To find out how much one teaspoon of nutmeg weighs, we need to follow these steps:
1. Convert the mixed number to an improper fraction: The box of ground nutmeg weighs [tex]\( 1 \frac{1}{3} \)[/tex] ounces. We convert the mixed number to an improper fraction.
[tex]\[
1 \frac{1}{3} = 1 + \frac{1}{3}
\][/tex]
Converting the whole number 1 to a fraction with a common denominator:
[tex]\[
1 = \frac{3}{3}
\][/tex]
Adding the fractions together:
[tex]\[
\frac{3}{3} + \frac{1}{3} = \frac{4}{3}
\][/tex]
Therefore:
[tex]\[
1 \frac{1}{3} = \frac{4}{3}
\][/tex]
2. Divide the total weight by the number of teaspoons: The total weight of the nutmeg is [tex]\( \frac{4}{3} \)[/tex] ounces, and there are 20 teaspoons of nutmeg in the box. To find the weight of one teaspoon, we divide the total weight by the number of teaspoons. Let's denote the weight of one teaspoon as [tex]\( x \)[/tex].
[tex]\[
x = \frac{\frac{4}{3}}{20}
\][/tex]
3. Simplify the fraction: Dividing by 20 is the same as multiplying by [tex]\( \frac{1}{20} \)[/tex]:
[tex]\[
x = \frac{4}{3} \times \frac{1}{20}
\][/tex]
Multiplying the fractions:
[tex]\[
x = \frac{4 \cdot 1}{3 \cdot 20} = \frac{4}{60}
\][/tex]
Simplifying [tex]\( \frac{4}{60} \)[/tex]:
[tex]\[
\frac{4}{60} = \frac{1}{15}
\][/tex]
Therefore, the weight of one teaspoon of nutmeg is [tex]\( \frac{1}{15} \)[/tex] of an ounce.
The correct answer is D. [tex]\( \frac{1}{15} \)[/tex] of an ounce.
