42/54 simplified
Understand the Problem
The question is asking for the simplification of the fraction 42/54. We will find the greatest common divisor (GCD) of the numerator and denominator to reduce it to its simplest form.
Answer
The simplified fraction is \( \frac{7}{9} \).
Answer for screen readers
The simplified fraction of ( \frac{42}{54} ) is ( \frac{7}{9} ).
Steps to Solve
- Find the GCD of 42 and 54
To simplify the fraction, we first need to find the greatest common divisor (GCD) of the numerator (42) and the denominator (54). We can do this by listing the factors or using the Euclidean algorithm.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The largest common factor is 6, so $GCD(42, 54) = 6$.
- 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 and the denominator by 6.
$$ \frac{42}{54} = \frac{42 \div 6}{54 \div 6} $$
This results in:
$$ \frac{7}{9} $$
- Write the final simplified fraction
The fraction $42/54$ can be simplified to $7/9$, which is its simplest form.
The simplified fraction of ( \frac{42}{54} ) is ( \frac{7}{9} ).
More Information
When simplifying fractions, finding the GCD is essential because it helps in reducing the fraction to its lowest terms. Applying the GCD method ensures accuracy while simplifying.
Tips
- Forgetting to find the GCD and directly reducing the fraction by any number.
- Dividing only the numerator or only the denominator instead of both by the GCD.
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