Answer :
We start with the mixed numbers:
[tex]$$
9 \frac{9}{15} \quad \text{and} \quad 2 \frac{13}{15}.
$$[/tex]
Step 1. Convert to Improper Fractions
For the first number, multiply the whole part by the denominator and add the numerator:
[tex]$$
9 \frac{9}{15} = \frac{9 \times 15 + 9}{15} = \frac{135 + 9}{15} = \frac{144}{15}.
$$[/tex]
For the second number:
[tex]$$
2 \frac{13}{15} = \frac{2 \times 15 + 13}{15} = \frac{30 + 13}{15} = \frac{43}{15}.
$$[/tex]
Step 2. Subtract the Improper Fractions
Since both fractions have the same denominator, subtract their numerators:
[tex]$$
\frac{144}{15} - \frac{43}{15} = \frac{144 - 43}{15} = \frac{101}{15}.
$$[/tex]
Step 3. Convert the Result to a Mixed Number
Divide the numerator by the denominator to find the whole number part:
[tex]$$
101 \div 15 = 6 \quad \text{(since } 6 \times 15 = 90\text{)}.
$$[/tex]
Then find the remainder:
[tex]$$
101 - 90 = 11.
$$[/tex]
So, the fraction [tex]$\frac{101}{15}$[/tex] can be written as the mixed number:
[tex]$$
6 \frac{11}{15}.
$$[/tex]
Final Answer:
[tex]$$
9 \frac{9}{15} - 2 \frac{13}{15} = 6 \frac{11}{15}.
$$[/tex]
[tex]$$
9 \frac{9}{15} \quad \text{and} \quad 2 \frac{13}{15}.
$$[/tex]
Step 1. Convert to Improper Fractions
For the first number, multiply the whole part by the denominator and add the numerator:
[tex]$$
9 \frac{9}{15} = \frac{9 \times 15 + 9}{15} = \frac{135 + 9}{15} = \frac{144}{15}.
$$[/tex]
For the second number:
[tex]$$
2 \frac{13}{15} = \frac{2 \times 15 + 13}{15} = \frac{30 + 13}{15} = \frac{43}{15}.
$$[/tex]
Step 2. Subtract the Improper Fractions
Since both fractions have the same denominator, subtract their numerators:
[tex]$$
\frac{144}{15} - \frac{43}{15} = \frac{144 - 43}{15} = \frac{101}{15}.
$$[/tex]
Step 3. Convert the Result to a Mixed Number
Divide the numerator by the denominator to find the whole number part:
[tex]$$
101 \div 15 = 6 \quad \text{(since } 6 \times 15 = 90\text{)}.
$$[/tex]
Then find the remainder:
[tex]$$
101 - 90 = 11.
$$[/tex]
So, the fraction [tex]$\frac{101}{15}$[/tex] can be written as the mixed number:
[tex]$$
6 \frac{11}{15}.
$$[/tex]
Final Answer:
[tex]$$
9 \frac{9}{15} - 2 \frac{13}{15} = 6 \frac{11}{15}.
$$[/tex]
