Final answer:
The family recycles 13 7/8 pounds of paper every week. This is calculated by converting the total paper used by the family into an improper fraction, then multiplying this by the fraction of waste that gets recycled.
Step-by-step explanation:
This is a fraction multiplication problem. The family uses 18 1/2 pounds of paper in a week and recycles about 3/4 of its waste. To find out how many pounds of paper the family recycles, you multiply the total amount of paper used by the fraction that gets recycled.
Step 1: Convert the mixed number 18 1/2 to an improper fraction, which is 37/2.
Step 2: Multiply the improper fraction 37/2 by 3/4.
Step 3: To multiply fractions, multiply the numerators (top numbers) to get the numerator of the answer, and multiply the denominators (bottom numbers) to get the denominator of the answer: (37 x 3)/(2 x 4) = 111/8.
Step 4: Change the improper fraction back to a mixed number to get the final answer. 111/8 is equal to 13 7/8 pounds. So, the family recycles 13 7/8 pounds of paper a week.
Learn more about Fraction Multiplication