# Scott bought a large bag of cookies at the bakery. He ate \frac{3}{

Scott bought a large bag of cookies at the bakery. He ate $$\displaystyle{\frac{{{3}}}{{{7}}}}$$ of a bag and his sister ate $$\displaystyle{\frac{{{1}}}{{{3}}}}$$ of a bag.
What fraction of the bag remains?

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Michele Tipton

Step 1
Scott ate $$\displaystyle{\frac{{{3}}}{{{7}}}}$$ of a bag and his sister ate $$\displaystyle{\frac{{{1}}}{{{3}}}}$$ of a bag.
so the remaining amount is given by
$$\displaystyle{x}={1}-{\frac{{{3}}}{{{7}}}}-{\frac{{{1}}}{{{3}}}}$$
Step 2
$$\displaystyle{x}={\frac{{{1}}}{{{1}}}}-{\frac{{{3}}}{{{7}}}}-{\frac{{{1}}}{{{3}}}}$$
$$\displaystyle{L}{C}{M}={7}\cdot{3}\cdot{1}$$
$$\displaystyle{L}{C}{M}={21}$$
Adjust Fractions based on the LCM
$$\displaystyle{x}={\frac{{{21}}}{{{21}}}}-{\frac{{{9}}}{{{21}}}}-{\frac{{{7}}}{{{21}}}}$$
$$\displaystyle{x}={\frac{{{21}-{9}-{7}}}{{{21}}}}$$
$$\displaystyle{x}={\frac{{{5}}}{{{21}}}}$$
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