Negative Times Positive — Rules & Examples

Properties of Multiplication: Negative Times Positive

When you are multiplying a negative number and a positive number, the product will be a negative number. This is one of the special cases for multiplying positive and negative numbers together.

Let's do another example.

Step One: Determine the Sign

Since we are multiplying $13,$ which is positive, and $-3,$ which is negative, our product will be negative.

Step Two: Pretend the Numbers are Positive and Multiply

$$13 \times 3 = 39$$

Step Three: Solution!

$$\text{negative } 39 = -39$$

A Negative Number Times 0

When you multiply any number, positive or negative, by $0,$ your result will be 0.

(Video) Integer Multiplication and Division

by Math Antics

Here’s a YouTube video by Math Antics that covers multiplying positives or zero, multiplying a negative by a negative, dividing positive integers, dividing negative integers , dividing a negative and a positive Integer , multiplying a negative by a positive or zero, product of an even number of negatives, and product of an odd number of negatives .

$\large{\text{Summary}}$

Multiplication with integers is the exact same as multiplication with whole numbers, but we need to find what sign to put on our final answer. A negative sign will change the sign of the answer. For instance, a single negative sign in the problem will change the answer from a positive number to a negative number. Two negative signs in the problem will change the answer from a negative number to a positive number.

He uses the example $3 \times 5$ and all of it's positive and negative variations. We're going to look at two of them: $$\begin{align} -3 &\times 5\\ 3&\times -5 \end{align}$$ First, we need to find $3 \times 5$. $$3\times 5 = 15$$ Now we need to find our sign for the answer. Both of our problems have one negative sign, so its going to change the answer from a positive number to a negative number. $$\begin{align} -3 \times 5 &= -15\\ 3 \times -5 &= 15 \end{align}$$

Try one for yourself:

Negative times positive is always negative

Negative numbers change the sign of an expression. For each negative number in it, an expression's sign will change once (it always starts out as positive). This means that an expression with one negative number (like multiplying a negative number by a positive one) will always turn out negative.

Otherwise, though, multiplying with negative numbers works just like multiplying positive numbers. I like to split the process up into two steps:

Step 1: Multiply the numbers.

Step 2: Worry about the signs.

Let's try it with $4 \times -2$.

Step 1: Multiply the numbers.

Since we're ignoring signs right now, we can pretend that both the numbers are positive. So, we can just multiply the same way we would if we were using positive numbers.

$$\begin{align} 4 \times 2&= 4 + 4\\ &=8 \end{align}$$

Good job!

Step 2: Worry about the signs.

Since we're multiplying a positive number by one negative number here, that means we have to flip the sign (starting from positive) once. So, our result will be negative:

$$4 \times -2 = 4\times 2\times -1=8\times -1=-8$$