# Thread: Solve for 4/10 - 30% +1/5 (was a question on a test; teacher & I disagree on ans.)

1. ## Solve for 4/10 - 30% +1/5 (was a question on a test; teacher & I disagree on ans.)

I recently had this question on a test:
4/10 - 30% +1/5

Me and my teacher have different answers for it. His solution is:
4/10 - 30% +1/5
4/10 - 3/10 +1/5
1/10+1/5*2/2=3/10
He tells me that the 30% is equal to 0.3 or 3/10, My solution is:

4/10 - 30% + 1/5
4/10 - 3/10*4/10 + 1/5
40/100 - 12/100 + 20/100
40-12/100 = 28/100
28/100+20/100=48/100=24/50=12/25 or 0.48
Excuse me if my English is bad or my calculations are unclear, but I want to know what is the right answer.

2. Originally Posted by emil
I recently had this question on a test:
4/10 - 30% +1/5

Me and my teacher have different answers for it. His solution is:
4/10 - 30% +1/5
4/10 - 3/10 +1/5
1/10+1/5*2/2=3/10
He tells me that the 30% is equal to 0.3 or 3/10, My solution is:

4/10 - 30% + 1/5
4/10 - 3/10*4/10 + 1/5
40/100 - 12/100 + 20/100
40-12/100 = 28/100
28/100+20/100=48/100=24/50=12/25 or 0.48
Excuse me if my English is bad or my calculations are unclear, but I want to know what is the right answer.
This is a matter of interpretation, and on that, your teacher rules!

We don't normally write expressions with a mix of fractions and percentages; but in order to be mathematically consistent, we must interpret it as your teacher did, treating a percentage as merely a different representation of a fraction.

But the reason we don't normally write like that is that one can interpret it as you do, making it somewhat ambiguous. In fact, many simple calculators do just that: entering "x + y%" is interpreted as "increase x by y percent", that is, as "x * (1 + y/100)". So your interpretation is understandable; it is just not what we expect it to mean mathematically. (And I dislike using those calculators, because if I use it for anything other than the applications they expect, I can't be quite sure what they will do. More advanced calculators, if they have a % button at all, treat it as your teacher does.)

Since your teacher agrees with me, you can take that as the truth within your class! Out in the real world, you would be wise to ask someone what they mean by it, if you ever see something written like this.

By the way, you wrote your explanation very clearly, as many students would not. Thanks for making it easy for us! The one thing I would have written differently is "40-12/100", which should be (40-12)/100.

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