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?
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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.
This gives you your new added numerator.
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.
20 × 0.75 = 15. 15 of 20 cards have been sold or lost.
20 – 15 = 5 cards remaining.
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.
This gives you your new added numerator.
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.
20 × 0.75 = 15. 15 of 20 cards have been sold or lost.
20 – 15 = 5 cards remaining.
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