simplify 72/90
Understand the Problem
The question is asking us to simplify the fraction 72/90. To do this, we will find the greatest common divisor (GCD) of the numerator and the denominator and divide both by that number.
Answer
The simplified form of the fraction $\frac{72}{90}$ is $\frac{4}{5}$.
Answer for screen readers
The simplified form of the fraction $\frac{72}{90}$ is $\frac{4}{5}$.
Steps to Solve
- Find the GCD of 72 and 90
To simplify the fraction $\frac{72}{90}$, we first need to find the greatest common divisor (GCD) of 72 and 90. The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
And the factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The common factors are: 1, 2, 3, 6, 9, 18. The greatest of these is 18, so the GCD is 18.
- Divide the numerator and denominator by the GCD
Now that we have the GCD, we can simplify the fraction by dividing both the numerator and the denominator by the GCD.
$$ \frac{72 \div 18}{90 \div 18} $$
Calculating the division:
$$ \frac{4}{5} $$
- Write the simplified fraction
Thus, the simplified fraction of $\frac{72}{90}$ is:
$$ \frac{4}{5} $$
The simplified form of the fraction $\frac{72}{90}$ is $\frac{4}{5}$.
More Information
The process of simplifying fractions is essential in various areas of mathematics, such as ratios, proportions, and basic arithmetic. Learning to find the GCD can help in further applications like simplifying algebraic expressions.
Tips
- A common mistake is mistakenly choosing a number that is not the greatest common divisor to simplify the fraction. Always ensure that you find the largest common factor.
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