Multiplying And Dividing With Negative Numbers

Multiplying And Dividing With Negative Numbers


Hello there. In his math post, I am going over multiplying and dividing negative numbers. For simplicity, the examples will use integers (whole numbers).

If you would like reasoning on why a negative multiplied/divided by a negative number is positive I would recommend this page from the mathisfun website.

 


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Multiplying With Negative Numbers


With regular multiplication, you have a positive number multiplied by a positive number which is positive.

If you have a negative number multiplied by a positive number, the product/answer is negative. The opposite order results in a negative number as well. That is a positive number multiplied by a negative number is a negative number.

A negative number multiplied by a negative number is a positive number.

 

Summary Chart

Here is a summary chart which goes over the four cases. A chart like this helps makes things clear.

 

Sign OneSign TwoSign Of Answer
+++
+--
-+-
--+

 

Example One

Multiplying 7 by -2 gives a product of -14.

 

Example Two

Negative Two multiplied by negative 10 is positive 20.

 

Example Three

The answers of negative ten multiplied by 5 is -50.

 


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Dividing With Negative Numbers


Division with negative numbers is not much different when it comes to the signs.

  • A positive number divided by a positive number is positive.

  • A negative number divided by a positive number is negative and a positive number divided by a negative number is a negative number.

  • A negative number divided by a negative number is a positive number.

 

Summary Chart

The summary chart for the divison case is the same as the one in multiplication.

 

Sign OneSign TwoSign Of Answer
+++
+--
-+-
--+

 

Example One

Thirty divided by negative two is negative fifteen.

 

Example Two

Having -100 divided by -5 is +20.

 

Example Three

Negative 91 divided by seven is -13.

 


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Dealing With More Than Two Numbers


What if we had to multiply and divide more than two numbers? This section will deal with that case.

The easiest case is where all the numbers are positive. The answer would be positive.

Recall that a negative number multiplied/divided by a positive number is negative. The same goes for the signs in reverse (positive with a negative). Notice how that there is one negative in the two numbers.

For more than two numbers being multiplied/divided, if there is an odd number of negative numbers, the answer would be negative. As an example 6 x -2 x 2 = -24. Another example includes -1 x -1 x 2 x 3 x -2 = -12.

 

Example One

What is 2 multiplied by -3 multiplied by 10?

Two multiplied by negative three gives -6. Then -6 multiplied by 10 gives -60.

 

Example Two

What is 100 divided by 4 divided by -5?

One hundred divided by four gives 25. Twenty-five divided by negative 5 gives -5.

 

Example Three

What is (-1) x (-1) x 2 x (-3) x (-2)?

With this many numbers treat this in pairs from left to right. Negative one multiplied by negative one is +1. Then 1 multiplied by 2 is 2. This two is multiplied by -3 which is -6. Negative six multiplied by negative two gives (positive) 12.

 


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Practice Problems


Evaluate each of the following. Answers to these practice problems are in the next section.

  1. 10 x (-3)

  2. 2 x 7 x (-2)

  3. (-7) x (-9)

  4. 2 x (-1) x (7) x (-10)

  5. (-5) x 2 x 3

  6. (-7) x 7

  7. 9 x (-2) x (-3)

  8. 1 x (-5) x (-2) x (-10) x (2)

 

Answers To Practice Problems


  1. -30

  2. -28

  3. 63

  4. 140

  5. -30

  6. -49

  7. 54

  8. -200

 


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Thank you for reading.

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