Question

You are doing a survey for your statistics class and discover that \(\frac{3}{4}\) of the students at the college take a math class; \(\frac{1}{6}\) of these students take statistics. What fraction of the students at the college take statistics?

Short answer

Answer: \(\frac{1}{8}\)

Step-by-step solution

Convert given fractions into equivalent fractions with a common denominator

To multiply the fractions, we first need to find a common denominator. In this case, the common denominator is the least common multiple (LCM) of 4 and 6, which is 12. Convert both fractions to equivalent fractions with denominator 12.

Find the equivalent fractions with a denominator of 12

To find the equivalent fraction of \(\frac{3}{4}\), multiply the numerator and denominator by 3 to get \(\frac{9}{12}\). To find the equivalent fraction of \(\frac{1}{6}\), multiply the numerator and denominator by 2 to get \(\frac{2}{12}\). Now we have the following fractions: - \(\frac{9}{12}\) of students take a math class - \(\frac{2}{12}\) of math students take statistics

Multiply the two equivalent fractions

We multiply the two fractions to find the fraction of students taking statistics. \(\frac{9}{12}\) * \(\frac{2}{12}\) To multiply the fractions, multiply the numerators together and then the denominators together: - Numerator: \(9 * 2 = 18\) - Denominator: \(12 * 12 = 144\) So, the fraction becomes \(\frac{18}{144}\).

Simplify the fraction

To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is 18. Divide both the numerator and denominator by the GCD: - Numerator: \(18 ÷ 18 = 1\) - Denominator: \(144 ÷ 18 = 8\) So, the simplified fraction is \(\frac{1}{8}\).

Write the final answer

The fraction of students at the college that take statistics is \(\frac{1}{8}\).