Question

Calculate the mean of : 2/3,1/2 and 3/4

Answer 1

`\sf Mean =(23)/(36)`

Explanation:

The mean is the sum of all data values divided by the total number of data values.

Therefore, to find the mean of 2/3, 1/2 and 3/4, add the fractions then divide the sum by 3.

When adding or subtracting fractions that have different denominators, first rewrite the fractions as equivalent fractions with the same denominator. To do this, find the lowest common multiple (LCM) of the denominators.

The given addition is:

`(2)/(3)+(1)/(2)+(3)/(4)`

The LCM of the denominators 3, 2 and 4 is 12.

Therefore, multiply the numerator and denominator of each fraction by the same amount so that the denominator is 12:

`\begin{aligned}\implies (2)/(3)+(1)/(2)+(3)/(4) & =(2 \cdot 4)/(3 \cdot 4)+(1 \cdot 6)/(2 \cdot 6)+(3 \cdot 3)/(4 \cdot 3)\\\\ &=(8)/(12)+(6)/(12)+(9)/(12)\end{aligned}`

To add fractions with the same denominator, simply add the numerators:

`\implies (8)/(12)+(6)/(12)+(9)/(12)=(8+6+9)/(12)=(23)/(12)`

Now we have calculated the sum of the three fractions, divide by 3 to find the mean:

`\begin{aligned}\implies \textsf{Mean}&=(23)/(12) / 3\\\\&=(23)/(12) * (1)/(3)\\\\&=(23 * 1)/(12 * 3)\\\\&=(23)/(36)\end{aligned}`