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

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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.
Trish drove a total of $$ 31\, \frac{19}{24} $$ miles in all. **Addition Sentence:** $$ 18\, \frac{1}{8} + 13\, \frac{2}{3} = 31\, \frac{19}{24} \text{ miles} $$

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

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