Answer :
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).
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).
