Answer :
Certainly! Let's solve the problem step-by-step:
### Problem:
Add the mixed numbers [tex]\(8 \frac{1}{5}\)[/tex] and [tex]\(6 \frac{2}{3}\)[/tex].
### Solution:
1. Convert mixed numbers to improper fractions:
- For [tex]\(8 \frac{1}{5}\)[/tex]:
- Multiply the whole number (8) by the denominator (5): [tex]\(8 \times 5 = 40\)[/tex].
- Add the numerator (1) to this result: [tex]\(40 + 1 = 41\)[/tex].
- So, [tex]\(8 \frac{1}{5}\)[/tex] becomes [tex]\(\frac{41}{5}\)[/tex].
- For [tex]\(6 \frac{2}{3}\)[/tex]:
- Multiply the whole number (6) by the denominator (3): [tex]\(6 \times 3 = 18\)[/tex].
- Add the numerator (2) to this result: [tex]\(18 + 2 = 20\)[/tex].
- So, [tex]\(6 \frac{2}{3}\)[/tex] becomes [tex]\(\frac{20}{3}\)[/tex].
2. Find a common denominator:
- The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.
3. Convert fractions to have a common denominator:
- For [tex]\(\frac{41}{5}\)[/tex]:
- Multiply both the numerator and the denominator by 3: [tex]\(\frac{41 \times 3}{5 \times 3} = \frac{123}{15}\)[/tex].
- For [tex]\(\frac{20}{3}\)[/tex]:
- Multiply both the numerator and the denominator by 5: [tex]\(\frac{20 \times 5}{3 \times 5} = \frac{100}{15}\)[/tex].
4. Add the fractions:
- Now that both fractions have the same denominator, add the numerators: [tex]\(\frac{123}{15} + \frac{100}{15} = \frac{223}{15}\)[/tex].
5. Convert the improper fraction back to a mixed number:
- Divide the numerator (223) by the denominator (15): [tex]\(223 \div 15\)[/tex].
- This division gives: 14 with a remainder of 13 (because [tex]\(223 = 14 \times 15 + 13\)[/tex]).
- So, [tex]\(\frac{223}{15}\)[/tex] can be written as [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].
### Final Answer
[tex]\(14 \frac{13}{15}\)[/tex]
### Problem:
Add the mixed numbers [tex]\(8 \frac{1}{5}\)[/tex] and [tex]\(6 \frac{2}{3}\)[/tex].
### Solution:
1. Convert mixed numbers to improper fractions:
- For [tex]\(8 \frac{1}{5}\)[/tex]:
- Multiply the whole number (8) by the denominator (5): [tex]\(8 \times 5 = 40\)[/tex].
- Add the numerator (1) to this result: [tex]\(40 + 1 = 41\)[/tex].
- So, [tex]\(8 \frac{1}{5}\)[/tex] becomes [tex]\(\frac{41}{5}\)[/tex].
- For [tex]\(6 \frac{2}{3}\)[/tex]:
- Multiply the whole number (6) by the denominator (3): [tex]\(6 \times 3 = 18\)[/tex].
- Add the numerator (2) to this result: [tex]\(18 + 2 = 20\)[/tex].
- So, [tex]\(6 \frac{2}{3}\)[/tex] becomes [tex]\(\frac{20}{3}\)[/tex].
2. Find a common denominator:
- The denominators are 5 and 3. The least common multiple (LCM) of 5 and 3 is 15.
3. Convert fractions to have a common denominator:
- For [tex]\(\frac{41}{5}\)[/tex]:
- Multiply both the numerator and the denominator by 3: [tex]\(\frac{41 \times 3}{5 \times 3} = \frac{123}{15}\)[/tex].
- For [tex]\(\frac{20}{3}\)[/tex]:
- Multiply both the numerator and the denominator by 5: [tex]\(\frac{20 \times 5}{3 \times 5} = \frac{100}{15}\)[/tex].
4. Add the fractions:
- Now that both fractions have the same denominator, add the numerators: [tex]\(\frac{123}{15} + \frac{100}{15} = \frac{223}{15}\)[/tex].
5. Convert the improper fraction back to a mixed number:
- Divide the numerator (223) by the denominator (15): [tex]\(223 \div 15\)[/tex].
- This division gives: 14 with a remainder of 13 (because [tex]\(223 = 14 \times 15 + 13\)[/tex]).
- So, [tex]\(\frac{223}{15}\)[/tex] can be written as [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].
### Final Answer
[tex]\(14 \frac{13}{15}\)[/tex]
