Question

3 2 ? start fraction, 2, divided by, 3, end fraction of the doughnuts in a box have frosting. \dfrac12 2 1 ? start fraction, 1, divided by, 2, end fraction of the doughnuts with frosting have sprinkles. What fraction of the doughnuts in the box have frosting and sprinkles?

Answer 1

`(1)/(3)` of the doughnuts in the box have frosting and sprinkles.

Explanation:

If there are
`x` doughnuts in the box. Then,
`(2)/(3) * x = (2x)/(3)` of the doughnuts in the box have frosting. Therefore,
`(1)/(2) * (2x)/(3) = (1)/(3)x` of the doughnuts with frosting have sprinkles. This implies that
`(1)/(3)` of the doughnuts in the box have frosting and sprinkles.