Question

1. jennifer had $3\frac{3}{4}$ lbs of tomatoes. she used $\frac{1}{3}$ of that amount to make a salad. how many pounds of tomatoes did she use? (multiply)

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \( 3\frac{3}{4} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 3\frac{3}{4} \), we have \( a = 3 \), \( b = 3 \), \( c = 4 \). Then \( 3\times4+3 = 15 \), so \( 3\frac{3}{4}=\frac{15}{4} \).

Step2: Multiply by the fraction used

We need to find \( \frac{1}{3} \) of \( \frac{15}{4} \), which means multiplying \( \frac{15}{4} \) by \( \frac{1}{3} \). The multiplication of fractions is \( \frac{n_1}{d_1}\times\frac{n_2}{d_2}=\frac{n_1\times n_2}{d_1\times d_2} \). So \( \frac{15}{4}\times\frac{1}{3}=\frac{15\times1}{4\times3}=\frac{15}{12} \).

Step3: Simplify the result

Simplify \( \frac{15}{12} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. \( \frac{15\div3}{12\div3}=\frac{5}{4} \), and \( \frac{5}{4} = 1\frac{1}{4} \).

Answer:

\( 1\frac{1}{4} \) (or \( \frac{5}{4} \)) pounds