Question

a large bakery runs two shifts to make pastries. the refrigerator had 8\frac{1}{3} blocks of butter before the first shift. shift 1 used 5\frac{1}{2} butter blocks. if shift 2 requires 12\frac{1}{3} butter blocks, how many more blocks are needed?
9\frac{1}{2} blocks of butter are needed for shift 2.
6\frac{5}{6} blocks of butter are needed for shift 2.
8\frac{3}{4} blocks of butter are needed for shift 2.
4 blocks of butter are needed for shift 2.

Explanation:

Step1: Convert mixed - numbers to improper fractions

The initial amount of butter is $8\frac{1}{3}=\frac{8\times3 + 1}{3}=\frac{25}{3}$, shift 1 used $5\frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2}$, and shift 2 requires $12\frac{1}{3}=\frac{12\times3 + 1}{3}=\frac{37}{3}$.

Step2: Find the remaining butter after shift 1

First, find a common denominator for the initial amount and the amount used in shift 1. The common denominator of 3 and 2 is 6. So, $\frac{25}{3}=\frac{25\times2}{3\times2}=\frac{50}{6}$ and $\frac{11}{2}=\frac{11\times3}{2\times3}=\frac{33}{6}$. The remaining butter after shift 1 is $\frac{50}{6}-\frac{33}{6}=\frac{50 - 33}{6}=\frac{17}{6}$.

Step3: Convert the remaining butter and the required amount for shift 2 to the same denominator

The amount required for shift 2 is $\frac{37}{3}=\frac{37\times2}{3\times2}=\frac{74}{6}$, and the remaining butter is $\frac{17}{6}$.

Step4: Calculate the additional butter needed

Subtract the remaining butter from the butter required for shift 2: $\frac{74}{6}-\frac{17}{6}=\frac{74 - 17}{6}=\frac{57}{6}=9\frac{1}{2}$.

Answer:

$9\frac{1}{2}$ blocks of butter are needed for shift 2.