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Introduction

QUICK LINKS


Introduction

Multiplying and Dividing Negative Numbers

INTRO
—
When it comes to multiplying and dividing negative numbers, we like to fast forward and rewind to help us determine whether the final answer should be positive or negative.
Hear us out! 🙏🏽 Let’s say we rewind a cute video of a puppy running forward.

⏮ Rewind

Notice the puppy now appears to be running backward. We can imagine that
  • The original motion of the puppy matches the sign of the first number (forwards = positive, backwards = negative).
  • The mode of the tv matches the sign of the second number (fast forward = positive, rewind = negative).
  • The new motion of the puppy matches the sign of the final answer.
Play around with this TV to test out which combos give us positive numbers and which give us negative numbers.

Motion:

Mode:

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CALCULATOR
—

Multiplying & Dividing Negative Numbers Calculator

Step 1. Imagine the first number.

Original Question:
The first number () is negative, so we imagine a video of someone running backward.

Step 2. Imagine the second number.

Original Question:
The second number () is negative, so we rewind our video.

⏮ Rewind

Step 3. Determine the sign of the final answer.

Original Question:
If we fast forward a video of someone running backward, it will look like they're still running backward.

⏮ Rewind

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is negative, so now we just need to multiply the numbers to get our answer: .
KEY STEPS
—

How to Multiply and Divide Negative Numbers

First number is and second number is.

Step 1. Imagine the first number.

If the first number is positive, imagine a video of someone running forward.
If the first number is negative, imagine a vieo of someone running backward.

Step 2. Imagine the second number.

If the second number is positive, imagine fast forwarding the video of someone running from Step 1.
If the second number is positive, imagine rewinding the video of someone running from Step 1.

Step 3. Determine the sign of the final answer.

A video of someone running forward that we rewind will look like a video of someone running backward. So our answer is negative.
A video of someone running backward that we rewind will look like a video of someone running forward. So our answer is positive.
A video of someone running backward that we fast forward will look like a video of someone still running backward. So our answer is negative.
A video of someone running forward that we fast forward will look like a video of someone still running forward. So our answer is positive.

⏮ Rewind

Step 4. Multiply/divide the numbers.

Determine the product/quotient of the numbers. Add the sign if the answer should be negative based on Step 3.
LESSON
— Multiplying Negative Numbers

Multiplying Negative Numbers

When we multiply negative numbers, we use the fast forward and rewind hack to determine the sign of the final answer before calculating the product.
ProblemImagine
positive × negative = negativeforward motion and rewind = backward motion
negative × positive = negativebackward motion and fast forward = backward motion
negative × negative = positivebackward motion and rewind = forward motion
Let's walk through a couple examples to see this in action!

EXAMPLE 1

Let’s start by looking at an example where we have a positive number multiplied by a negative number 👀.

Step 1. Imagine the first number.

Original Question:
The first number () is positive, so we imagine a video of someone running forward.

Step 2. Imagine the second number.

Original Question:
The second number () is negative, so we rewind our video.

⏮ Rewind

Step 3. Determine the sign of the final answer.

Original Question:
If we rewind a video of someone running forward, it will look like they're running backward.

⏮ Rewind

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is negative, so now we just need to multiply the numbers to get our answer: .

EXAMPLE 2

Now, let’s see what happens when we have a negative number multiplied by a positive number 👀.

Step 1. Imagine the first number.

Original Question:
The first number () is negative, so we imagine a video of someone running backward.

Step 2. Imagine the second number.

Original Question:
The second number () is positive, so we fast forward our video.

⏭ Fast Forward

Step 3. Determine the sign of the final answer.

Original Question:
If we fast forward a video of someone running backward, it will look like they're still running backward.

⏭ Fast Forward

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is negative, so now we just need to multiply the numbers to get our answer: .

EXAMPLE 3

Now, let’s see what happens when we have a negative number multiplied by a negative number 👀.

Step 1. Imagine the first number.

Original Question:
The first number () is negative, so we imagine a video of someone running backward.

Step 2. Imagine the second number.

Original Question:
The second number () is negative, so we rewind our video.

⏮ Rewind

Step 3. Determine the sign of the final answer.

Original Question:
If we rewind a video of someone running backward, it will look like they're running forward .

⏮ Rewind

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is positive, so now we just need to multiply the numbers to get our answer: .
Awesome! Expand the
Practice
below to try some more problems or expand the next
Lesson
to explore what we do when we're dividing negative numbers.
PRACTICE
— Multiplying Negative Numbers

Practice: Multiplying Negative Numbers

Question 1 of 4:

Step 1. Imagine the first number.

Is the first number positive or negative?
That's right! Since the first number is positive we imagine a video of someone running.
Question 1 of 4:

Step 2. Imagine the second number.

Is the second number positive or negative?
That's right! Since the second number is negative we the video.
Question 1 of 4:

Step 3. Determine the sign of the final answer.

A video of someone running forward that we rewind will look like a video of someone running, which means our final answer will be.
Question 1 of 4:

Step 4. Multiply the numbers

We know our answer is negative, so what is the answer?

⏮ Rewind

⏮ Rewind

Nice! A positive number multiplied by a negative number equals a negative number. Now that we know the sign, we can solve for the final answer!
Nice work! Our answer is
LESSON
— Dividing Negative Numbers

Dividing Negative Numbers

Our rules for dividing are the same as our rules for multiplying:
ProblemImagine
positive ÷ negative = negativeforward motion and rewind = backward motion
negative ÷ positive = negativebackward motion and fast forward = backward motion
negative ÷ negative = positivebackward motion and rewind = forward motion
Let's walk through a couple examples to see this in action!

EXAMPLE 1

Let’s start by looking at an example where we have a positive number divided by a negative number 👀.

Step 1. Imagine the first number.

Original Question:
The first number () is positive, so we imagine a video of someone running forward.

Step 2. Imagine the second number.

Original Question:
The second number () is negative, so we rewind our video.

⏮ Rewind

Step 3. Determine the sign of the final answer.

Original Question:
If we rewind a video of someone running forward, it will look like they're running backward.

⏮ Rewind

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is negative, so now we just need to divide the numbers to get our answer: .

EXAMPLE 2

Now, let’s see what happens when we have a negative number divided by a positive number 👀.

Step 1. Imagine the first number.

Original Question:
The first number () is negative, so we imagine a video of someone running backward.

Step 2. Imagine the second number.

Original Question:
The second number () is positive, so we fast forward our video.

⏭ Fast Forward

Step 3. Determine the sign of the final answer.

Original Question:
If we fast forward a video of someone running backward, it will look like they're still running backward.

⏭ Fast Forward

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is negative, so now we just need to divide the numbers to get our answer: .

EXAMPLE 3

Now, let’s see what happens when we have a negative number divided by a negative number 👀.

Step 1. Imagine the first number.

Original Question:
The first number () is negative, so we imagine a video of someone running backward.

Step 2. Imagine the second number.

Original Question:
The second number () is negative, so we rewind our video.

⏮ Rewind

Step 3. Determine the sign of the final answer.

Original Question:
If we rewind a video of someone running backward, it will look like they're running forward .

⏮ Rewind

Step 4. Multiply/divide the numbers.

Original Question:
We know our answer is positive, so now we just need to divide the numbers to get our answer: .
Awesome! If you’d like to practice additional problems dividing negative numbers, expand the
Practice
below before closing out this lesson! ⚡
PRACTICE
— Dividing Negative Numbers

Practice: Dividing Negative Numbers

Question 1 of 4:

Step 1. Imagine the first number.

Is the first number positive or negative?
That's right! Since the first number is positive we imagine a video of someone running.
Question 1 of 4:

Step 2. Imagine the second number.

Is the second number positive or negative?
That's right! Since the second number is negative we the video.
Question 1 of 4:

Step 3. Determine the sign of the final answer.

A video of someone running forward that we rewind will look like a video of someone running, which means our final answer will be.
Question 1 of 4:

Step 4. Divide the numbers

We know our answer is negative, so what is the answer?

⏮ Rewind

⏮ Rewind

Nice! A positive number divided by a negative number equals a negative number. Now that we know the sign, we can solve for the final answer!
Nice work! Our answer is
CONCLUSION
—
Dang, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?
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