In the bakery 1⁄3 of the cakes have strawberry frosting and 3⁄7 of the cakes with strawberry frosting have vanilla filling. What fraction of the cakes at the bakery have both strawberry frosting and vanilla filling?

Step-by-step explanation:

Let the number of cakes in the bakery be x.

Given:

Fraction of cakes with strawberry frosting = 1/3 of x

Fraction of cakes with strawberry frosting that have vanilla frosting = 3/7

Fraction of cakes with strawberry frosting with vanilla frosting in the bakery = 1/3 * 3/7 * x

= 1/7 x

fraction of the cakes at the bakery have both strawberry frosting and vanilla filling = 1/7

The fraction of cakes with strawberries frosting and vanilla filling is 1/7

Step-by-step explanation:

Fraction of cakes with strawberries frosting = 1/3

But 3/7 of the 1/3 cakes have both strawberry and vanilla fillings.

Therefore the fraction of cakes with both strawberry and vanilla filling will be:

1/3 * 3/7 = 3/21

Reducing 3/21 to its lowest term, we divide both numerator and denominator by 3, this leaves us with:

(3/3) / (21/3) = 1/7

Fraction of cakes with both strawberry frosting and vanilla filling is 1/7