Kylie wanted to make bread pudding with lemon sauce for dessert for her family. however, she couldn't find a recipe that would make four servings. she decided to use a recipe for eight servings. the recipe for eight called for 1 1/3 cups of raisins. how many cups of raisins will she need for four people?

First, we need to figure out what portion of the recipe we should make. The recipe makes 8 servings, but we only want 4 servings. 4/8 simplifies to 1/2 (if you divide both the numerator and the denominator by the GCF of 4), so we need to halve the recipe. Now, we must find 1/2 of 1 1/3, which is 1/2 * 1 1/3 (because the word "of" refers to multiplication in math). However, we cannot just multiply a fraction by a mixed number, we must first convert the mixed number 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:

1 1/3 = (3*1 + 1)/3 = (3+1)/3 = 4/3

If we substitute in our improper fraction value, we get:

1/2 * 1 1/3

1/2 * 4/3

Now, we are ready to multiply. We just multiply the two numerators together and the two denominators together.

(1 *4) / (3*2) = 4/6

To simplify, we must divide both the numerator and the denominator by their shared greatest common factor, or GCF. The greatest number that both 4 and 6 can be divided by is 2, so we divide both the numerator and denominator by this number, as follows:

(4/2) / (6/2) = 2/3

Therefore, your answer is 2/3 cups of raisins.

Hope this helps!

is only a line? i think so

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)