Question

Mary is going to make a birthday cake. She will need 1 2/3 cups of sugar for the cake and 2 1/2 cups of sugar for the frosting. How many cups of sugar will Mary need for the frosted birthday cake?

Answer 1

Mary will need a total of 4 1/6 cups of sugar for both the cake and the frosting, which is the sum of 1 2/3 cups and 2 1/2 cups.

Step-by-step explanation:

Calculating the Total Cups of Sugar Needed

Mary needs to combine the amount of sugar for the cake and for the frosting to find out how much she needs in total. To do this, we can add the fractions following these steps:

1. Convert the mixed numbers to improper fractions.
2. Add the fractions.
3. Simplify the sum if necessary.

For the cake, 1 2/3 cups of sugar can be expressed as 5/3 (since 1 * 3/3 + 2/3 = 5/3). For the frosting, 2 1/2 cups of sugar can be expressed as 5/2 (since 2 * 2/2 + 1/2 = 5/2).

Next, we find a common denominator, which in this case is 6. The sum of the fractions is:

(5/3 * 2/2) + (5/2 * 3/3) = 10/6 + 15/6 = 25/6

Finally, converting the improper fraction back to a mixed number gives us 4 1/6 cups of sugar in total.

Mary will need 4 1/6 cups of sugar to make her frosted birthday cake.