Question
6. Diana has \( 3 \frac{1}{4} \) bags of nuts. Each bag holds \( 4 \frac{1}{2} \) pounds. How many pounds of nuts does Diana have? Diana has pounds of nuts.
Ask by Welch Parry. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Diana has 14 5/8 pounds of nuts.
Solution
To find the total pounds of nuts Diana has, multiply the number of bags by the pounds per bag.
Step 1. Convert the mixed numbers to improper fractions.
• 3 1/4 = (3 × 4 + 1)/4 = 13/4
• 4 1/2 = (4 × 2 + 1)/2 = 9/2
Step 2. Multiply the fractions:
13/4 × 9/2 = (13 × 9)/(4 × 2) = 117/8
Step 3. Convert 117/8 to a mixed number.
Divide 117 by 8:
8 goes into 117 exactly 14 times (since 14 × 8 = 112) with a remainder of 5.
So, 117/8 = 14 5/8
Thus, Diana has 14 5/8 pounds of nuts.
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Simplify this solution Extra Insights
To find out how many pounds of nuts Diana has, we need to multiply the number of bags by the weight of each bag. First, convert \( 3 \frac{1}{4} \) to an improper fraction: \( 3 \frac{1}{4} = \frac{13}{4} \). Next, convert \( 4 \frac{1}{2} \) to an improper fraction as well: \( 4 \frac{1}{2} = \frac{9}{2} \). Now, multiply these two fractions: \[ \frac{13}{4} \times \frac{9}{2} = \frac{117}{8}. \] Finally, convert \( \frac{117}{8} \) back to a mixed number to find out how many pounds Diana has. Dividing, we get \( 14 \frac{5}{8} \) pounds. So, Diana has \( 14 \frac{5}{8} \) pounds of nuts. Diana has \( 14 \frac{5}{8} \) pounds of nuts.
