Simplify: (13a)/(4a^2) + (5a)/(4a^2)
Understand the Problem
The question is asking us to add two fractions with the same denominator. We will add the numerators and keep the denominator.
Answer
$\frac{9}{2a}$
Answer for screen readers
$\frac{9}{2a}$
Steps to Solve
- Add the numerators
Since the fractions have the same denominator, we can add the numerators:
$13a + 5a = 18a$
- Write the result over the common denominator
Place the sum of the numerators over the original denominator:
$\frac{18a}{4a^2}$
- Simplify the fraction
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. The greatest common factor of $18a$ and $4a^2$ is $2a$. Divide both the numerator and denominator by $2a$:
$\frac{18a \div 2a}{4a^2 \div 2a} = \frac{9}{2a}$
$\frac{9}{2a}$
More Information
When simplifying fractions, always look for common factors in both the numerator and the denominator. Dividing both by these factors simplifies the fraction without changing its value.
Tips
A common mistake is forgetting to simplify the fraction after adding the numerators. Always check to see if the resulting fraction can be simplified further.
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