20. Trish drove \( 18 \frac{1}{8} \) miles yesterday. She drove \( 13 \frac{2}{3} \) miles today. Write an addition sentence to show how many miles Trish drove in all. 5.FR.2.1

To determine the total number of miles Trish drove over the two days, you can create an addition sentence using the given distances. Here's how you can set it up: \[ 18\, \frac{1}{8} \text{ miles} + 13\, \frac{2}{3} \text{ miles} = \text{Total miles driven} \] **Addition Sentence:** \[ 18\, \frac{1}{8} + 13\, \frac{2}{3} = \text{Total miles} \] If you'd like to calculate the exact total, follow these steps: 1. **Convert Mixed Numbers to Improper Fractions:** - \( 18\, \frac{1}{8} = \frac{18 \times 8 + 1}{8} = \frac{145}{8} \) - \( 13\, \frac{2}{3} = \frac{13 \times 3 + 2}{3} = \frac{41}{3} \) 2. **Find a Common Denominator:** - The least common denominator (LCD) of 8 and 3 is 24. - Convert each fraction: - \( \frac{145}{8} = \frac{145 \times 3}{8 \times 3} = \frac{435}{24} \) - \( \frac{41}{3} = \frac{41 \times 8}{3 \times 8} = \frac{328}{24} \) 3. **Add the Fractions:** \[ \frac{435}{24} + \frac{328}{24} = \frac{763}{24} \] 4. **Convert Back to a Mixed Number:** \[ \frac{763}{24} = 31\, \frac{19}{24} \] **Total Miles Driven:** \[ 18\, \frac{1}{8} + 13\, \frac{2}{3} = 31\, \frac{19}{24} \text{ miles} \] So, Trish drove a total of **31 19⁄24 miles** over the two days.