Expert: Josh - 9/3/2009

Question
Hello:

Have I determined the averages for the following correctly?

3 + 4 + 5 = 12/3 = an average of 4 or (1/2 X 3) + (1/3 X 4) + (1/3 X 5) = 3/3 + 4/3 + 5/3 = 12/3 = 4 same as previous example.

Here's one with a negative number: 3 + -4 + 5 = 4/3 = average of 1 & 1/3

Here's one with all fractions: 1/2 + 2/3 + 3/4 = 6/12 + 8/12 + 4/12 = 18/12 = and average of 1 & 1/3.

Are these examples correct?

I thank you for your reply.

Answer
Hi Kenneth,

Line 2: idea is correct (1/2 should be 1/3).
Line 3: is correct.
Line 4: 3/4 = 9/12, not 4/12

Word of advice -- please do not mix words with maths operators. Keep equations simple and separate from explanation.

IMPORTANT: Use the "=" sign only when the expression on the left hand side actually EQUALS the expression on the right hand side.

Here is an example where notations have been abused.
3 + 4 + 5 = 12/3 is simply false. The LHS represents the sum of three numbers, it is NOT the same as its average (which appears on the RHS). To say what you wanted to say, write average{3,4,5}=12/3 instead. Alternatively, you can describe it in words. The average of 3, 4 and 5 is 12/3.