Answer :
Sure, let's break down the addition of the mixed fractions step by step.
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.
For [tex]\(8 \frac{1}{5}\)[/tex]:
- The integer part is 8.
- The fractional part is [tex]\(\frac{1}{5}\)[/tex].
To convert this to an improper fraction:
[tex]\[ 8 \frac{1}{5} = 8 + \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{40 + 1}{5} = \frac{41}{5} \][/tex]
For [tex]\(6 \frac{2}{3}\)[/tex]:
- The integer part is 6.
- The fractional part is [tex]\(\frac{2}{3}\)[/tex].
To convert this to an improper fraction:
[tex]\[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \][/tex]
### Step 2: Find a Common Denominator
We need a common denominator to add the fractions. The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.
Convert [tex]\(\frac{41}{5}\)[/tex] to a fraction with a denominator of 15:
[tex]\[ \frac{41}{5} = \frac{41 \times 3}{5 \times 3} = \frac{123}{15} \][/tex]
Convert [tex]\(\frac{20}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[ \frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15} \][/tex]
### Step 3: Add the Fractions
Now, we add the two fractions:
[tex]\[ \frac{123}{15} + \frac{100}{15} = \frac{123 + 100}{15} = \frac{223}{15} \][/tex]
### Step 4: Convert Back to a Mixed Number
To convert [tex]\(\frac{223}{15}\)[/tex] back to a mixed number:
- Divide 223 by 15 to get the integer part:
[tex]\[ 223 \div 15 = 14 \text{ remainder } 13 \][/tex]
So, [tex]\( \frac{223}{15} = 14 \frac{13}{15} \)[/tex].
### Final Answer
The sum of [tex]\( 8 \frac{1}{5} \)[/tex] and [tex]\( 6 \frac{2}{3} \)[/tex] is:
[tex]\[ 14 \frac{13}{15} \][/tex]
So, the correct answer is:
[tex]\[ 14 \frac{13}{15} \][/tex]
### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.
For [tex]\(8 \frac{1}{5}\)[/tex]:
- The integer part is 8.
- The fractional part is [tex]\(\frac{1}{5}\)[/tex].
To convert this to an improper fraction:
[tex]\[ 8 \frac{1}{5} = 8 + \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{40 + 1}{5} = \frac{41}{5} \][/tex]
For [tex]\(6 \frac{2}{3}\)[/tex]:
- The integer part is 6.
- The fractional part is [tex]\(\frac{2}{3}\)[/tex].
To convert this to an improper fraction:
[tex]\[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3} \][/tex]
### Step 2: Find a Common Denominator
We need a common denominator to add the fractions. The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.
Convert [tex]\(\frac{41}{5}\)[/tex] to a fraction with a denominator of 15:
[tex]\[ \frac{41}{5} = \frac{41 \times 3}{5 \times 3} = \frac{123}{15} \][/tex]
Convert [tex]\(\frac{20}{3}\)[/tex] to a fraction with a denominator of 15:
[tex]\[ \frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15} \][/tex]
### Step 3: Add the Fractions
Now, we add the two fractions:
[tex]\[ \frac{123}{15} + \frac{100}{15} = \frac{123 + 100}{15} = \frac{223}{15} \][/tex]
### Step 4: Convert Back to a Mixed Number
To convert [tex]\(\frac{223}{15}\)[/tex] back to a mixed number:
- Divide 223 by 15 to get the integer part:
[tex]\[ 223 \div 15 = 14 \text{ remainder } 13 \][/tex]
So, [tex]\( \frac{223}{15} = 14 \frac{13}{15} \)[/tex].
### Final Answer
The sum of [tex]\( 8 \frac{1}{5} \)[/tex] and [tex]\( 6 \frac{2}{3} \)[/tex] is:
[tex]\[ 14 \frac{13}{15} \][/tex]
So, the correct answer is:
[tex]\[ 14 \frac{13}{15} \][/tex]
