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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:
• $\mathrm{Positive number}÷\mathrm{positive number}=\mathrm{positive number}$
• $\mathrm{Positive number}÷\mathrm{negative number}=\mathrm{negative number}$
• $\mathrm{Negative number}÷\mathrm{positive number}=\mathrm{negative number}$
• $\mathrm{Negative number}÷\mathrm{negative number}=\mathrm{positive number}$
Example 2
Let's look at the simple division problem of $12÷4$ , which we know is 3. But let's again modify it to look like each of our cases above.
$12÷4=3$
$12÷\left(4\right)=-3$
$-12÷4=-3$
$-12÷\left(4\right)=3$

## 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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