Ask Dr. Math

Middle School Archive

Browse Middle School Negative Numbers
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Inequalities and negative numbers.
    Positive/negative integer rules.

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Adding a Negative: Absolute Value and Parentheses [08/25/2001]

When we get into the absolute value symbols and the parentheses it goes completely over my head! For example: 0-(-2).

Converting Words to Numbers [06/03/1998]

Can you help me find integers to represent phrases such as "5 degrees below zero"?

Distributive Law [8/2/1996]

Why does "-(y sq - y)" become "-y sq + y?" Why does the subtraction sign change to addition?

Dividing by a Negative Fraction [01/24/2002]

I understand how to divide fractions, but what if one of them is negative?

Dividing Negative Exponents [10/14/1998]

Why does a negative exponent become positive when you divide by it?

Exponents and Negative numbers [03/02/1997]

Why wouldn't the answer to -3 squared, standing alone and without parenthesis or brackets, be -9?

Introduction to Negative Numbers [08/11/1998]

What is 11 - 12? How can you subtract more than what you have?

Manipulating Positive and Negative Numbers [8/9/1996]

Could you explain the rules for adding, subtracting, multiplying, and dividing positive and negative numbers?

Multiplying Negative by Negative [11/6/1994]

Neg x Neg = Pos just doesn't make sense. Does it ever happen in real life?

Negative Bases [06/10/1999]

Are there such things as negative bases?

Negative Number Rules [01/05/1998]

When do two negative numbers equal a positive?

Negative Times a Negative [01/12/1997]

Can you give an example why a negative times a negative is positive?

Negative Times Negative [10/17/1998]

An example using videotaping to explain how a negative times a negative is a positive.

Operating on Negative Numbers [10/21/1996]

I have lots of problems multiplying and dividing integers - the negative and positive numbers give me a really hard time.

Picturing Negative Numbers [11/03/2002]

If I have 4 apples and eat them, I get 0 apples. But I can't eat another apple, so how do I get to minus 1?

Prove That -(-a) = a [09/11/2001]

How do you prove that -(-a) = a using the properties of real numbers? What about -1 * -1 = 1?

Signs: Rules, Number Line [07/13/2001]

What is (-) - (+) = ? or (+) + (-) = ?

Squaring Negative Numbers [02/19/2002]

Does -9^2 = 81 or -81?

Subtracting Negative Integers - Number Line [10/15/1996]

How do you subtract integers like 5-(-6) ?

Subtracting Negative Numbers [03/30/1997]

I have trouble explaining subtracting negative numbers to my students. I think the underlying problem is that I truly don't understand it myself.

Subtracting Numbers by Walking a Number Line [09/12/2001]

For example: -8.1- -6.9 = -1.2 and -9.9- -11.1 = 1.2. All the numbers are negative, so why is the answer to the first problem negative but the second isn't?

Subtracting Positive and Negative Numbers [5/21/1996]

How would you figure out the answer to -13 - 6 = ? and how can you subtract a negative number from a positive number or a positive number from a negative number?

Tips for Negative and Positive Numbers [11/30/2001]

I really get confused when adding a negative and a positive.

Working with Integers [01/12/1999]

Could you explain how to divide, multiply, add, and subtract integers?

-6 times -6 [11/3/1994]

I really need to know what the answer to this problem is. -6 X -6

91 - 92 = ? [01/23/1997]

What does 91 - 92 equal?

Adding and Subtracting Integers [12/31/1997]

Adding and subtracting integers like 12 + (-4) = ...

Adding and Subtracting Integers [04/17/2006]

Can you explain how to add and subtract negative numbers?

Adding and Subtracting Negative Integers as Temperatures [01/08/2004]

If it's -20 degrees outside and it decreases 3 degrees what temperature is it? I know the answer is -23 degrees but it seems like it should be -17 degrees.

Adding and Subtracting Negative Numbers [02/07/2002]

What is (-1) - 5 + -8 equal to?

Adding Negative Numbers [03/12/1997]

What are examples of adding negative numbers in the real world?

Adding Negatives [12/04/1997]

What is -2 - 7/10 ? Is it -1 3/10 or -2 7/10?

Adding Positives and Negatives [12/01/1998]

I'm having trouble solving problems like these: -31+(-46)=b, a=16+(- 36), and 74+(-63)=d.

Algebra and Exponents: -4^2 = ? [06/30/1998]

I had an argument with a professor over this topic. I say 16, he says - 16.

Algebraic Proof That Positive Times Negative Equals Negative [03/28/2004]

Is there an algebraic proof that a positive times a negative equals a negative?

Algebra Tiles and Negatives [11/05/2001]

Use a model (algebra tiles) to demonstrate that a negative times a negative = a positive.

Avoiding Careless Mistakes [01/30/2002]

How can I avoid careless mistakes?

Can a Number to the Zero Power be -1? [01/25/2002]

My teacher told me that (-3^0) is equal to -1. Is this true?

Celsius to Fahrenheit [04/26/1999]

How do you convert Celsius to Fahrenheit?

Converting Negative Mixed Numbers to Improper Fractions [10/25/2006]

When converting a negative mixed number into an improper fraction, it seems like we ignore the rules for integer addition. For example, to convert -4 1/7 we think -4 1/7 = -4 * 7 + 1 = -28 + 1 = -27/7. But the correct answer is -29/7. How does -28 + 1 make -29?

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