Question
Find a rational number exactly halfway between. $\frac{5}{-13}$ and $\frac{-7}{9}$
✓
Answer
We know that, a rational number, which is haifway between two rational number
i.e. $a$ and $b =\frac{\text{a}+\text{b}}{2}.$
Given rational numbers are $\frac{5}{-13}$ and $\frac{-7}{9}.$
Hence, $\text{a} =-\frac{5}{13}$ and $\text{b}=-\frac{7}{9}$
$\therefore\frac{\text{a}+\text{b}}{2}=\frac{\frac{-5}{13}+\big(-\frac{7}{9}\big)}{2}=\frac{\frac{-5}{13}-\frac{7}{9}}{2}$
$=\frac{\frac{-5\times9}{13\times9}-\frac{7\times13}{9\times13}}{2}$
$=\frac{\frac{-45}{117}-\frac{91}{117}}{2}=\frac{\frac{-45-49}{117}}{2}$
$=\frac{-136}{117\times2}=\frac{-136}{234}$
Hecne, the exaclty halfway betweenm $\frac{5}{-13}$ and $\frac{-7}{9}$ is $-\frac{136}{234}.$
i.e. $a$ and $b =\frac{\text{a}+\text{b}}{2}.$
Given rational numbers are $\frac{5}{-13}$ and $\frac{-7}{9}.$
Hence, $\text{a} =-\frac{5}{13}$ and $\text{b}=-\frac{7}{9}$
$\therefore\frac{\text{a}+\text{b}}{2}=\frac{\frac{-5}{13}+\big(-\frac{7}{9}\big)}{2}=\frac{\frac{-5}{13}-\frac{7}{9}}{2}$
$=\frac{\frac{-5\times9}{13\times9}-\frac{7\times13}{9\times13}}{2}$
$=\frac{\frac{-45}{117}-\frac{91}{117}}{2}=\frac{\frac{-45-49}{117}}{2}$
$=\frac{-136}{117\times2}=\frac{-136}{234}$
Hecne, the exaclty halfway betweenm $\frac{5}{-13}$ and $\frac{-7}{9}$ is $-\frac{136}{234}.$
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