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Introduction

Multiplying & Dividing Negative Numbers

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:

Check out our calculator or continue the lesson to explore how we use our imagination to help us add and subtract negative numbers!

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: .

Recap 🧢 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.

Learn how to visualize the multiplication and division of negative numbers in more detail. Pick where you want to start!
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