Write the ratio 6 to 42 as a fraction in simplest form.
Understand the Problem
The question is asking to simplify the ratio of 6 to 42 and express it as a fraction in its simplest form.
Answer
The simplest form of the ratio \(6\) to \(42\) is \(\frac{1}{7}\).
Answer for screen readers
The simplest form of the ratio (6) to (42) is (\frac{1}{7}).
Steps to Solve
-
Write the ratio as a fraction
Express the ratio of 6 to 42 as a fraction:
$$ \frac{6}{42} $$ -
Find the greatest common divisor (GCD)
To simplify the fraction, find the GCD of 6 and 42. The GCD is 6. -
Divide both the numerator and the denominator by the GCD
Divide both parts of the fraction by 6:
$$ \frac{6 \div 6}{42 \div 6} = \frac{1}{7} $$ -
Express the result
The fraction in simplest form is:
$$ \frac{1}{7} $$
The simplest form of the ratio (6) to (42) is (\frac{1}{7}).
More Information
When simplified, the ratio expresses how many parts of the first number (6) fit into the second number (42). In this case, for every 1 part of 6, there are 7 parts of 42.
Tips
- Not finding the GCD: Sometimes, students may simplify by dividing by numbers that aren’t the GCD, leading to incorrect answers.
- Incorrect division: Ensure that both the numerator and the denominator are divided accurately.
