A baker made 20 pies. A Boy Scout troop buys one-fourth of his pies, a preschool teacher buys one-third of his pies, and a caterer buys one-sixth of his pies. How many pies does the baker have left?

A baker made 20 pies. A Boy Scout troop buys one-fourth of his pies, a preschool teacher buys one-third of his pies, and a caterer buys one-sixth of his pies. How many pies does the baker 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 3/12. (1/4 = 3/12).

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 pies have been sold.

\(\frac{\mathrm{9} }{\mathrm{12}}\) can be reduced to \(\frac{\mathrm{3} }{\mathrm{4}}\). \(\frac{\mathrm{3} }{\mathrm{4}}\) or 75% of the pies have been sold.

20 × 0.75 = 15. 15 of 20 pies have been sold. 20 – 15 = 5 pies remaining.

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 3/12. (1/4 = 3/12).

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 pies have been sold.

\(\frac{\mathrm{9} }{\mathrm{12}}\) can be reduced to \(\frac{\mathrm{3} }{\mathrm{4}}\). \(\frac{\mathrm{3} }{\mathrm{4}}\) or 75% of the pies have been sold.

20 × 0.75 = 15. 15 of 20 pies have been sold. 20 – 15 = 5 pies remaining.