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.