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?

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

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