Question

Question 101.
Katrina rode her bicycle $6\frac{1}{2}$ km in the morning and $8\frac{3}{4}$ km in the evening. Find the distance traveled by her altogether on that day.

Answer 1

Given that

Katrina rode her bicycle $6\frac{1}{2}$ km in the morning and $8\frac{3}{4}$ km in the evening.

Distance traveled by her altogether on that day = $6\frac{1}{2}$ + $8\frac{3}{4}$ km

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

$\therefore$ $6\frac{1}{2}+8\frac{3}{4}=\frac{6\times 2+1}{2}+\frac{8\times 4+3}{4}=\frac{13}{2}+\frac{32+3}{4}=\frac{13}{2}+\frac{35}{4}$

Now, the LCM of the denominator of the fractions $\frac{13}{2}$ and $\frac{35}{4}$ i.e. the LCM of 2 and 4 is 4.

$\therefore \frac{13}{2}+\frac{35}{4}=\frac{13\times 2}{2\times 2}+\frac{35\times 1}{4\times 1}=\frac{26}{4}+\frac{35}{4}=\frac{26+35}{4}=\frac{61}{4}$ km

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 $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\left[\begin{array}{c}4\left)61\right(15\\ \frac{4}{21}\\ \frac{20}{1}\end{array}\right]$

$\therefore 6\frac{1}{2}$ + $8\frac{3}{4}=\frac{61}{4}=15\frac{1}{4}km.$
Hence, the distance traveled by Katrina together on that day is $15\frac{1}{4}km.$