Ask Dr. Math

High School Archive

Browse High 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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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?

Negative Bases [06/10/1999]

Are there such things as negative bases?

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.

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?

Squaring Negative Numbers [02/19/2002]

Does -9^2 = 81 or -81?

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

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

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.

Are Negative Exponents Like Other Exponents? [08/21/2002]

Is there a general rule for doing all exponents, or does a negative exponent have nothing in common with positive exponents?

Avoiding Careless Mistakes [01/30/2002]

How can I avoid careless mistakes?

Calculating Percent Change when the Base is a Negative Number [01/18/2002]

In preparing financial statements, I must calculate the percent change of the net income between years...

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?

Distributive Property with Negatives [10/13/2004]

When using the distributive property with negative numbers, I don't understand when, why, and how the operator changes (from addition to subtraction, or the other way). Sometimes it changes, sometimes it doesn't. Can you explain when to change it, and why?

Dividing Negative Numbers in Real Life [03/03/2004]

Why and when do we divide by a negative number in real life? I can't find a convincing example to make my child happy.

Exponents Containing Negative Integers [12/15/1998]

Order of operations and raising a negative number to a power.

Mod Function and Negative Numbers [04/28/2000]

What is the correct value for the function MOD(-340,60)? Microsoft Excel returns the value 20, while Lotus 1-2-3 returns the value -40. Can you explain the difference?

Multiplying or Dividing by a Negative Number [04/08/1999]

When x(x-4) is less than 0...

Negative Bases [05/13/2002]

How would you represent a number (e.g., 16) in base -2?

Negative Number History [11/25/2001]

What happened in the 16th century that caused people to need to use negative numbers, and what was their image of a negative number before that?

Negative Numbers Combined with Exponentials [03/09/2001]

Why in the order of operations is negation a multiplication done after exponentiation, rather than as a part of the base? What about polynomials?

Negative Numbers in Base 2, 16, etc. [01/24/2003]

Are there negative numbers in alternate bases? Our calculator says that 1-2 in base16 is FFFFFFFFFF. This can't be right!

Negatives [1/10/1995]

Can anyone explain why two negatives make a positive in sign multiplication?

Negatives and Inequalities [09/10/1998]

Why when we multiply or divide an inequality by a negative number do we reverse the inequality sign?

Polynomial Inequality [06/23/2004]

How do I solve an inequality like (x^2 + x - 12)/(x + 1) >= 0?

Product of Negative Numbers [02/04/1997]

Can you give a proof of why the product of two negative numbers is positive?

Put the Variable in Parentheses [10/15/2001]

Squaring -4.

Reversing the Inequality Symbol [03/09/1999]

Why do we reverse the inequality symbol when dividing/multiplying by a negative number?

Rounding Negative Numbers [05/23/2007]

I was wondering what -0.5 is rounded to the nearest integer?

Solving Absolute Value Equations [01/12/2004]

How do I solve an absolute value equation with variable expressions on each side, such as abs(x + 1) = abs(x - 1)?

Square root of a negative number [11/23/1994]

Is it theoretically possible to calculate the square root of a negative number?

Square Root of a Negative Number Squared [01/23/1997]

Is Sqrt(-6)^2 equal to 6 or -6?

Subtracting and Borrowing in a Column [09/05/2002]

A student borrowed in a column as follows: 6.9 - 7.92, to get -2.98. Why won't borrowing work with this number?

"Subtraction" and "Negative"--Same Sign, Different Concepts? [12/14/2005]

Why do we use "-" to mean both "subtraction" and "negative", when those are two different concepts?

Talking About Zero, Absolute Zero and Negative Numbers [11/12/2003]

Are there any useful strategies other than temperature to introduce negative numbers, and also to teach about zero, its properties, and how they differ from those of absolute zero?

What If There Was No Zero? [10/21/2003]

Why did it take so long to discover zero? Why did early civilizations not need zero? How would math as we know it be different if there was no zero?

Why Aren't There Negative Prime Numbers? [12/10/1999]

Why can't negative numbers be prime numbers?

Why Does a Negative Times a Negative Equal a Positive? [03/01/1998]

Using the distributive law to reason why a negative times a negative equals a positive.

Why Flip the Inequality Sign? [10/26/2001]

Please tell me why you flip the inequality sign when dividing by a negative number.

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