Question

iii. simplifying expressions to solve problems
topic practice
a. solve each problem.

1. elena is baking cookies. she has $6\frac{7}{8}$ cups of sugar. each batch of cookies requires $\frac{3}{4}$ cup of sugar. how many full batches of cookies can elena make? how much sugar will she have left over?
2. a construction company is building concrete pillars at the entra of an auditorium. each pillar requires 5.75 cubic yards of concr

Explanation:

Step1: Convert mixed number to improper fraction

Elena has \( 6\frac{7}{8} \) cups of sugar. Convert this mixed number to an improper fraction: \( 6\frac{7}{8}=\frac{6\times8 + 7}{8}=\frac{55}{8} \) cups.

Step2: Divide total sugar by sugar per batch

Each batch requires \( \frac{3}{4} \) cup of sugar. To find the number of batches, divide \( \frac{55}{8} \) by \( \frac{3}{4} \): \( \frac{55}{8}\div\frac{3}{4}=\frac{55}{8}\times\frac{4}{3}=\frac{55}{6}=9\frac{1}{6} \). So, the number of full batches is 9.

Step3: Calculate sugar used for 9 batches

Sugar used for 9 batches: \( 9\times\frac{3}{4}=\frac{27}{4}=6\frac{3}{4} \) cups.

Step4: Convert \( 6\frac{3}{4} \) to eighths

Convert \( 6\frac{3}{4} \) to a fraction with denominator 8: \( 6\frac{3}{4}=6\frac{6}{8} \).

Step5: Subtract to find leftover sugar

Subtract the sugar used from the total sugar: \( 6\frac{7}{8}-6\frac{6}{8}=\frac{1}{8} \) cup.

Answer:

Elena can make 9 full batches of cookies, and she will have \( \frac{1}{8} \) cup of sugar left over.