To solve the problem, we want to find the total weight of all 12 bags if each bag weighs [tex]\(2 \frac{4}{9}\)[/tex] pounds.
1. Convert the mixed number to an improper fraction:
The weight of each bag is given as [tex]\(2 \frac{4}{9}\)[/tex] pounds. First, let's convert this mixed number to an improper fraction.
[tex]\[
2 \frac{4}{9} = 2 + \frac{4}{9}
\][/tex]
Converting the integer part (2) to a fraction with a denominator of 9:
[tex]\[
2 = \frac{18}{9}
\][/tex]
Now adding the fractions:
[tex]\[
\frac{18}{9} + \frac{4}{9} = \frac{18 + 4}{9} = \frac{22}{9}
\][/tex]
Thus, the weight of each bag is [tex]\(\frac{22}{9}\)[/tex] pounds.
2. Calculate the total weight of all 12 bags:
Now we need to find the total weight of 12 bags, each weighing [tex]\(\frac{22}{9}\)[/tex] pounds.
[tex]\[
\text{Total weight} = 12 \times \frac{22}{9}
\][/tex]
3. Multiply to find the total weight:
Perform the multiplication:
[tex]\[
12 \times \frac{22}{9} = \frac{12 \times 22}{9} = \frac{264}{9}
\][/tex]
4. Convert the fraction to a decimal (if needed):
To convert [tex]\(\frac{264}{9}\)[/tex] to a decimal:
[tex]\[
\frac{264}{9} \approx 29.333333333333336
\][/tex]
Thus, the total weight of all the bags is approximately 29.33 pounds (rounded to two decimal places), and each bag weighs approximately 2.44 pounds (rounded to two decimal places).
