40/35 simplified
Understand the Problem
The question is asking to simplify the fraction 40/35. To do this, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number.
Answer
The simplified fraction is \( \frac{8}{7} \).
Answer for screen readers
The simplified fraction of ( \frac{40}{35} ) is ( \frac{8}{7} ).
Steps to Solve
- Identify the numerator and denominator
The fraction is given as ( \frac{40}{35} ). Here, the numerator is 40 and the denominator is 35.
- Find the GCD of 40 and 35
To simplify the fraction, we first need to determine the greatest common divisor (GCD) of 40 and 35. The factors of each are:
- Factors of 40: ( 1, 2, 4, 5, 8, 10, 20, 40 )
- Factors of 35: ( 1, 5, 7, 35 )
The largest common factor between these two sets is 5. Therefore, ( \text{GCD}(40, 35) = 5 ).
- Divide the numerator and denominator by the GCD
Now, we can simplify the fraction by dividing both the numerator and the denominator by their GCD:
$$ \frac{40 \div 5}{35 \div 5} = \frac{8}{7} $$
- State the simplified fraction
The simplified form of ( \frac{40}{35} ) is ( \frac{8}{7} ).
The simplified fraction of ( \frac{40}{35} ) is ( \frac{8}{7} ).
More Information
The fraction ( \frac{8}{7} ) is an improper fraction since the numerator is greater than the denominator, which means it can also be expressed as a mixed number: ( 1 \frac{1}{7} ).
Tips
- Forgetting to find the GCD correctly can lead to incorrect simplification. Always list out the factors or use the Euclidean algorithm to find the GCD accurately.
- Dividing only one part of the fraction instead of both the numerator and the denominator by the GCD.
