Ms. Clark put icing on 1/3 of a batch of cupcakes. She let Mackenzie put icing on 1/4 of the remaining cupcakes.
A. What fraction of all of the cupcakes did Mackenzie out icing on?
B. What fraction of the cupcakes have no icing?
Solution
A. If Ms. Clark put icing on 1/3 of a batch of cupcakes, then 1 - 1/3 of the batch of cupcakes do not have icing.
1 - 1/3 = 3/3 - 1/3 = 2/3
Then, Mackenzie put icing on 1/4 of 2/3.
1/4 of 2/3 = 1/4 × 2/3 = 2/12 = 1/6
Mackenzie put icing on 1/6 of the batch of cupcakes.
B.
Clark and Mackenzie put icing on 1/3 and 1/6 of the batch of cupcakes.
1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
Clark and Mackenzie put icing on 1/2 of the batch of cupcakes.
The fraction of the cupcakes that have no icing is 1 - 1/2.
1 - 1/2 = 2/2 - 1/2 = 1/2
The fraction of the cupcakes that have no icing is 1/2.