64/72 simplified
Understand the Problem
The question is asking to simplify the fraction 64/72. To solve this, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both by that number to simplify the fraction to its lowest terms.
Answer
$ \frac{8}{9} $
Answer for screen readers
The simplified fraction of $ \frac{64}{72} $ is $ \frac{8}{9} $.
Steps to Solve
- Find the GCD of 64 and 72
The first step is to find the greatest common divisor (GCD) of the numbers 64 and 72. The GCD is the largest number that divides both numbers.
The prime factorization of 64 is: $$ 64 = 2^6 $$
The prime factorization of 72 is: $$ 72 = 2^3 \times 3^2 $$
The GCD can be determined by taking the lowest power of the common prime factors. Here, the common prime factor is 2: $$ \text{GCD}(64, 72) = 2^3 = 8 $$
- Divide both the numerator and denominator by the GCD
Now that we know the GCD is 8, we divide both the numerator and the denominator by 8 to simplify the fraction.
$$ \frac{64}{72} = \frac{64 \div 8}{72 \div 8} = \frac{8}{9} $$
- State the simplified fraction
The simplified form of the fraction 64/72 is: $$ \frac{8}{9} $$
The simplified fraction of $ \frac{64}{72} $ is $ \frac{8}{9} $.
More Information
When simplifying fractions, finding the GCD is crucial because it helps reduce the fraction to its simplest form. This method can be applied to any pair of integers.
Tips
- Not finding the GCD correctly: Make sure to carefully identify the prime factors.
- Forgetting to divide both numerator and denominator: It’s important to apply the GCD to both parts of the fraction to ensure the simplification is valid.
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