I'm really stumped on some of the equivalent expression practice problems. The expected answers really aren't making sense to me at all. Screenshot of a particular practice problem below.
Could someone help me understand why 7 + 1 = 6 in this problem?
Hi.
You are looking at the problem incorrectly. It is actually (-7) + 1 = (-6).
When you see a subtraction sign infront of a number, it just means the number is negative. That subtraction sign follows it wherever it goes! (Unless you are dividing both sides by a negative. Then all the positive and negative numbers flip!)
Thanks for that, that definitely cleared up the problem for me. Though it's raise a couple of questions for me if you don't mind.
To clarify, does that mean that when reading algebraic equations or problems, that subtraction signs always denote a negative number rather than a subtraction? But addition signs still signal an addition operation?
Or am I completely on the wrong track, and should just treat the subtraction and addition as kind of implied.
When a number has a subtraction sign, it will always always always denote a negative number. That is because (from what I understand) that number has the subtraction operation and it is its own thing.
So if you have 20-3+1, you can look at 3. The whole number would technically be minus 3 (unless it was something like 20(-3) which would mean multiplication). So where ever you move it it will always mean minus 3. So if you start dividing by it or multiplying it, it will represent itself as a minus 3 (or better known as a negative 3).
It is just kinda implied that positive numbers are any numbers without a minus sign in front of them and negative numbers have them. Addition can be done with negative numbers too though.
Such as (20-(3)). What that would really show is +20 - (+3), with + denoting the numbers to be positive. That in turn can just be translated to 20 - 3.
To sum it all up, if you have a minus sign in front of any number, that minus sign follows it and denotes it that it is negative.
One more example to make sure you understand.
20-3+2-10. This is the same thing as stating -10-3+20+2.
Another way to think about it is how to make subtraction associative and commutative. That means how can you move those numbers around so that the result is always the same? (Hint: Just keep the minus sign near them).
Wow, thanks so much for the detailed explanation. I've always been terrible at getting my head around maths, maybe partly because it's so abstract, but your explanation really helped cement it for me. It's made solving the algebra problems I've been having trouble with much more simple for me.
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