Question

1. now he has to find the median to the given set of fractions: 1/4, 1/3, 5/6, 1/2. all answers must be in lowest terms.

options:
1/2
10/24
5/12
5/6
clear all

Explanation:

Step1: Order the fractions

First, find a common denominator for \(\frac{1}{4}\), \(\frac{1}{3}\), \(\frac{5}{6}\), \(\frac{1}{2}\). The least common denominator (LCD) of 4, 3, 6, 2 is 12. Convert each fraction:

• \(\frac{1}{4}=\frac{1\times3}{4\times3}=\frac{3}{12}\)
• \(\frac{1}{3}=\frac{1\times4}{3\times4}=\frac{4}{12}\)
• \(\frac{5}{6}=\frac{5\times2}{6\times2}=\frac{10}{12}\)
• \(\frac{1}{2}=\frac{1\times6}{2\times6}=\frac{6}{12}\)

Now, order the fractions: \(\frac{3}{12}\), \(\frac{4}{12}\), \(\frac{6}{12}\), \(\frac{10}{12}\) (which correspond to \(\frac{1}{4}\), \(\frac{1}{3}\), \(\frac{1}{2}\), \(\frac{5}{6}\) in original form).

Step2: Find the median

Since there are 4 (even number) values, the median is the average of the two middle numbers. The two middle numbers are the 2nd and 3rd values: \(\frac{4}{12}\) and \(\frac{6}{12}\).

Calculate the average: \(\frac{\frac{4}{12}+\frac{6}{12}}{2}=\frac{\frac{10}{12}}{2}=\frac{10}{12}\times\frac{1}{2}=\frac{10}{24}=\frac{5}{12}\) (simplify \(\frac{10}{24}\) by dividing numerator and denominator by 2).

Step3: Check the options

• \(1/2 = 6/12\) (not the median)
• \(10/24\) is not in lowest terms (simplifies to \(5/12\))
• \(5/12\) is the simplified median
• \(5/6 = 10/12\) (not the median)

Answer:

C. 5/12 (assuming the third option is labeled C, but based on the options, the correct one is the option with 5/12)