrm{Multiply\:the\:numbers:}\:5\times \:7=35$

$=-\dfrac{6}{35}$

$=-\dfrac{6}{35}-\dfrac{1}{14}-\dfrac{3}{7}\times \dfrac{3}{5}$

$\dfrac{3}{7}\times \dfrac{3}{5}$

$\mathrm{Multiply\:fractions}:\quad \dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\:\times \:c}{b\:\times \:d}$

$=\dfrac{3\times \:3}{7\times \:5}$

$\mathrm{Multiply\:the\:numbers:}\:3\times \:3=9$

$=\dfrac{9}{7\times \:5}$

$\mathrm{Multiply\:the\:numbers:}\:7\times \:5=35$

$=\dfrac{9}{35}$

$=-\dfrac{6}{35}-\dfrac{1}{14}-\dfrac{9}{35}$

$\mathrm{Combine\:the\:fractions\:}-\dfrac{6}{35}-\dfrac{9}{35}$

$\mathrm{Apply\:rule}\:\dfrac{a}{c}\pm \dfrac{b}{c}=\dfrac{a\pm \:b}{c}$

$=\dfrac{-6-9}{35}$

$\mathrm{Subtract\:the\:numbers:}\:-6-9=-15$

$=\dfrac{-15}{35}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{-a}{b}=-\dfrac{a}{b}$

$=-\dfrac{15}{35}$

$\mathrm{Cancel\:the\:common\:factor:}\:5$

$=-\dfrac{3}{7}$

$=-\dfrac{3}{7}-\dfrac{1}{14}$

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

$Least\:Common\:Multiplier\:\left(LCM\right)$

• $\mathrm{The\:LCM\:of\:}a,\:b\mathrm{\:is\:the\:smallest\:positive\:number\:that\:is\:divisible\:by\:both\:}a\mathrm{\:and\:}b$

$\mathrm{Prime\:factorization\:of\:}7:\quad 7$

$\mathrm{Prime\:factorization\:of\:}14:\quad 2\times \:7$

$\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}7\mathrm{\:or\:}14$

$=7\times \:2$

$\mathrm{Multiply\:the\:numbers:}\:7\times \:2=14$

$=14$

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

$\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}$ $\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:14$

$\mathrm{For}\:\dfrac{3}{7}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:2$

$\dfrac{3}{7}=\dfrac{3\times \:2}{7\times \:2}=\dfrac{6}{14}$

$=-\dfrac{6}{14}-\dfrac{1}{14}$

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

$=\dfrac{-6-1}{14}$

$\mathrm{Subtract\:the\:numbers:}\:-6-1=-7$

$=\dfrac{-7}{14}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \dfrac{-a}{b}=-\dfrac{a}{b}$

$=-\dfrac{7}{14}$

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

$=-\dfrac{1}{2}$