simplify 45/60
Understand the Problem
The question is asking us to simplify the fraction 45/60 by finding the greatest common divisor and reducing the fraction accordingly.
Answer
\( \frac{3}{4} \)
Answer for screen readers
The final answer is ( \frac{3}{4} )
Steps to Solve
- Find the Greatest Common Divisor (GCD) of 45 and 60
The first step is to find the GCD of 45 and 60. The GCD is the largest number that divides both 45 and 60 without a remainder.
List the factors of each number:
- Factors of 45: 1, 3, 5, 9, 15, 45
- Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The common factors are 1, 3, 5, and 15. Thus, the GCD of 45 and 60 is 15.
- Divide the numerator and denominator by the GCD
Divide both the numerator (45) and the denominator (60) by their GCD (15).
$$ \frac{45 \div 15}{60 \div 15} = \frac{3}{4} $$
- Write the simplified fraction
After dividing both the numerator and the denominator by their GCD, we get the simplified fraction ( \frac{3}{4} ).
The final answer is ( \frac{3}{4} )
More Information
Reducing a fraction by dividing both the numerator and the denominator by their greatest common divisor ensures the fraction is in its simplest form.
Tips
A common mistake is not finding the largest common divisor (GCD) and thereby not fully simplifying the fraction. Always ensure both the numerator and the denominator are divided by the GCD.
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