High School

Evaluate the expression shown below and write your answer as a fraction in simplest form.

[tex]\frac{13}{15} + \frac{1}{9}[/tex]

Answer :

Let's evaluate the expression [tex]\(\frac{13}{15} + \frac{1}{9}\)[/tex] and express it as a fraction in simplest form.

1. Find a Common Denominator:
To add fractions, we need to find a common denominator. The denominators are 15 and 9. The least common multiple (LCM) of 15 and 9 is 45. So, 45 is our common denominator.

2. Convert Each Fraction:
- For [tex]\(\frac{13}{15}\)[/tex]: Convert it to a fraction with denominator 45.
Multiply both the numerator and the denominator by 3 to get [tex]\(\frac{39}{45}\)[/tex].
- For [tex]\(\frac{1}{9}\)[/tex]: Convert it to a fraction with denominator 45.
Multiply both the numerator and the denominator by 5 to get [tex]\(\frac{5}{45}\)[/tex].

3. Add the Fractions:
Now that the fractions have the same denominator, add the numerators:
[tex]\[
\frac{39}{45} + \frac{5}{45} = \frac{39 + 5}{45} = \frac{44}{45}
\][/tex]

4. Simplify the Result:
The fraction [tex]\(\frac{44}{45}\)[/tex] is already in its simplest form because 44 and 45 have no common factors other than 1.

Therefore, the sum of the fractions is [tex]\(\frac{44}{45}\)[/tex].

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