Question

The jogging track at Rahul's school is $\frac{3}{4}$ mile long. Yesterday Rahul completed two laps on the track. If he ran $\frac{1}{3}$ of the distance and walked the remainder of the way, how far did he walk?

Answer 1

The jogging track is $\dfrac{3}{4}$ miles long, and Rahul completed two laps around the track, so to find how far he has completed you would multiply only the numerator of $\dfrac{3}{4}$ by 2 (because if you multiplied both the numerator and the denominator by 2, it would just be an equivalent fraction of $\dfrac{3}{4}$).

$\dfrac{3}{4} \times \dfrac{2}{1} = \dfrac{6}{4}$, so Rahul has completed $\dfrac{6}{4}$ miles ($1\dfrac{1}{2}$).

Rahul ran $\dfrac{1}{3}$ of the distance, so divide $\dfrac{6}{4}$ by 3 to find out how much is one-third of the total distance he has completed.

$\dfrac{6}{4} \div 3$ → $\dfrac{6}{4} \times \dfrac{1}{3}$ (multiplying by the reciprocal is the same thing as dividing)

$\dfrac{6}{4} \times \dfrac{1}{3}$ = $\dfrac{6}{12}$, or $\dfrac{1}{2}$

Subtract one-third of the total distance, which we just found is $\dfrac{1}{2}$ miles, from the total distance Rahul completed, $\dfrac{6}{4}$ miles.

$\dfrac{6}{4} - \dfrac{1}{2}$

Multiply $\dfrac{1}{2}$ by $\dfrac{2}{2}$ to make both fractions have common denominators. Your new subtraction problem should look like:

$\dfrac{6}{4} - \dfrac{2}{4} = \dfrac{4}{4}$, which is equivalent to 1, so this means that Rahul walked 1 mile.