72/81 simplified
Understand the Problem
The question is asking for the simplification of the fraction 72/81. To solve it, we need to find the greatest common divisor (GCD) of 72 and 81 and then divide both the numerator and the denominator by this GCD.
Answer
The simplified fraction is \( \frac{8}{9} \).
Answer for screen readers
The final answer is ( \frac{8}{9} ).
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction, we first need to determine the GCD of 72 and 81.
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The prime factorization of 72 is: $$ 72 = 2^3 \times 3^2 $$
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The prime factorization of 81 is: $$ 81 = 3^4 $$
The common prime factor is $3$, and the lowest exponent is $2$. So, the GCD of 72 and 81 is: $$ GCD(72, 81) = 3^2 = 9 $$
- Divide Both the Numerator and Denominator by the GCD
Now that we have the GCD, we can simplify the fraction by dividing both the numerator (72) and the denominator (81) by 9:
$$ \frac{72 \div 9}{81 \div 9} = \frac{8}{9} $$
- Final Result
The simplified fraction is: $$ \frac{8}{9} $$
The final answer is ( \frac{8}{9} ).
More Information
Simplifying fractions is a fundamental concept in arithmetic, making calculations easier and presenting numbers in their simplest form.
Tips
- A common mistake is miscalculating the GCD. It's essential to ensure that you correctly identify the common prime factors and their lowest exponents.
- Another mistake can occur when dividing the numerator and denominator by a number other than the GCD, leading to incorrect simplification.
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