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Answer :
To solve the problem [tex]\(8 \frac{1}{5} + 6 \frac{2}{3}\)[/tex], we need to add these two mixed numbers. Here's a step-by-step guide to find the sum:
1. Convert the Mixed Numbers to Improper Fractions:
- For [tex]\(8 \frac{1}{5}\)[/tex]:
[tex]\[
8 \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{41}{5}
\][/tex]
- For [tex]\(6 \frac{2}{3}\)[/tex]:
[tex]\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3}
\][/tex]
2. Find a Common Denominator:
- The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15, which will be our common denominator.
3. Convert the Fractions to have the Same Denominator:
- Convert [tex]\(\frac{41}{5}\)[/tex] to have 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 have a denominator of 15:
[tex]\[
\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}
\][/tex]
4. Add the Fractions:
- Now that both fractions have the same denominator, we can add them:
[tex]\[
\frac{123}{15} + \frac{100}{15} = \frac{223}{15}
\][/tex]
5. Convert the Improper Fraction Back to a Mixed Number:
- Divide the numerator by the denominator to find the whole number and the remaining fraction:
[tex]\[
223 \div 15 = 14 \quad \text{remainder} \quad 13
\][/tex]
- So, [tex]\(\frac{223}{15}\)[/tex] can be expressed as the mixed number [tex]\(14 \frac{13}{15}\)[/tex].
Thus, the sum [tex]\(8 \frac{1}{5} + 6 \frac{2}{3}\)[/tex] equals [tex]\(14 \frac{13}{15}\)[/tex].
1. Convert the Mixed Numbers to Improper Fractions:
- For [tex]\(8 \frac{1}{5}\)[/tex]:
[tex]\[
8 \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{41}{5}
\][/tex]
- For [tex]\(6 \frac{2}{3}\)[/tex]:
[tex]\[
6 \frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3}
\][/tex]
2. Find a Common Denominator:
- The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15, which will be our common denominator.
3. Convert the Fractions to have the Same Denominator:
- Convert [tex]\(\frac{41}{5}\)[/tex] to have 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 have a denominator of 15:
[tex]\[
\frac{20}{3} = \frac{20 \times 5}{3 \times 5} = \frac{100}{15}
\][/tex]
4. Add the Fractions:
- Now that both fractions have the same denominator, we can add them:
[tex]\[
\frac{123}{15} + \frac{100}{15} = \frac{223}{15}
\][/tex]
5. Convert the Improper Fraction Back to a Mixed Number:
- Divide the numerator by the denominator to find the whole number and the remaining fraction:
[tex]\[
223 \div 15 = 14 \quad \text{remainder} \quad 13
\][/tex]
- So, [tex]\(\frac{223}{15}\)[/tex] can be expressed as the mixed number [tex]\(14 \frac{13}{15}\)[/tex].
Thus, the sum [tex]\(8 \frac{1}{5} + 6 \frac{2}{3}\)[/tex] equals [tex]\(14 \frac{13}{15}\)[/tex].
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