45/72 simplified
Understand the Problem
The question is asking for the simplification of the fraction 45/72 to its simplest form. To solve this, we need to find the greatest common divisor (GCD) of 45 and 72 and divide both the numerator and the denominator by that number.
Answer
The simplified form of $ \frac{45}{72} $ is $ \frac{5}{8} $.
Answer for screen readers
The simplified form of $ \frac{45}{72} $ is $ \frac{5}{8} $.
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction $ \frac{45}{72} $, we first need to find the GCD of 45 and 72.
The factors of 45 are:
- $ 1, 3, 5, 9, 15, 45 $
The factors of 72 are:
- $ 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 $
The common factors are $ 1, 3, 9 $. The greatest one is $ 9$.
- Divide Both Numerator and Denominator by the GCD
Now we divide both the numerator and the denominator of the fraction by the GCD we just found.
$$ \frac{45 \div 9}{72 \div 9} = \frac{5}{8} $$
- Write the Final Simplified Fraction
The fraction $ \frac{45}{72} $ simplifies to $ \frac{5}{8} $.
The simplified form of $ \frac{45}{72} $ is $ \frac{5}{8} $.
More Information
The process of simplifying fractions helps us express them in the simplest form. This makes calculations easier and helps in comparing fractions more effectively. The GCD can often be found using the Euclidean algorithm, a very efficient method for larger numbers.
Tips
- Forgetting to find the GCD before simplifying.
- Dividing only one part of the fraction (either the numerator or the denominator) instead of both by the GCD.