To solve this problem, we need to multiply 2/3 by 3 1/2. We do this because we are making the recipe 3 1/2 times, which means we need the amount of milk for one recipe multiplied by the amount of times you are completing the recipe. To multiply these two numbers, we first need to convert 3 1/2 to an improper fraction. To do this, we multiply the denominator by the whole number and add the numerator, while keeping the same denominator. This is modeled below:
3 1/2 = (2*3 + 1)/2 = (6+1)/2 = 7/2
Now that we have this information, we can multiply our fractions together by simply multiplying the numerators and denominators together (straight across).
2/3 * 7/2 = (2*7)/(3*2) = 14/6
To simplify this fraction, we need to divide both the numerator and the denominator by the GCF, or greatest common factor, of the two numbers. The greatest common factor is 2.
(14/2) / (6/2) = 7/3
To convert this fraction into a mixed number, we must divide, and make the remainder into a fraction.
7/3 = 2 r 1 = 2 1/3
Therefore, your answer is 2 1/3 cups of milk.
Hope this helps!
