28/32 simplified
Understand the Problem
The question is asking to simplify the fraction 28/32 to its lowest terms. This involves finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that value.
Answer
7/8
Answer for screen readers
The final answer is 7/8
Steps to Solve
- Find the GCD of 28 and 32
The Greatest Common Divisor (GCD) of 28 and 32 is the largest number that divides both of them without leaving a remainder.
Using the Euclidean algorithm:
$$egin{align*} 32 ext{ mod } 28 &= 4 \ 28 ext{ mod } 4 &= 0 \ ext{So, the GCD is } 4. \ ext{Hence, the GCD of 28 and 32 is } 4. \ ext{The GCD of 28 and 32 is 4.} \ ext{Therefore, the greatest common divisor is 4} \ ext{lists of the factors involved gives us:} \ 28: 1,2,4,7,14,28 \ 32: 1,2,4,8,16,32 \ ext{Common factors: }4,2,1 \ 4 is the highest. \ ext{From this we derive that the highest common factor is }4. \ \\end{align*}$$
- Divide the numerator and denominator by the GCD
Divide both the numerator and the denominator by 4:
$$\frac{28 / 4}{32 / 4} = \frac{7}{8}$$
- Simplify the fraction
The fraction $\frac{28}{32}$ simplified to its lowest terms is $\frac{7}{8}$.
The final answer is 7/8
More Information
Simplifying fractions is a process of dividing the numerator and denominator by their greatest common divisor (GCD). This helps in reducing the fraction to its lowest terms, making it simpler to understand and use in further calculations.
Tips
A common mistake is to incorrectly identify the GCD. Ensure you correctly determine the GCD by either listing the factors or using the Euclidean algorithm.
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