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Mathematics

What should be added to -2 to get 38\dfrac{3}{8} ?

Rational Numbers

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Answer

Let xx be added to -2.

2+x=3821+x=38x=3821-2 + x = \dfrac{3}{8}\\[1em] \Rightarrow \dfrac{-2}{1} + x = \dfrac{3}{8}\\[1em] \Rightarrow x = \dfrac{3}{8} - \dfrac{-2}{1}

LCM of 8 and 1 is 2 x 2 x 2 = 8

x=3×18×12×81×8x=38168x=3(16)8x=3+168x=198x=238\Rightarrow x = \dfrac{3 \times 1}{8 \times 1} - \dfrac{-2 \times 8}{1 \times 8}\\[1em] \Rightarrow x = \dfrac{3}{8} - \dfrac{-16}{8}\\[1em] \Rightarrow x = \dfrac{3 - (-16)}{8}\\[1em] \Rightarrow x = \dfrac{3 + 16}{8}\\[1em] \Rightarrow x = \dfrac{19}{8}\\[1em] \Rightarrow x = 2\dfrac{3}{8}

The number added to -2 to get 38\dfrac{3}{8} is 2382\dfrac{3}{8}.

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