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Answer :
Let's find the sum of the mixed numbers [tex]\( 8 \frac{1}{5} \)[/tex] and [tex]\( 6 \frac{2}{3} \)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\( 8 \frac{1}{5} \)[/tex]:
[tex]\[
8 \frac{1}{5} = 8 + \frac{1}{5} = \frac{40}{5} + \frac{1}{5} = \frac{41}{5}
\][/tex]
- For [tex]\( 6 \frac{2}{3} \)[/tex]:
[tex]\[
6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3}
\][/tex]
2. Find a Common Denominator and Add the Fractions:
- The common denominator for 5 and 3 is 15.
- Convert [tex]\( \frac{41}{5} \)[/tex] to fifteenths:
[tex]\[
\frac{41}{5} = \frac{41 \times 3}{5 \times 3} = \frac{123}{15}
\][/tex]
- Convert [tex]\( \frac{20}{3} \)[/tex] to fifteenths:
[tex]\[
\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}
\][/tex]
- Add the fractions:
[tex]\[
\frac{123}{15} + \frac{100}{15} = \frac{223}{15}
\][/tex]
3. Convert the Improper Fraction Back to a Mixed Number:
- Divide 223 by 15:
[tex]\[
223 \div 15 = 14 \quad \text{remainder: } 13
\][/tex]
- So, the mixed number is:
[tex]\[
14 \frac{13}{15}
\][/tex]
Therefore, the sum of [tex]\( 8 \frac{1}{5} \)[/tex] and [tex]\( 6 \frac{2}{3} \)[/tex] is [tex]\( 14 \frac{13}{15} \)[/tex], which matches option [tex]\( 4 \)[/tex].
1. Convert Mixed Numbers to Improper Fractions:
- For [tex]\( 8 \frac{1}{5} \)[/tex]:
[tex]\[
8 \frac{1}{5} = 8 + \frac{1}{5} = \frac{40}{5} + \frac{1}{5} = \frac{41}{5}
\][/tex]
- For [tex]\( 6 \frac{2}{3} \)[/tex]:
[tex]\[
6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3}
\][/tex]
2. Find a Common Denominator and Add the Fractions:
- The common denominator for 5 and 3 is 15.
- Convert [tex]\( \frac{41}{5} \)[/tex] to fifteenths:
[tex]\[
\frac{41}{5} = \frac{41 \times 3}{5 \times 3} = \frac{123}{15}
\][/tex]
- Convert [tex]\( \frac{20}{3} \)[/tex] to fifteenths:
[tex]\[
\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}
\][/tex]
- Add the fractions:
[tex]\[
\frac{123}{15} + \frac{100}{15} = \frac{223}{15}
\][/tex]
3. Convert the Improper Fraction Back to a Mixed Number:
- Divide 223 by 15:
[tex]\[
223 \div 15 = 14 \quad \text{remainder: } 13
\][/tex]
- So, the mixed number is:
[tex]\[
14 \frac{13}{15}
\][/tex]
Therefore, the sum of [tex]\( 8 \frac{1}{5} \)[/tex] and [tex]\( 6 \frac{2}{3} \)[/tex] is [tex]\( 14 \frac{13}{15} \)[/tex], which matches option [tex]\( 4 \)[/tex].
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