Lesson video

Hello, I'm Mr. Lund and this lesson is on multiplying and dividing directed numbers.

We're going to calculate three times by negative four.

Let's use counters to help us.

Here is an array, three lots of negative four counters.

Three times by negative four is therefore equal to negative 12.

What about this, calculate negative three multiplied by four.

I have negative three multiplied four times.

Look, I end up with the same answer.

Negative three multiplied by four is equal to negative 12.

Let's use our array to see if we can spot some patterns.

Here I've shown you that the pattern is increasing by four each time.

Let's continue the pattern on.

Notice originally the numbers were negative.

This leads us to an important mathematical concept.

When we multiply two positive numbers together, we end up with a positive answer.

When we multiply two numbers together but one is negative, we end up with a negative answer.

When we multiply two negative numbers together, we end up with a positive answer.

And when we multiply a negative and a positive, we end up with a negative answer.

When the signs are the same, our answers are positive.

When the signs are different, we end up with a negative answer.

So have a look at the four questions underneath.

Positive times a positive, it gives you a positive answer.

What do you think about the next one? Positive times a negative, well that gives you a negative.

The signs are different.

A negative and a positive, are the signs the same of they're different? They are different here so we're going to end up with a negative answer.

And then finally negative and a negative, the signs are the same so our answer is positive.

Here are some questions for you to try.

Pause the video and when you want to check your answers, return.

Let's try questions two and three.

Pause the video and when you want to check your answers, return.

Here are the solutions to questions two and three.

Remember, two signs that are the same find a positive answer, and different signs find a negative answer when multiplying two numbers together.

Let's move our attention to dividing negative numbers.

Follows the same rules though.

Calculate negative 12 divided by positive three.

The signs are different, what do you think our answer will be? That's right, negative 12 divided by three equals negative four.

Here's another example.

In this example, I'm dividing two numbers that have the same sign, negative 12 divided by negative three.

What's going to happen here? That's right, I end up with positive answer.

Let's use our understanding of inverse operations to help us understand how to divide negative numbers.

Here negative three multiplied by negative four finds us a positive answer of 12.

Rearranging that equation, I could say that 12 divided by negative three is going to equal negative four.

You can also think about 12 divided by negative three having two different signs, and so you end up with a negative answer.

So I'll look in the next example.

12 divided by negative four.

As we said previously, negative three times by negative four equals 12.

Rearrange that equation, then 12 divided by negative four is equal to negative three.

Hopefully that helps you think about what's happening in terms of dividing with negative numbers.

Can you spot the patterns on the page? Take a look.

Now let's see if we can use those patterns to answer the questions underneath.

Positive divided by a positive, two signs are the same, what's our answer going to be? We end up with a positive answer.

Positive divided by a negative, signs are different so we end up with a negative answer.

Negative divided by a positive, the signs are different, we end with a negative answer.

Negative divided by a negative, we end up with a positive answer.

Here are some questions for you to try.

Pause the video and return to check your answers.

Here are the solutions to questions four and five.

Question four asks you to rearrange an equation.

Hopefully, you've got that skill in the bag.

Let's try question six and seven.

Pause the video.

Once you complete your task, return to check your answers.

Here are the solutions to questions six and seven.

Which card does not belong? Well it is the card that does not equal negative four.

Question six, we have to arrange our solutions in ascending order, going from small to large, ascending.