Question
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Lin 5 ent \( 2 \frac{7}{2} \) hours on beth math and andra rode her bike \( 9 \frac{1}{3} \) miles on Monday and \( 6 \frac{4}{5} \) miles on Tuesday How many more miles did ee ride on Monday than on Tuesday?

Ask by Chen Chandler. in the United States
Jan 22,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Andra rode \( 2 \frac{8}{15} \) more miles on Monday than on Tuesday.

Solution

It looks like you're trying to determine how many more miles Andra rode her bike on Monday compared to Tuesday. Let's break it down step by step. **Given:** - **Monday:** Andra rode \( 9 \frac{1}{3} \) miles. - **Tuesday:** Andra rode \( 6 \frac{4}{5} \) miles. **Objective:** Find out how many more miles Andra rode on Monday than on Tuesday. --- ### Step 1: Convert Mixed Numbers to Improper Fractions To make the subtraction easier, let's convert the mixed numbers to improper fractions. 1. **Monday's Distance:** \[ 9 \frac{1}{3} = \frac{(9 \times 3) + 1}{3} = \frac{27 + 1}{3} = \frac{28}{3} \] 2. **Tuesday's Distance:** \[ 6 \frac{4}{5} = \frac{(6 \times 5) + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5} \] --- ### Step 2: Subtract Tuesday's Distance from Monday's Distance Now, subtract the two distances to find the difference. \[ \frac{28}{3} - \frac{34}{5} \] To subtract these fractions, they need a common denominator. The least common denominator (LCD) of 3 and 5 is 15. 1. **Convert Both Fractions to Have a Denominator of 15:** \[ \frac{28}{3} = \frac{28 \times 5}{3 \times 5} = \frac{140}{15} \] \[ \frac{34}{5} = \frac{34 \times 3}{5 \times 3} = \frac{102}{15} \] 2. **Now Subtract:** \[ \frac{140}{15} - \frac{102}{15} = \frac{140 - 102}{15} = \frac{38}{15} \] --- ### Step 3: Convert the Result Back to a Mixed Number \[ \frac{38}{15} = 2 \frac{8}{15} \] **Interpretation:** Andra rode \( 2 \frac{8}{15} \) more miles on Monday than on Tuesday. --- **Final Answer:** Andra rode **\( 2 \frac{8}{15} \)** more miles on Monday than on Tuesday.

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To find out how many more miles Andrea rode on Monday than on Tuesday, we need to subtract the distance she rode on Tuesday from the distance she rode on Monday. On Monday, she rode \( 9 \frac{1}{3} \) miles, which can be converted to an improper fraction: \( 9 \frac{1}{3} = \frac{27}{3} + \frac{1}{3} = \frac{28}{3} \) miles. On Tuesday, she rode \( 6 \frac{4}{5} \) miles, which can also be converted to an improper fraction: \( 6 \frac{4}{5} = \frac{30}{5} + \frac{4}{5} = \frac{34}{5} \) miles. Next, we need a common denominator to subtract these fractions. The least common multiple of 3 and 5 is 15. Now we convert the distances: \( \frac{28}{3} = \frac{28 \times 5}{3 \times 5} = \frac{140}{15} \) miles (Monday), \( \frac{34}{5} = \frac{34 \times 3}{5 \times 3} = \frac{102}{15} \) miles (Tuesday). Now subtract: \( \frac{140}{15} - \frac{102}{15} = \frac{38}{15} \) miles. So, Andrea rode \( 2 \frac{8}{15} \) miles more on Monday than on Tuesday.

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