A recipe requires 3/4 cups of nuts for 1 cake. Enter the maximum number of cakes that can be made using 7 1/2 cups of nuts

7.5 / 0.75 = 10 cakes

To determine the maximum number of cakes that can be made using 7 1/2 cups of nuts, we need to divide the total amount of nuts by the amount required for one cake.

First, let's convert the mixed number 7 1/2 to an improper fraction. The whole number, 7, is multiplied by the denominator, 2, and added to the numerator, 1. This gives us 15/2.

Next, we divide 15/2 by 3/4. Dividing fractions involves multiplying by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3.

So, we have (15/2) ÷ (3/4) = (15/2) x (4/3).

To simplify the multiplication, we cancel out any common factors between the numerators and denominators. In this case, 2 can be evenly divided by 2 and 3 can be evenly divided by 3.

After simplification, we have (15/1) x (2/1), which equals 30.

Therefore, the maximum number of cakes that can be made using 7 1/2 cups of nuts is 30.