Question

What mumber should be added to $8\frac{2}{3}$ to get $12\frac{5}{6}$?

Answer 1

Let the number that should be added in $8\frac{2}{3}$ be $x$ to get $12\frac{5}{6}$

$\Rightarrow$ $8\frac{2}{3}+x=12\frac{5}{6}$
Now, we have :

$8\frac{2}{3}+x=12\frac{5}{6}$

$\text{Mixed Fraction}=\frac{\text{Integral part}\times \text{Denominator}+\text{Numerator}}{\text{Denominator}}$

We will use the above formula to convert the mixed fraction into improper fraction.

$\frac{8\times 3+2}{3}+x=\frac{12\times 6+5}{6}$

$\Rightarrow$ $\frac{24+2}{3}+x=\frac{72+5}{6}$

$\Rightarrow$ $\frac{26}{3}+x=\frac{77}{6}$

$\Rightarrow$ $x=\frac{77}{6}-\frac{26}{3}$

$x=\frac{77}{6}-\frac{26\times 2}{3\times 2}$

[LCM of $(6,3)=6$]

$x=\frac{77}{6}-\frac{52}{6}=\frac{77-52}{6}=\frac{25}{6}$

Hence, $\frac{25}{6}$ or $4\frac{1}{6}$ should be added to $8\frac{2}{3}$ to get $12\frac{5}{6}$