simplify 48/56
Understand the Problem
The question is asking to simplify the fraction 48/56 to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number.
Answer
The simplified fraction is \( \frac{6}{7} \).
Answer for screen readers
The simplified fraction of ( \frac{48}{56} ) is ( \frac{6}{7} ).
Steps to Solve
- Find the GCD of 48 and 56
To simplify the fraction, we first need to find the greatest common divisor (GCD) of the two numbers, 48 and 56. We can do this by listing out the factors of each number.
The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56
The common factors are: 1, 2, 4, 8
The greatest of these is 8, so we have GCD(48, 56) = 8.
- Divide both the numerator and the denominator by the GCD
Now that we have the GCD, we divide both the numerator (48) and the denominator (56) by 8.
For the numerator:
$$ \frac{48}{8} = 6 $$
For the denominator:
$$ \frac{56}{8} = 7 $$
- Write the simplified fraction
Now we can write the simplified fraction using the results from the previous step.
So,
$$ \frac{48}{56} = \frac{6}{7} $$
The simplified fraction of ( \frac{48}{56} ) is ( \frac{6}{7} ).
More Information
Simplifying fractions is a useful skill that helps in making calculations easier, especially when working with ratios or proportions. The greatest common divisor (GCD) can be found using various methods including prime factorization or the Euclidean algorithm.
Tips
- Not finding the GCD correctly can lead to incorrect simplification. Ensure to check all factors.
- Forgetting to divide both the numerator and the denominator by the GCD.
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