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Answer :
Sure, I'd be happy to help you understand how to solve this problem step-by-step!
First, we need to add the three mixed number weights together: [tex]\( 45 \frac{2}{5}\)[/tex] pounds, [tex]\(126 \frac{1}{2}\)[/tex] pounds, and [tex]\(88 \frac{3}{4}\)[/tex] pounds.
### Step 1: Convert each mixed number to an improper fraction
To make the addition easier, we'll convert each mixed number to an improper fraction first.
1. Convert [tex]\( 45 \frac{2}{5} \)[/tex] to an improper fraction:
- [tex]\( 45 \frac{2}{5} = 45 + \frac{2}{5} \)[/tex]
- [tex]\( 45 = \frac{45 \cdot 5}{5} = \frac{225}{5} \)[/tex]
- [tex]\( 45 \frac{2}{5} = \frac{225}{5} + \frac{2}{5} = \frac{225+2}{5} = \frac{227}{5} \)[/tex]
2. Convert [tex]\( 126 \frac{1}{2} \)[/tex] to an improper fraction:
- [tex]\( 126 \frac{1}{2} = 126 + \frac{1}{2} \)[/tex]
- [tex]\( 126 = \frac{126 \cdot 2}{2} = \frac{252}{2} \)[/tex]
- [tex]\( 126 \frac{1}{2} = \frac{252}{2} + \frac{1}{2} = \frac{252+1}{2} = \frac{253}{2} \)[/tex]
3. Convert [tex]\( 88 \frac{3}{4} \)[/tex] to an improper fraction:
- [tex]\( 88 \frac{3}{4} = 88 + \frac{3}{4} \)[/tex]
- [tex]\( 88 = \frac{88 \cdot 4}{4} = \frac{352}{4} \)[/tex]
- [tex]\( 88 \frac{3}{4} = \frac{352}{4} + \frac{3}{4} = \frac{352+3}{4} = \frac{355}{4} \)[/tex]
### Step 2: Find a common denominator and add the fractions
Next, we need a common denominator to add these fractions together. The least common multiple (LCM) of the denominators (5, 2, and 4) is 20.
1. Convert [tex]\(\frac{227}{5}\)[/tex] to a fraction with a denominator of 20:
- [tex]\(\frac{227}{5} = \frac{227 \cdot 4}{5 \cdot 4} = \frac{908}{20}\)[/tex]
2. Convert [tex]\(\frac{253}{2}\)[/tex] to a fraction with a denominator of 20:
- [tex]\(\frac{253}{2} = \frac{253 \cdot 10}{2 \cdot 10} = \frac{2530}{20}\)[/tex]
3. Convert [tex]\(\frac{355}{4}\)[/tex] to a fraction with a denominator of 20:
- [tex]\(\frac{355}{4} = \frac{355 \cdot 5}{4 \cdot 5} = \frac{1775}{20}\)[/tex]
Now, add the fractions together:
[tex]\[ \frac{908}{20} + \frac{2530}{20} + \frac{1775}{20} = \frac{908 + 2530 + 1775}{20} = \frac{5213}{20} \][/tex]
### Step 3: Convert the improper fraction back to a mixed number
To find the mixed number form, divide the numerator by the denominator:
[tex]\[ 5213 \div 20 = 260 \text{ R } 13 \][/tex]
Therefore,
[tex]\[ \frac{5213}{20} = 260 \frac{13}{20} \][/tex]
### Final Answer
The total weight of the shipment is [tex]\( 260 \frac{13}{20} \)[/tex] pounds.
First, we need to add the three mixed number weights together: [tex]\( 45 \frac{2}{5}\)[/tex] pounds, [tex]\(126 \frac{1}{2}\)[/tex] pounds, and [tex]\(88 \frac{3}{4}\)[/tex] pounds.
### Step 1: Convert each mixed number to an improper fraction
To make the addition easier, we'll convert each mixed number to an improper fraction first.
1. Convert [tex]\( 45 \frac{2}{5} \)[/tex] to an improper fraction:
- [tex]\( 45 \frac{2}{5} = 45 + \frac{2}{5} \)[/tex]
- [tex]\( 45 = \frac{45 \cdot 5}{5} = \frac{225}{5} \)[/tex]
- [tex]\( 45 \frac{2}{5} = \frac{225}{5} + \frac{2}{5} = \frac{225+2}{5} = \frac{227}{5} \)[/tex]
2. Convert [tex]\( 126 \frac{1}{2} \)[/tex] to an improper fraction:
- [tex]\( 126 \frac{1}{2} = 126 + \frac{1}{2} \)[/tex]
- [tex]\( 126 = \frac{126 \cdot 2}{2} = \frac{252}{2} \)[/tex]
- [tex]\( 126 \frac{1}{2} = \frac{252}{2} + \frac{1}{2} = \frac{252+1}{2} = \frac{253}{2} \)[/tex]
3. Convert [tex]\( 88 \frac{3}{4} \)[/tex] to an improper fraction:
- [tex]\( 88 \frac{3}{4} = 88 + \frac{3}{4} \)[/tex]
- [tex]\( 88 = \frac{88 \cdot 4}{4} = \frac{352}{4} \)[/tex]
- [tex]\( 88 \frac{3}{4} = \frac{352}{4} + \frac{3}{4} = \frac{352+3}{4} = \frac{355}{4} \)[/tex]
### Step 2: Find a common denominator and add the fractions
Next, we need a common denominator to add these fractions together. The least common multiple (LCM) of the denominators (5, 2, and 4) is 20.
1. Convert [tex]\(\frac{227}{5}\)[/tex] to a fraction with a denominator of 20:
- [tex]\(\frac{227}{5} = \frac{227 \cdot 4}{5 \cdot 4} = \frac{908}{20}\)[/tex]
2. Convert [tex]\(\frac{253}{2}\)[/tex] to a fraction with a denominator of 20:
- [tex]\(\frac{253}{2} = \frac{253 \cdot 10}{2 \cdot 10} = \frac{2530}{20}\)[/tex]
3. Convert [tex]\(\frac{355}{4}\)[/tex] to a fraction with a denominator of 20:
- [tex]\(\frac{355}{4} = \frac{355 \cdot 5}{4 \cdot 5} = \frac{1775}{20}\)[/tex]
Now, add the fractions together:
[tex]\[ \frac{908}{20} + \frac{2530}{20} + \frac{1775}{20} = \frac{908 + 2530 + 1775}{20} = \frac{5213}{20} \][/tex]
### Step 3: Convert the improper fraction back to a mixed number
To find the mixed number form, divide the numerator by the denominator:
[tex]\[ 5213 \div 20 = 260 \text{ R } 13 \][/tex]
Therefore,
[tex]\[ \frac{5213}{20} = 260 \frac{13}{20} \][/tex]
### Final Answer
The total weight of the shipment is [tex]\( 260 \frac{13}{20} \)[/tex] pounds.
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