Answer :
To find the sum of [tex]\(6 \frac{3}{5}\)[/tex] and [tex]\(2 \frac{4}{5}\)[/tex], follow these steps:
1. Convert each mixed number to an improper fraction:
- For [tex]\(6 \frac{3}{5}\)[/tex]:
- Multiply the whole number 6 by the denominator 5: [tex]\(6 \times 5 = 30\)[/tex].
- Add the numerator 3: [tex]\(30 + 3 = 33\)[/tex].
- The improper fraction is [tex]\(\frac{33}{5}\)[/tex].
- For [tex]\(2 \frac{4}{5}\)[/tex]:
- Multiply the whole number 2 by the denominator 5: [tex]\(2 \times 5 = 10\)[/tex].
- Add the numerator 4: [tex]\(10 + 4 = 14\)[/tex].
- The improper fraction is [tex]\(\frac{14}{5}\)[/tex].
2. Add the improper fractions:
- The fractions have the same denominator, so you can add the numerators.
- [tex]\(33 + 14 = 47\)[/tex].
- The sum is [tex]\(\frac{47}{5}\)[/tex].
3. Convert the sum back to a mixed number:
- Divide the numerator by the denominator to get the whole number: [tex]\(47 \div 5 = 9\)[/tex] with a remainder of 2.
- The remainder becomes the numerator of the fractional part: [tex]\(\frac{2}{5}\)[/tex].
- So, [tex]\( \frac{47}{5} = 9 \frac{2}{5}\)[/tex].
Thus, the sum of [tex]\(6 \frac{3}{5}\)[/tex] and [tex]\(2 \frac{4}{5}\)[/tex] is [tex]\(9 \frac{2}{5}\)[/tex].
The correct option from the given choices is [tex]\(9 \frac{2}{5}\)[/tex].
1. Convert each mixed number to an improper fraction:
- For [tex]\(6 \frac{3}{5}\)[/tex]:
- Multiply the whole number 6 by the denominator 5: [tex]\(6 \times 5 = 30\)[/tex].
- Add the numerator 3: [tex]\(30 + 3 = 33\)[/tex].
- The improper fraction is [tex]\(\frac{33}{5}\)[/tex].
- For [tex]\(2 \frac{4}{5}\)[/tex]:
- Multiply the whole number 2 by the denominator 5: [tex]\(2 \times 5 = 10\)[/tex].
- Add the numerator 4: [tex]\(10 + 4 = 14\)[/tex].
- The improper fraction is [tex]\(\frac{14}{5}\)[/tex].
2. Add the improper fractions:
- The fractions have the same denominator, so you can add the numerators.
- [tex]\(33 + 14 = 47\)[/tex].
- The sum is [tex]\(\frac{47}{5}\)[/tex].
3. Convert the sum back to a mixed number:
- Divide the numerator by the denominator to get the whole number: [tex]\(47 \div 5 = 9\)[/tex] with a remainder of 2.
- The remainder becomes the numerator of the fractional part: [tex]\(\frac{2}{5}\)[/tex].
- So, [tex]\( \frac{47}{5} = 9 \frac{2}{5}\)[/tex].
Thus, the sum of [tex]\(6 \frac{3}{5}\)[/tex] and [tex]\(2 \frac{4}{5}\)[/tex] is [tex]\(9 \frac{2}{5}\)[/tex].
The correct option from the given choices is [tex]\(9 \frac{2}{5}\)[/tex].