Write the ratio 6 to 42 as a fraction in simplest form.

Question image

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

  1. Write the ratio as a fraction
    Express the ratio of 6 to 42 as a fraction:
    $$ \frac{6}{42} $$

  2. Find the greatest common divisor (GCD)
    To simplify the fraction, find the GCD of 6 and 42. The GCD is 6.

  3. Divide both the numerator and the denominator by the GCD
    Divide both parts of the fraction by 6:
    $$ \frac{6 \div 6}{42 \div 6} = \frac{1}{7} $$

  4. 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.
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