Answer :

To solve the problem of subtracting two mixed numbers, [tex]\(9 \frac{9}{15} - 2 \frac{13}{15}\)[/tex], follow these steps:

1. Convert the Mixed Numbers to Improper Fractions:

- For [tex]\(9 \frac{9}{15}\)[/tex], first convert 9 to a fraction with the same denominator. Multiply 9 (the whole number) by 15 (the denominator) to get 135. Add 9 to get the numerator for the improper fraction:
[tex]\[
\frac{135}{15} + \frac{9}{15} = \frac{144}{15}
\][/tex]

- For [tex]\(2 \frac{13}{15}\)[/tex], do the same: Multiply 2 by 15 to get 30, then add 13 to the numerator:
[tex]\[
\frac{30}{15} + \frac{13}{15} = \frac{43}{15}
\][/tex]

2. Subtract the Improper Fractions:

Now that both numbers are improper fractions with a common denominator, subtract the second fraction from the first:
[tex]\[
\frac{144}{15} - \frac{43}{15} = \frac{101}{15}
\][/tex]

3. Convert Back to a Mixed Number:

- Divide the numerator by the denominator to separate the whole number from the fractional part. [tex]\(101 \div 15\)[/tex] gives 6 as the whole number.
- The remainder is 11, which becomes the numerator of the fractional part:
[tex]\[
6 \frac{11}{15}
\][/tex]

Therefore, the answer to [tex]\(9 \frac{9}{15} - 2 \frac{13}{15}\)[/tex] is [tex]\(6 \frac{11}{15}\)[/tex].

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