40/64 simplified
Understand the Problem
The question is asking to simplify the fraction 40/64. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number.
Answer
The simplified fraction is \( \frac{5}{8} \).
Answer for screen readers
The simplified fraction of ( \frac{40}{64} ) is ( \frac{5}{8} ).
Steps to Solve
- Find the GCD of 40 and 64
To simplify the fraction, first, we need to find the greatest common divisor (GCD) of 40 and 64. The GCD is the largest number that divides both.
The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40.
The factors of 64 are: 1, 2, 4, 8, 16, 32, 64.
The common factors are: 1, 2, 4. Therefore, the GCD of 40 and 64 is 8.
- Divide both the numerator and denominator by the GCD
Now that we have the GCD, we can divide both the numerator and the denominator by this value.
$$ \text{Numerator: } \frac{40}{8} = 5 $$
$$ \text{Denominator: } \frac{64}{8} = 8 $$
- Write the simplified fraction
After performing the division, the simplified fraction is:
$$ \frac{5}{8} $$
The simplified fraction of ( \frac{40}{64} ) is ( \frac{5}{8} ).
More Information
The process of simplifying fractions helps in reducing complexity in calculations and making it easier to work with. The fraction ( \frac{5}{8} ) represents a portion of a whole and cannot be simplified further because 5 and 8 have no common factors other than 1.
Tips
- Not finding the GCD properly: Sometimes, mistakes occur when identifying the GCD. Ensure to list all factors clearly.
- Dividing incorrectly: Make sure to divide both the numerator and the denominator by the GCD accurately. Double-check calculations.
