Question

What should be added to -7/3 to get 3/7

Answer 1

Step-by-step explanation:

$Let \: us \: add \: x \: to \: - \frac{7}{3} \: to \: get \: \frac{3}{7} \\ \implies \: - \frac{7}{3} + x = \frac{3}{7} \\ \implies \: x = \frac{3}{7} + \frac{7}{3} \: \\ \implies \: x = \: \frac{3 \times 3 + 7 \times 7}{3 \times 7} \\ \implies \: x = \: \frac{9 + 49}{21} \\ \implies \: x = \frac{58}{21} \\ so \: we \: should \: add \: \frac{58}{21} \\ \: to \: - \frac{7}{3} \: to \: get \: \frac{3}{7} \:$

Answer 2

Answer:

$\dfrac{-7}{3}+x=\dfrac{3}{7}\quad :\quad x=\dfrac{58}{21}\quad \left(\mathrm{Decimal}:\quad x=2.76190\dots \right)$

Step-by-step explanation:

$\textrm{Let the number to be found be } x \textrm{.}$

$\textrm{So, our equation will be;}$

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

$\gray{\mathrm{Subtract\:}\dfrac{-7}{3}\mathrm{\:from\:both\:sides}}$

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

$\gray{\mathrm{Simplify}}$

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

$\mathrm{Simplify\:}\dfrac{-7}{3}+x-\dfrac{-7}{3}:\quad x$

$\dfrac{-7}{3}+x-\dfrac{-7}{3}$

$\gray{\mathrm{Add\:similar\:elements:}\:\dfrac{-7}{3}-\dfrac{-7}{3}=0}$

$=x$

$\mathrm{Simplify\:}\dfrac{3}{7}-\dfrac{-7}{3}$

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

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

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

$\gray{\mathrm{Apply\:rule}\:-\left(-a\right)=a}$

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

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

$=\dfrac{9}{21}+\dfrac{49}{21}$

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

$=\dfrac{9+49}{21}$

$\gray{\mathrm{Add\:the\:numbers:}\:9+49=58}$

$=\dfrac{58}{21}$

$x=\dfrac{58}{21}$