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# Multiplying and Dividing with Negatives

Multiplying
and
dividing
with negative numbers require us to pay a little extra attention.
There are specific rules to follow to figure out if the solution
will be a negative or a positive number. Let's look at the rules for
both multiplication and division with negative numbers.

## Multiplying with negative numbers

There's a simple, four-pronged rule to multiplying with negatives.
It goes as follows:

- $\mathrm{Positive\; number}\ast \mathrm{positive\; number}=\mathrm{positive\; number}$
- $\mathrm{Positive\; number}\ast \mathrm{negative\; number}=\mathrm{negative\; number}$
- $\mathrm{Negative\; number}\ast \mathrm{positive\; number}=\mathrm{negative\; number}$
- $\mathrm{Negative\; number}\ast \mathrm{negative\; number}=\mathrm{positive\; number}$

**Example 1**

Let's look at the simple multiplication problem of
$4\ast 6$
. We know the answer is 24, but let's modify it to look like each of
the cases above.

$4\ast 6=24$

$4\ast \left(-6\right)=-24$

$-4\ast 6=-24$

$-4\ast \left(-6\right)=24$

One item to note here is that since a positive times a positive
equals a positive, and since a negative times a negative equals a
negative, any number times itself is therefore a positive.

$9\ast 9=81$

$-9\ast \left(-9\right)=81$

That's why, when you find the
square root
of a number, such as 81, it is often written as ±9. Because either
positive or negative 9 is the square root of 81.

## Dividing with negative numbers

A similar, four-pronged rule applies to dividing with negative
numbers. It goes as follows:

- $\mathrm{Positive\; number}\xf7\mathrm{positive\; number}=\mathrm{positive\; number}$
- $\mathrm{Positive\; number}\xf7\mathrm{negative\; number}=\mathrm{negative\; number}$
- $\mathrm{Negative\; number}\xf7\mathrm{positive\; number}=\mathrm{negative\; number}$
- $\mathrm{Negative\; number}\xf7\mathrm{negative\; number}=\mathrm{positive\; number}$

**Example 2**

Let's look at the simple division problem of
$12\xf74$
, which we know is 3. But let's again modify it to look like each of
our cases above.

$12\xf74=3$

$12\xf7\left(4\right)=-3$

$-12\xf74=-3$

$-12\xf7\left(4\right)=3$

## Topics related to the Multiplying and Dividing with Negatives

## Flashcards covering the Multiplying and Dividing with Negatives

## Practice tests covering the Multiplying and Dividing with Negatives

## Get help learning about multiplying and dividing with negatives

If your student needs help learning to work with multiplying and
dividing negative numbers, a good idea is to connect them with a
professional math tutor. A tutor who has the expertise to help
students learn to memorize the positive/ negative number rules can
meet with your student in a 1-on-1 setting with no distractions.
This gives the tutor the opportunity to focus solely on your student
as they work through problems together until your student
understands multiplying and dividing negative numbers. Contact
Varsity Tutors today and speak with our Educational Directors to
learn more about how tutoring can help your student.

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