Answer :
To solve the expression [tex]\frac{4}{15} + \frac{13}{15} - \frac{7}{15}[/tex], we can use properties of fractions, specifically the fact that when adding or subtracting fractions with the same denominator, you simply add or subtract the numerators and keep the same denominator.
Here's how you can solve it step-by-step:
Identify the common denominator:
All the fractions [tex]\frac{4}{15}[/tex], [tex]\frac{13}{15}[/tex], and [tex]\frac{7}{15}[/tex] have the same denominator, which is 15.Add the numerators of the first two fractions:
[tex]\frac{4}{15} + \frac{13}{15} = \frac{4 + 13}{15} = \frac{17}{15}[/tex]Subtract the numerator of the last fraction:
[tex]\frac{17}{15} - \frac{7}{15} = \frac{17 - 7}{15} = \frac{10}{15}[/tex]Simplify the fraction if possible:
Both 10 and 15 can be divided by their greatest common divisor, which is 5.
[tex]\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}[/tex]
Therefore, the simplest form of [tex]\frac{4}{15} + \frac{13}{15} - \frac{7}{15}[/tex] is [tex]\frac{2}{3}[/tex].
