Simplify 56/72.
Understand the Problem
The question is asking us to simplify the fraction 56/72 to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator.
Answer
The simplest form of the fraction is $\frac{7}{9}$.
Answer for screen readers
The simplest form of the fraction $\frac{56}{72}$ is $\frac{7}{9}$.
Steps to Solve
- Find the GCD of 56 and 72
To simplify the fraction $\frac{56}{72}$, we first need to find the greatest common divisor (GCD) of 56 and 72. We can use the prime factorization method to find the GCD:
- The prime factorization of 56 is $2^3 \times 7$.
- The prime factorization of 72 is $2^3 \times 3^2$.
Now, we take the lowest power of the common prime factors:
- The common prime factor is 2, and the lowest power is $2^3 = 8$.
Thus, the GCD of 56 and 72 is 8.
- Divide both the numerator and denominator by the GCD
Next, we simplify the fraction by dividing both the numerator and the denominator by the GCD (8):
- For the numerator: $56 \div 8 = 7$.
- For the denominator: $72 \div 8 = 9$.
So, the simplified fraction is:
$$ \frac{7}{9} $$
- Present the final simplified fraction
The final step is to present the fraction in its simplest form, which we found to be:
$$ \frac{7}{9} $$
The simplest form of the fraction $\frac{56}{72}$ is $\frac{7}{9}$.
More Information
Simplifying fractions is a fundamental skill in mathematics, allowing you to express ratios in their simplest forms. The GCD helps identify common factors to reduce fractions efficiently.
Tips
- Forgetting to check all prime factors when computing GCD.
- Dividing only one of the numbers by the GCD instead of both.
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