Question

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Answer 1

(1) 2/8

THE ADDITIVE INVERSE OF 2/8 IS -2/8

(2) -5/9

THE ADDITIVE INVERSE OF -5/9 IS +5/9

(3) -6/-5=6/5

THE ADDITIVE INVERSE OF 6/5 IS -6/5

(4) (-1+4/17)       (LCM=17)

= -17/17+4/17= -13/17  

THE ADDITIVE INVERSE OF -13/17 IS +13/17    

Answer 2

SOLUTION :-

$\displaystyle{\sf{(i)\ \frac{2}{8} }}$

$\displaystyle{\sf{Additive\ inverse\ of\ \frac{2}{8}\ is\ \frac{-2}{8}. }}$

Check :--

$\displaystyle{\sf{\frac{2}{8}+\frac{-2}{8} }}\\\\\displaystyle{\sf{=\frac{2}{8}-\frac{2}{8} =0 }}$

$\rule{100}{2}$

$\displaystyle{\sf{(ii)\ \frac{-5}{9} }}$

$\displaystyle{\sf{Additive\ inverse\ of\ \frac{-5}{9}\ is\ -\frac{-5}{9}=\frac{5}{9} . }}$

Check :--

$\displaystyle{\sf{\frac{-5}{9}+\frac{5}{9}=0 }}$

$\rule{100}{2}$

$\displaystyle{\sf{(iii)\ \frac{-6}{-5}=\frac{6}{5} }}$

$\displaystyle{\sf{Additive\ inverse\ of\ \frac{-5}{-6}\ is\ \frac{-5}{6}. }}$

Check :--

$\displaystyle{\sf{\frac{-5}{-6}+\frac{-5}{6} }}\\\\\displaystyle{\sf{=\frac{5}{6} -\frac{5}{6} =0 }}$

$\rule{100}{2}$

$\displaystyle{\sf{(iv)\ (-1+\frac{4}{17} ) }}$

$\displaystyle{\sf{=\frac{-17+4}{17} }}\\\\\displaystyle{\sf{=\frac{-13}{17} }}$

$\sf{Additive\ inverse\ of\ \displaystyle{\sf{(iv)\ (-1+\frac{4}{17} )\ is\ \frac{13}{17}. }}}$

Check :--

$\displaystyle{\sf{\frac{-13}{17}+\frac{13}{17} =0}}$

$\underline{\rule{250}{2}}$

$\dashrightarrow$ An additive inverse is a number which when added to the same number with different magnitude gives a sum of zero.

$\dashrightarrow$ Some logic used :-

• (-) × (+) = (-)

• (+) × (-) = (-)

• (-) × (-) = (+)

• (+) × (+) = (+)

• (-) ÷ (+) = (-)

• (+) ÷ (-) = (-)

• (-) ÷ (-) = (+)

• (+) ÷ (+) = (+)