Sure, let's break down the problem step-by-step.
1. Convert the mixed fractions to improper fractions:
- For [tex]\(8 \frac{7}{15}\)[/tex]:
[tex]\[
\text{Improper fraction} = 8 \times 15 + 7 = 120 + 7 = 127 \quad \text{so,} \quad \frac{127}{15}
\][/tex]
- For [tex]\(3 \frac{44}{75}\)[/tex]:
[tex]\[
\text{Improper fraction} = 3 \times 75 + 44 = 225 + 44 = 269 \quad \text{so,} \quad \frac{269}{75}
\][/tex]
2. Find a common denominator:
The denominators are 15 and 75. The least common multiple (LCM) of 15 and 75 is 75. Hence, the common denominator is 75.
3. Convert the fractions to have the common denominator:
- For [tex]\(\frac{127}{15}\)[/tex]:
[tex]\[
\frac{127}{15} = \frac{127 \times 5}{15 \times 5} = \frac{635}{75}
\][/tex]
Here we multiply numerator and denominator by 5 to adjust the denominator to 75.
4. Now, perform the subtraction with the common denominator:
[tex]\[
\frac{635}{75} - \frac{269}{75} = \frac{635 - 269}{75} = \frac{366}{75}
\][/tex]
5. Simplify the resulting fraction:
- Find the greatest common divisor (GCD) of 366 and 75, which is 3.
- Simplify the fraction by dividing both the numerator and the denominator by the GCD:
[tex]\[
\frac{366 \div 3}{75 \div 3} = \frac{122}{25}
\][/tex]
6. Convert back to a mixed number if necessary:
Divide the numerator by the denominator:
[tex]\[
\frac{122}{25} = 4 \frac{22}{25}
\][/tex]
Here, 122 divided by 25 equals 4 with a remainder of 22. Hence, the mixed number is [tex]\(4 \frac{22}{25}\)[/tex].
The final result of the subtraction [tex]\(8 \frac{7}{15} - 3 \frac{44}{75}\)[/tex] is:
[tex]\[
4 \frac{22}{25}
\][/tex]
