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# Billy and Ken, the school's cross-country stars, were each running at cross-country practice. Billy was going to run $\frac{3}{4}$ of the training course, and Ken was going to run $\frac{1}{2}$ of the course. However, during practice it started raining, so they could not finish their runs. Billy had finished $\frac{1}{3}$ of his run, while Ken had finished $\frac{1}{2}$ of his run. Draw a picture to determine which cross-country star ran the farthest.

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Billy was going to run $\dfrac{3}{4}$ of the training course, and Ken was going to run $\dfrac{1}{2}$ of the course.

Find the Lowest Common Multiple of the denominators i.e. $4$ and $2$

$2=\textcolor{#c34632}{2} \times 1$

$4=\textcolor{#c34632}{2} \times 2$

The common multiple is $2$. Using the common multiple only once, the LCM of $4$ and $2$ is

$2 \times 2=4$

Use the LCM to find the equivalent fractions i.e. the denominator should be $4$

Billy's area to be completed is

$\frac{3}{4}$

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