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 1/4 to x/12, divide 12 (the new common denominator) by 4 (the old common denominator) to get 3. Then multiply 1/4 by 3/3 (another way of saying 1). The product is 3/12. (1/4 = 3/12). Do the same calculation for the other fractions: 1/3 = 4/12 and 1/6 = 2/12. 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 9/12 of the pies have been sold. 9/12 can be reduced to 3/4. 3/4 or 75% of the pies have been sold. 20 × 0.75 = 15. 15 of 20 pies have been sold. 20 – 15 = 5 pies remaining.