High School

Evaluate the expression:

[tex]\[ 9 \frac{9}{15} - 2 \frac{13}{15} \][/tex]

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]