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Theodore has 20 baseball cards. He sells $$\frac{\mathrm{1} }{\mathrm{4}}$$ of his cards to Tom, $$\frac{\mathrm{1} }{\mathrm{3}}$$ of his cards to Larry, and his Mom accidently throws away 1/6 of his cards. How many baseball cards does Theodore have left?
Detailed Explanation
Convert the different denominators to a common denominator that all the denominators can divide into evenly. 4, 3, and 6 all divide evenly into 12.
To convert $$\frac{\mathrm{1} }{\mathrm{4}}$$ to $$\frac{\mathrm{x} }{\mathrm{12}}$$, divide 12 (the new common denominator) by 4 (the old common denominator) to get 3.
Then multiply $$\frac{\mathrm{1} }{\mathrm{4}}$$ by $$\frac{\mathrm{3} }{\mathrm{3}}$$ (another way of saying 1).
The product is $$\frac{\mathrm{3} }{\mathrm{12}}$$. ($$\frac{\mathrm{1} }{\mathrm{4}}$$ = $$\frac{\mathrm{3} }{\mathrm{12}}$$).
Do the same calculation for the other fractions: $$\frac{\mathrm{1} }{\mathrm{3}}$$ = $$\frac{\mathrm{4} }{\mathrm{12}}$$ and $$\frac{\mathrm{1} }{\mathrm{6}}$$ = $$\frac{\mathrm{2} }{\mathrm{12}}$$.
Then add the new numerators together: 3 + 4 + 2 = 9.
Place the added numerator over the new denominator, and you can see that $$\frac{\mathrm{9} }{\mathrm{12}}$$ of the cards have been sold or lost.
$$\frac{\mathrm{9} }{\mathrm{12}}$$ can be reduced to $$\frac{\mathrm{3} }{\mathrm{4}}$$.
$$\frac{\mathrm{3} }{\mathrm{4}}$$ or 75% of the cards have been sold or lost.