Question

Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari’s bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari’s bag is compared to Juan’s bag.
1 and one-half pounds
mc013-4.jpg pounds
mc013-5.jpg pounds
10 and one-half pounds

Answer 1

To estimate how much heavier Ari's bag is compared to Juan's bag, we can start with the weights given:

- Juan's bag of apples: \(\frac{31}{7}\) pounds
- Ari's bag of oranges: \(\frac{19}{3}\) pounds

First, we can convert these fractions to mixed numbers to make them easier to estimate.

1. For Juan’s bag:
\(\frac{31}{7}\) can be converted to a mixed number:
\[
31 \div 7 = 4 \quad \text{(remainder 3)}
\]
So, \(\frac{31}{7} = 4 \frac{3}{7}\) which is approximately 4.5 pounds.

2. For Ari’s bag:
\(\frac{19}{3}\) can be converted to a mixed number:
\[
19 \div 3 = 6 \quad \text{(remainder 1)}
\]
So, \(\frac{19}{3} = 6 \frac{1}{3}\) which is approximately 6.3 pounds.

Now, we can compare the weights:
- Juan’s bag is approximately 4.5 pounds.
- Ari’s bag is approximately 6.3 pounds.

To find the difference:
\[
6.3 - 4.5 = 1.8
\]

This is approximately 1 and one-half pounds, or \(1.5\) pounds.

Therefore, the final answer is:
**1 and one-half pounds.**