# Tag Info

### Explaining the order of negative integers

To my mind, the problem is the word smallest. If you asked me which is smaller, $-1$ or $-9$, I'd ask you to clarify in what sense. Colloquial use of small refers to magnitude rather than ordering. It ...
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### Parentheses around negative numbers

It is not a good idea to against a convention, unless you have strong reasons for it. That said, you might not want to punish those going against the convention, either. An obvious reason for having ...
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### Why don’t American school textbooks recognize negative numbers as whole numbers?

I’m more curious about incorrect things in them. Yet, this is the first thing I found. There's absolutely nothing "incorrect" about this. As Dave L Renfro noted in a comment: and whole ...

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

I don't think that "textbooks" decided this, usage did. The term "integer" covers positive and negative, so it would be redundant for whole numbers to refer to that category. And ...
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### Parentheses around negative numbers

Others have talked about legibility, so I want to address the importance of the parentheses in an expression like $$17\color{red}{-}(\color{blue}{-}59)$$ from the perspective of educational psychology....
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### Explaining the order of negative integers

It seems to me that what you asked wasn't really right. -9 is the "lowest one-digit integer" but (at least it can reasonably argued) 0 is the smallest. Maybe making this difference explicit would ...

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

I'm going to answer with something of a polemical frame challenge: FOIL is evil, and probably shouldn't even be taught. Okay... that's a bit extreme. How's this: FOIL is a mnemonic that is, in my ...
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### Why don’t American school textbooks recognize negative numbers as whole numbers?

You seem to describe "whole numbers" in this American usage as describing $\mathbb {N}$, the set of natural numbers, whereas you expected it to describe $\mathbb{Z}$, the set of integers. As ...
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### Explaining the order of negative integers

All 8 answers so far seem to have missed the following issue: Ask the student why he picked $-1$ rather than $1$ or $0$. If he changes his mind and says that $0$ is the smallest, then he is using ...
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Accepted

### Explaining the order of negative integers

He wants to know the why, not per se the logic behind it. So give him a reason he can understand. Explain to him that many hundreds of years ago the concept of zero didn't exist. There was no number ...
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### Explaining the order of negative integers

So $-9$ is "smaller" than $-1$? By that terminology, a bank account overdrawn by $9$ dollars (balance $-9$) would be said to carry a "smaller debt" than a bank account overdrawn by $1$ dollar (...

### Negative Denominator in Fractions; Importance and Applications

I would say you're doing your student a disservice if you were to seriously disallow a negative denominator. A fraction is simply a ratio of two integers (where the denominator is not allowed to be ...
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### Parentheses around negative numbers

Are there any reasons why this notation is necessary? Yes, of course - it is necessary to avoid easily avoidable errors introduced by unclear writing. While it may usually be obvious from context if ...
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### Why in the FOIL Method the terms are taken with their signs?

The issue isn't unique to factoring or the FOIL process. The roots of $(ax^2 + bx + c)$ can be found via the quadratic equation. $$x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}$$ Now, this prompts the ...

### Explaining the order of negative integers

I will only add to the other excellent answers that even the words "less than" (the conventional name of the $<$ sign) can reinforce the (incorrect) notion that $<$ is used to compare the ...
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### Exponents with Negative Base; with or without Parentheses

You might explain that BEDMAS is not the whole story when it comes to the order of operations. There is an operation called negation. It reverses the sign on numerical quantifies. It gives the ...
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### Exponents with Negative Base; with or without Parentheses

I like the presentation on the NCTM Math Forum/Dr. Math website: We don't usually list unary operators in PEMDAS because they're thought of as being implied by the rules for binary operations. You ...
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### Explaining the order of negative integers

If he's ignoring the + or - signs, then that needs to get remediated. My approach is to: Define negative numbers as running to the left on the number line. (In other words, the "-" means "in the ...
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### Explaining the order of negative integers

Help him first to understand that subtracting 1 make numbers lower, lower and lower. Each time you subtract 1, you have less than before. Just like adding 1 will make them higher, higher and higher. (...
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### Why in the FOIL Method the terms are taken with their signs?

Simple answer: Including the signs/negative numbers is algorithmic. Working out the sign afterwards requires thinking. Imagine writing computer code to multiply out the brackets. You would do it by ...
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### Exponents with Negative Base; with or without Parentheses

If your students already understand that exponents precede multiplication, and that multiplying by $-1$ is the "negation" operator, then you should be able to convince them that -5^2 = -1*5^2 = -1*...
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### How to explain that a negative number multiplied by a negative number is a positive number, and that $-(-x)=x$?

I won't try to give a specific explanation here because I think that depends highly on the level of knowledge of the student. Rather, I'd like to emphasize some general points that I think are helpful ...
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Accepted

### Why are fractions taught before negative numbers?

In the US, we have the controversial Common Core. A summary of it is available here. In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole ...

### Negative Denominator in Fractions; Importance and Applications

There are numbers that one (or many) may never use, is this a reason to eliminate them. Is there a reason to have 1 to any non-negative integer power? When responding to questions of this type "Why ...