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Answer :
To solve the addition of mixed numbers [tex]\(8 \frac{1}{5} + 6 \frac{2}{3}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(8 \frac{1}{5}\)[/tex]: Multiply the whole number 8 by the denominator 5 and add the numerator 1, resulting in the improper fraction [tex]\(\frac{41}{5}\)[/tex].
- For [tex]\(6 \frac{2}{3}\)[/tex]: Multiply the whole number 6 by the denominator 3 and add the numerator 2, resulting in the improper fraction [tex]\(\frac{20}{3}\)[/tex].
2. Find a common denominator:
- The denominators are 5 and 3. The least common multiple (LCM) is 15.
3. Adjust the improper fractions to have the common denominator of 15:
- For [tex]\(\frac{41}{5}\)[/tex]: Multiply both the numerator and the denominator by 3 to get [tex]\(\frac{123}{15}\)[/tex].
- For [tex]\(\frac{20}{3}\)[/tex]: Multiply both the numerator and the denominator by 5 to get [tex]\(\frac{100}{15}\)[/tex].
4. Add the adjusted fractions:
- Add [tex]\(\frac{123}{15} + \frac{100}{15} = \frac{223}{15}\)[/tex].
5. Convert the improper fraction to a mixed number:
- Divide the numerator 223 by the denominator 15. The quotient is 14 with a remainder of 13.
- Therefore, [tex]\(\frac{223}{15}\)[/tex] converts to the mixed number [tex]\(14 \frac{13}{15}\)[/tex].
Thus, the sum of [tex]\(8 \frac{1}{5} + 6 \frac{2}{3}\)[/tex] is [tex]\(14 \frac{13}{15}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- For [tex]\(8 \frac{1}{5}\)[/tex]: Multiply the whole number 8 by the denominator 5 and add the numerator 1, resulting in the improper fraction [tex]\(\frac{41}{5}\)[/tex].
- For [tex]\(6 \frac{2}{3}\)[/tex]: Multiply the whole number 6 by the denominator 3 and add the numerator 2, resulting in the improper fraction [tex]\(\frac{20}{3}\)[/tex].
2. Find a common denominator:
- The denominators are 5 and 3. The least common multiple (LCM) is 15.
3. Adjust the improper fractions to have the common denominator of 15:
- For [tex]\(\frac{41}{5}\)[/tex]: Multiply both the numerator and the denominator by 3 to get [tex]\(\frac{123}{15}\)[/tex].
- For [tex]\(\frac{20}{3}\)[/tex]: Multiply both the numerator and the denominator by 5 to get [tex]\(\frac{100}{15}\)[/tex].
4. Add the adjusted fractions:
- Add [tex]\(\frac{123}{15} + \frac{100}{15} = \frac{223}{15}\)[/tex].
5. Convert the improper fraction to a mixed number:
- Divide the numerator 223 by the denominator 15. The quotient is 14 with a remainder of 13.
- Therefore, [tex]\(\frac{223}{15}\)[/tex] converts to the mixed number [tex]\(14 \frac{13}{15}\)[/tex].
Thus, the sum of [tex]\(8 \frac{1}{5} + 6 \frac{2}{3}\)[/tex] is [tex]\(14 \frac{13}{15}\)[/tex].
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