The sum of two rational numbers is −23\dfrac{-2}{3}3−2. If one of them is −815\dfrac{-8}{15}15−8, find the other.
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Let xxx be the other number. −815+x=−23⇒x=−23−−815\dfrac{-8}{15} + x = \dfrac{-2}{3}\\[1em] ⇒ x = \dfrac{-2}{3} - \dfrac{-8}{15}15−8+x=3−2⇒x=3−2−15−8
LCM of 3 and 15 is 3 x 5 = 15
⇒x=−2×53×5−−8×115×1⇒x=−1015−−815⇒x=−10−(−8)15⇒x=−10+815⇒x=−215⇒ x = \dfrac{-2 \times 5}{3 \times 5} - \dfrac{-8 \times 1}{15 \times 1}\\[1em] ⇒ x = \dfrac{-10}{15} - \dfrac{-8}{15}\\[1em] ⇒ x = \dfrac{-10 - (-8)}{15}\\[1em] ⇒ x = \dfrac{-10 + 8}{15}\\[1em] ⇒ x = \dfrac{-2}{15}⇒x=3×5−2×5−15×1−8×1⇒x=15−10−15−8⇒x=15−10−(−8)⇒x=15−10+8⇒x=15−2
The sum of two rational numbers is −23\dfrac{-2}{3}3−2, if one of them is −815\dfrac{-8}{15}15−8, the other number is −215\dfrac{-2}{15}15−2.
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