Question

$\frac{3}{5} + \frac{2}{7}$
​

Answer 1

Step-by-step explanation:

=3/5 + 2/7

=21+10/35

=31/35

I hope it help you..

Answer 2

Answer:

$\dfrac{3}{5}+\dfrac{2}{7}=\dfrac{31}{35}\quad \left(\mathrm{Decimal:\quad }\:0.88571\dots \right)$

Step-by-step explanation:

$\dfrac{3}{5}+\dfrac{2}{7}$

$\mathrm{Least\:Common\:Multiplier\:of\:}5,\:7$

$\mathrm{Prime\:factorization\:of\:}5:\quad 5$

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

$\gray{\mathrm{Multiply\:each\:factor\:the\:greatest\:number\:of\:times\:it\:occurs\:in\:either\:}5\mathrm{\:or\:}7}$

$=5\cdot \:7$

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

$=35$

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

$\gray{\mathrm{Multiply\:each\:numerator\:by\:the\:same\:amount\:needed\:to\:multiply\:its}}$ $\gray{\mathrm{corresponding\:denominator\:to\:turn\:it\:into\:the\:LCM}\:35}$

$\gray{\mathrm{For}\:\dfrac{3}{5}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:7}$

$\dfrac{3}{5}=\dfrac{3\cdot \:7}{5\cdot \:7}=\dfrac{21}{35}$

$\gray{\mathrm{For}\:\dfrac{2}{7}:\:\mathrm{multiply\:the\:denominator\:and\:numerator\:by\:}\:5}$

$\dfrac{2}{7}=\dfrac{2\cdot \:5}{7\cdot \:5}=\dfrac{10}{35}$

$=\dfrac{21}{35}+\dfrac{10}{35}$

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

$=\dfrac{21+10}{35}$

$\gray{\mathrm{Add\:the\:numbers:}\:21+10=31}$

$=\dfrac{31}{35}$