Gujarat BoardEnglish MediumSTD 7MATHSRational Numbers2 Marks
Question
Find a rational number exactly halfway between. $\frac{1}{6}$ and $\frac{1}{9}$
✓
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 $\frac{1}{6}$ and $\frac{1}{9}.$
Hence, $\text{a} =\frac{1}{6}$ and $\text{b}=\frac{1}{9}$
$\therefore\frac{\text{a}+\text{b}}{2}=\frac{\frac{1}{6}+\frac{1}{9}}{2}=\frac{\frac{1\times3}{6\times3}+\frac{1\times2}{9\times2}}{2}$
$=\frac{\frac{3}{18}+\frac{2}{18}}{2}$
$=\frac{\frac{3+2}{18}}{2}=\frac{\frac{5}{18}}{2}=\frac{5}{18\times2}=\frac{5}{36}$
Hecne, the exaclty halfway betweenm $\frac{1}{6}$ and $\frac{1}{9}$ is $\frac{5}{36.}$
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