Answer :
Sure, let's solve the problem step by step:
We're given two mixed numbers: [tex]\(6 \frac{9}{15}\)[/tex] and [tex]\(6 \frac{14}{15}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- [tex]\(6 \frac{9}{15}\)[/tex] can be converted as follows:
- The whole number part is 6.
- The fraction part is [tex]\(\frac{9}{15}\)[/tex], which can be simplified to [tex]\(\frac{3}{5}\)[/tex] by dividing the numerator and the denominator by 3.
- So, the mixed number becomes [tex]\(6 + \frac{3}{5} = \frac{30}{5} + \frac{3}{5} = \frac{33}{5}\)[/tex].
- [tex]\(6 \frac{14}{15}\)[/tex] can be converted as follows:
- The whole number part is 6.
- The fraction part is [tex]\(\frac{14}{15}\)[/tex].
- So, the mixed number becomes [tex]\(6 + \frac{14}{15} = \frac{90}{15} + \frac{14}{15} = \frac{104}{15}\)[/tex].
2. Find a common denominator and add the fractions:
- The common denominator for 5 and 15 is 15.
- Convert [tex]\(\frac{33}{5}\)[/tex] to a fraction with a denominator of 15:
- Multiply both the numerator and the denominator by 3: [tex]\(\frac{33}{5} = \frac{33 \times 3}{5 \times 3} = \frac{99}{15}\)[/tex].
- Now we can add [tex]\(\frac{99}{15}\)[/tex] and [tex]\(\frac{104}{15}\)[/tex]:
- [tex]\(\frac{99}{15} + \frac{104}{15} = \frac{99 + 104}{15} = \frac{203}{15}\)[/tex].
3. Convert the sum back to a mixed number:
- Divide 203 by 15:
- [tex]\(203 \div 15 = 13\)[/tex] with a remainder of 8.
- The mixed number is [tex]\(13 \frac{8}{15}\)[/tex].
Therefore, [tex]\(6 \frac{9}{15} + 6 \frac{14}{15} = 13 \frac{8}{15}\)[/tex].
We're given two mixed numbers: [tex]\(6 \frac{9}{15}\)[/tex] and [tex]\(6 \frac{14}{15}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- [tex]\(6 \frac{9}{15}\)[/tex] can be converted as follows:
- The whole number part is 6.
- The fraction part is [tex]\(\frac{9}{15}\)[/tex], which can be simplified to [tex]\(\frac{3}{5}\)[/tex] by dividing the numerator and the denominator by 3.
- So, the mixed number becomes [tex]\(6 + \frac{3}{5} = \frac{30}{5} + \frac{3}{5} = \frac{33}{5}\)[/tex].
- [tex]\(6 \frac{14}{15}\)[/tex] can be converted as follows:
- The whole number part is 6.
- The fraction part is [tex]\(\frac{14}{15}\)[/tex].
- So, the mixed number becomes [tex]\(6 + \frac{14}{15} = \frac{90}{15} + \frac{14}{15} = \frac{104}{15}\)[/tex].
2. Find a common denominator and add the fractions:
- The common denominator for 5 and 15 is 15.
- Convert [tex]\(\frac{33}{5}\)[/tex] to a fraction with a denominator of 15:
- Multiply both the numerator and the denominator by 3: [tex]\(\frac{33}{5} = \frac{33 \times 3}{5 \times 3} = \frac{99}{15}\)[/tex].
- Now we can add [tex]\(\frac{99}{15}\)[/tex] and [tex]\(\frac{104}{15}\)[/tex]:
- [tex]\(\frac{99}{15} + \frac{104}{15} = \frac{99 + 104}{15} = \frac{203}{15}\)[/tex].
3. Convert the sum back to a mixed number:
- Divide 203 by 15:
- [tex]\(203 \div 15 = 13\)[/tex] with a remainder of 8.
- The mixed number is [tex]\(13 \frac{8}{15}\)[/tex].
Therefore, [tex]\(6 \frac{9}{15} + 6 \frac{14}{15} = 13 \frac{8}{15}\)[/tex].
