# Questions tagged [negative-numbers]

For questions on teaching students about negative numbers. Both formally and intuitively.

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### Why don’t American school textbooks recognize negative numbers as whole numbers?

Looking up for definition for whole numbers on Google yields a result which mentions: The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included). I ...
156 views

### Is a clear distinction made between signs and operators?

This question about FOIL, comments and answers made me think about the two roles of $-$: as a sign and as an operator. This struck me because the title "Why in the FOIL Method the terms are taken ...
246 views

### Why in the FOIL Method the terms are taken with their signs?

That was the most boring title I could choose but in all honesty, it is what the question is. Here is a reminder of the FOIL method that is used for multiplying two binomials. For example, to multiply ...
605 views

### Exponents with Negative Base; with or without Parentheses

How can I convincingly and mathematically explain the reason behind difference between $(-1)^2$ and $-1^2$? I used to add "negation" to the order of operations, in the same row as multiplication and ...
233 views

### Why are fractions taught before negative numbers?

I'm not a math educator but I'm curious about this. Is this always true, or are there some schools/educational programs where students are shown negative numbers before fractions? Why is it done in ...
650 views

### Negative Denominator in Fractions; Importance and Applications

Why do we need fractions such as $\dfrac{3}{-5}$? I need a convincing answer suitable for 8th grade students. Here's what I've already thought of (which don't fully satisfy me!): Solving the equation ...
2k views

### Explaining the order of negative integers

Today I happen to have an interesting discussion with a primary school kid. I asked him "Which is the smallest one - digit integer?" He instantly replied $-1$. I told him that he's wrong and the ...
417 views

### Subtraction to Addition Conversion; how important is it?

Is it important to convert subtractions to addition, while simplyfing algebraic expressions (For example converting $3x-2y+7x-7y$ to $3x+(-2y)+7x+(-7y)$)? If yes, why and when?
172 views

### Online Resources to Explain Negative Numbers and Scientific Notation

I have to teach someone whose English isn't her native language (and her English skills aren't advanced) the concept of negative numbers + exponents, and how to read scientific / engineering numbers. ...
139 views

### How to preserve axioms from the positive numbers in the negative numbers?

It isn't so hard to convince students of grade 8. 9 that $-2$ is greater than $-4$, but it still make some confusion with an axiom says that ( The whole is greater than part ), which is true in the ...
372 views

### Should we rename the greater than sign?

As math teachers, sometimes we may wish that we could enter our students' minds to see how they think. In early years, while children are learning language, they build the concept of the word greater ...
### How to explain that a negative number multiplied by a negative number is a positive number, and that $-(-x)=x$?
Actually, there is no algebraic problem to show that $-(-x) = x$. This proof can be build upon the concept of the addition of the opposite like this: $- x + x = - x + [- ( - x) ]$, and thus by ...
### How to teach someone that $-3>-4$?
I am trying to teach a teenage person math, but he doesn't seem to be able to grasp the concept of negative numbers and $0$. Again and again he finds $-4$ greater than $-3$ because he has spent ...