To determine how many ounces the kitten gained before it went home with its new owner, we start by analyzing the given information:
1. The kitten's initial weight at birth was [tex]\(3 \frac{3}{8}\)[/tex] ounces.
2. The kitten’s final weight when it was sold was [tex]\(5 \frac{1}{2}\)[/tex] ounces.
To find the weight gain, we need to subtract the initial weight from the final weight. Let's break this down step-by-step:
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers to improper fractions for easier subtraction.
#### Initial Weight:
[tex]\[ 3 \frac{3}{8} = 3 + \frac{3}{8} \][/tex]
Convert the whole number 3 into a fraction with a denominator of 8:
[tex]\[ 3 = \frac{3 \times 8}{8} = \frac{24}{8} \][/tex]
Add the fractions:
[tex]\[ 3 \frac{3}{8} = \frac{24}{8} + \frac{3}{8} = \frac{27}{8} \][/tex]
#### Final Weight:
[tex]\[ 5 \frac{1}{2} = 5 + \frac{1}{2} \][/tex]
Convert the whole number 5 into a fraction with a denominator of 2:
[tex]\[ 5 = \frac{5 \times 2}{2} = \frac{10}{2} \][/tex]
Add the fractions:
[tex]\[ 5 \frac{1}{2} = \frac{10}{2} + \frac{1}{2} = \frac{11}{2} \][/tex]
### Step 2: Find a Common Denominator
To subtract the fractions, we need a common denominator. The least common multiple (LCM) of 8 and 2 is 8.
Convert [tex]\(\frac{11}{2}\)[/tex] to a fraction with a denominator of 8:
[tex]\[ \frac{11}{2} = \frac{11 \times 4}{2 \times 4} = \frac{44}{8} \][/tex]
### Step 3: Subtract the Fractions
Now, subtract the initial weight from the final weight:
[tex]\[ \text{Weight Gain} = \frac{44}{8} - \frac{27}{8} = \frac{44 - 27}{8} = \frac{17}{8} \][/tex]
### Step 4: Convert Improper Fraction to a Mixed Number
Convert [tex]\(\frac{17}{8}\)[/tex] to a mixed number:
[tex]\[ \frac{17}{8} = 2 \frac{1}{8} \][/tex]
Thus, the kitten gained [tex]\( 2 \frac{1}{8} \)[/tex] ounces before it went home with its new owner.
Therefore, the correct answer is:
B. [tex]\( 2 \frac{1}{8} \)[/tex] ounces
