To find out how many quarts of potting soil Mr. Nelson will use to pot a radish plant, we need to determine \( \frac{3}{8} \) of the amount of soil he uses for a pepper plant.
First, we know that Mr. Nelson used \( 3 \frac{2}{3} \) quarts of soil for a pepper plant. To do the calculation conveniently, we should convert \( 3 \frac{2}{3} \) into an improper fraction:
\[ 3 \frac{2}{3} = 3 + \frac{2}{3} = \frac{9}{3} + \frac{2}{3} = \frac{11}{3} \text{ quarts} \]
Next, we need to calculate \( \frac{3}{8} \) of \( \frac{11}{3} \):
\[ \frac{3}{8} \times \frac{11}{3} \]
When multiplying fractions, we multiply the numerators and the denominators:
\[ = \frac{3 \times 11}{8 \times 3} = \frac{33}{24} \]
Now, we simplify \( \frac{33}{24} \):
Both 33 and 24 can be divided by 3:
\[ = \frac{33 \div 3}{24 \div 3} = \frac{11}{8} \]
Next, we convert \( \frac{11}{8} \) back into a mixed number:
\[ \frac{11}{8} = 1 \frac{3}{8} \]
Thus, Mr. Nelson will use \( 1 \frac{3}{8} \) quarts of potting soil to pot a radish plant.
To summarize:
- He uses \( 3 \frac{2}{3} \) quarts for a pepper plant.
- Calculate \( \frac{3}{8} \) of that amount, which leads to \( 1 \frac{3}{8} \) quarts for the radish plant.
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