simplify 32/56
Understand the Problem
The question is asking to simplify the fraction 32/56 to its simplest form. We will find the greatest common divisor of the numerator and the denominator and divide both by that number.
Answer
The simplest form of the fraction $\frac{32}{56}$ is $\frac{4}{7}$.
Answer for screen readers
The simplest form of the fraction $\frac{32}{56}$ is $\frac{4}{7}$.
Steps to Solve
- Find the greatest common divisor (GCD)
To simplify the fraction $\frac{32}{56}$, we first need to find the GCD of the numerator (32) and the denominator (56).
- The factors of 32 are 1, 2, 4, 8, 16, and 32.
- The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
The largest common factor is 8, so $GCD(32, 56) = 8$.
- Divide both the numerator and denominator by the GCD
Now, we divide both the numerator and the denominator by the GCD we found:
$$ \frac{32 \div 8}{56 \div 8} $$
This simplifies to:
$$ \frac{4}{7} $$
- Final Result
Thus, the fraction $\frac{32}{56}$ simplified to its lowest terms is $\frac{4}{7}$.
The simplest form of the fraction $\frac{32}{56}$ is $\frac{4}{7}$.
More Information
When simplifying fractions, the process of finding the greatest common divisor is essential. In this case, both 32 and 56 can be divided by 8, making it easier to express the fraction in its simplest form. Simplifying fractions is useful in various mathematical applications, such as algebra and ratio comparisons.
Tips
- A common mistake is to overlook finding the correct GCD. Always list out the factors or use the Euclidean algorithm to find the GCD accurately.
- Another mistake is misunderstanding how to simplify: dividing one of the numbers instead of both by the GCD.