This arithmetic question is about a 7th or 8th grade question, surely not beyond the 9th grade and possibly even 6th grade. I really do not recall when one learns the rules about the use of parentheses or their absence in evaluating expressions like this. The answer is 1 (one). I didn’t look it up. I’m relying on my math knowledge. If I cannot do this, then something is seriously wrong with me or my education. I’m no math expert or math major and I wasn’t taught by New Math, but I had 18 hours of undergrad math and at least that much graduate math.
9 – 3 ÷ 1/3 + 1 = ?
For utmost clarity, 3 ÷ 1/3 should be in parentheses and so should 1/3. Then the answer would clearly be 9 – 9 + 1 = 1. In the absence of parentheses, one can go by an ordering of operations, which is to do multiplication and divisions first and additions and subtractions second. Do 3 ÷ 1/3 first, assuming that 1/3 is supposed to signify one-third. The result is 9. Then do the summing: 9 – 9 + 1 = 1.
Clearly one should not take 9 – 3 first and the divide the result by 1/3, the reason being that there are no parentheses telling us to do that. Such an operation would require us to see (9 – 3) ÷ 1/3, which we do not see. Parentheses have precedence over any arithmetical operation. that is, we evaluate expressions within parentheses first.
There is, however, an issue in the expression, which is that 1/3 is not in parentheses and it should be to be really clear. I’ve assumed above that the “/” is meant to mean that one-third is to be considered a unit. The slash is not meant to be the same as the division sign, ÷. (If it were interpreted as division, we’d be seeing 9 – 3 ÷ 1 ÷ 3 + 1. This expression’s answer depends on which division is done first. We then follow the rule of working left to right. We get 9 – 1 + 1 = 9. But the slash is not meant to be division here, and I reject this solution.)
So, is a slash the same as ÷? If it were the same, why use both in the same expression? Why ask for trouble? My answer to this is that a slash is not the same as ÷. It does not indicate division. It indicates a fraction. The solution is therefore 1.
6:31 am on May 14, 2016
