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We are given that:

- Jeanette collects **42 1/2** gallons of water.
- She uses **1 1/4** gallons to water her plants.
- She uses **1/2** of the remaining water to wash her laundry.

Let's break it down step-by-step:

### Step 1: Convert the mixed numbers to improper fractions
- **42 1/2** = \( 42 + \frac{1}{2} = \frac{84}{2} + \frac{1}{2} = \frac{85}{2} \)
- **1 1/4** = \( 1 + \frac{1}{4} = \frac{4}{4} + \frac{1}{4} = \frac{5}{4} \)

### Step 2: Subtract the amount used for watering plants
She used **1 1/4** gallons for the plants, so subtract that from **42 1/2** gallons.

\[
\frac{85}{2} - \frac{5}{4}
\]

To subtract, we need a common denominator. The least common denominator (LCD) of 2 and 4 is 4.

\[
\frac{85}{2} = \frac{170}{4}
\]

Now subtract:

\[
\frac{170}{4} - \frac{5}{4} = \frac{165}{4}
\]

### Step 3: Find half of the remaining water
Now Jeanette uses **1/2** of the remaining water to wash her laundry. So we take half of **165/4**.

\[
\frac{1}{2} \times \frac{165}{4} = \frac{165}{8}
\]

### Step 4: Simplify the fraction
The fraction **165/8** is already in its simplest form, but we can convert it to a mixed number.

\[
165 \div 8 = 20 \text{ remainder } 5
\]

So, **165/8** is equal to **20 5/8**.

### Final Answer:
Jeanette uses **20 5/8** gallons of water to wash her laundry.

Would you like more details on any part of this solution? Here are some related questions you might find helpful:

1. How do you convert mixed numbers to improper fractions?
2. Why do we need a common denominator for subtraction of fractions?
3. How do you simplify fractions and convert them to mixed numbers?
4. What are some real-world applications of fractions and mixed numbers?
5. How do you calculate half of a fraction?

**Tip:** When working with fractions, always remember to find the least common denominator when adding or subtracting fractions.

During a rain shower, Jeanette collects 42 1/2 gallons of water in a rain barrel outside her home. She uses 1 1/4 gallons to water plants inside her house. Then, she uses 1/2 of the remaining water to wash a load of dirty laundry. How many gallons of water does Jeanette use to wash her laundry?

Learn how to solve a problem involving mixed numbers and fractions where Jeanette collects 42 1/2 gallons of water, uses 1 1/4 gallons to water plants, and finds half of the remaining water for laundry. This solution covers mixed numbers, subtraction, and multiplication of fractions.

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