simplify 35/45
Understand the Problem
The question is asking to simplify the fraction 35/45, which involves finding the greatest common divisor (GCD) and dividing the numerator and denominator by that number to reduce it to its simplest form.
Answer
The simplified form of the fraction is $\frac{7}{9}$.
Answer for screen readers
The simplified form of the fraction $\frac{35}{45}$ is $\frac{7}{9}$.
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction $\frac{35}{45}$, we first need to find the GCD of the numerator (35) and the denominator (45). We can do this by finding the prime factors of both numbers:
- The prime factors of 35 are: $5 \times 7$.
- The prime factors of 45 are: $3^2 \times 5$.
The common factor is $5$. Thus, the GCD is $5$.
- Divide the Numerator and Denominator by the GCD
Next, we divide both the numerator and the denominator by the GCD we found:
$$ \text{Numerator: } \frac{35}{5} = 7 $$
$$ \text{Denominator: } \frac{45}{5} = 9 $$
- Write the Simplified Fraction
Now we can write the simplified fraction:
$$ \frac{35}{45} = \frac{7}{9} $$
The simplified form of the fraction $\frac{35}{45}$ is $\frac{7}{9}$.
More Information
When simplifying fractions, you can always start by finding the GCD of the numerator and denominator. This process makes it easier to reduce fractions to their simplest forms. Additionally, knowing how to factor numbers helps in finding the GCD quickly.
Tips
- Forgetting to find the GCD correctly. Double-check the factors of both numbers.
- Not dividing both the numerator and denominator by the GCD, which can lead to incorrect simplification.