42/18 in simplest form
Understand the Problem
The question is asking how to simplify the fraction 42/18 to its lowest terms. To solve this, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both by this number.
Answer
The simplified form of the fraction $\frac{42}{18}$ is $\frac{7}{3}$.
Answer for screen readers
The simplified form of the fraction $\frac{42}{18}$ is $\frac{7}{3}$.
Steps to Solve
- Find the GCD of 42 and 18
To simplify the fraction, we need the greatest common divisor (GCD) of 42 and 18. We can find the GCD using the prime factorization method or the Euclidean algorithm.
- Prime factorization of 42: $42 = 2 \times 3 \times 7$
- Prime factorization of 18: $18 = 2 \times 3^2$
The common factors are $2$ and $3$. Hence, the GCD is $2 \times 3 = 6$.
- Divide both numerator and denominator by the GCD
Now that we have the GCD, we will divide both the numerator (42) and the denominator (18) by 6.
$$ \frac{42 \div 6}{18 \div 6} = \frac{7}{3} $$
- Result
Thus, after dividing, we find that the simplified form of the fraction is
$$ \frac{7}{3} $$
The simplified form of the fraction $\frac{42}{18}$ is $\frac{7}{3}$.
More Information
When simplifying fractions, it's essential to find the GCD, as it helps to reduce the fraction to its simplest form. The concept of GCD is fundamental in number theory and helps in many areas of math.
Tips
- Forgetting to find the GCD properly can lead to incorrect simplification. Always verify the factors of the numbers.
- Dividing only one part of the fraction by the GCD instead of both the numerator and denominator.