Question

Question 100.
Add $1\frac{1}{4}$ and $6\frac{1}{2}$

Answer 1

As per the question we have to find $1\frac{1}{4}+6\frac{1}{2}$

$1\frac{1}{4}+6\frac{1}{2}$

We can express a mixed fraction as an improper fraction as $\frac{(\text{Whole}\times \text{Denominator})\text{+ Numerator}}{\text{Denominator}}$.

=$\frac{1\times 4+1}{4}+\frac{6\times 2+1}{2}$
=$\frac{5}{4}+\frac{13}{2}$

Now, the LCM of the denominator of the fractions $\frac{5}{4}$ and $\frac{13}{2}$ i.e. the LCM of 4 and 2 is 4.

$\therefore$ $\frac{5}{4}+\frac{13}{2}$

=$\frac{5\times 1}{4\times 1}+\frac{13\times 2}{2\times 2}$
=$\frac{5}{4}+\frac{26}{4}$
=$\frac{5+26}{4}=\frac{31}{4}$

We can express an improper fraction as a mixed fraction by dividing the numerator by denominator to obtain the quotient and the remainder.

Then the mixed fraction will be written as $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\therefore 1\frac{1}{4}+6\frac{1}{2}=\frac{31}{4}=7\frac{3}{4}$

$\left[\begin{array}{c}\because 4\left)31\right(7\\ \frac{28}{3}\end{array}\right]$