45/20 simplified
Understand the Problem
The question is asking to simplify the fraction 45/20 to its lowest terms, which involves dividing both the numerator and the denominator by their greatest common divisor.
Answer
The simplified form of the fraction $\frac{45}{20}$ is $\frac{9}{4}$.
Answer for screen readers
The simplified form of the fraction $\frac{45}{20}$ is $\frac{9}{4}$.
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction, we first need to find the GCD of the numerator (45) and the denominator (20).
The factors of 45 are: 1, 3, 5, 9, 15, 45
The factors of 20 are: 1, 2, 4, 5, 10, 20
The highest common factor is 5, so the GCD is 5.
- Divide the Numerator and Denominator by the GCD
Now we will divide both the numerator and the denominator by the GCD (5):
$$ \frac{45 \div 5}{20 \div 5} $$
Calculating this gives us:
$$ \frac{9}{4} $$
- State the Simplified Fraction
The fraction $ \frac{45}{20} $ simplifies to $ \frac{9}{4} $.
The simplified form of the fraction $\frac{45}{20}$ is $\frac{9}{4}$.
More Information
When you simplify fractions, you are making them more understandable and easier to work with. The GCD helps you reduce fractions to their simplest form. In this case, $\frac{9}{4}$ is an improper fraction because the numerator is larger than the denominator.
Tips
Some common mistakes include:
- Not finding the correct GCD. Make sure to list all factors or use the Euclidean algorithm.
- Forgetting to divide both the numerator and the denominator by the GCD.
- Simplifying incorrectly by changing the numbers instead of dividing properly.
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