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## 7th grade

### Course: 7th grade > Unit 5

Lesson 1: Multiply with negatives# Multiplying a positive and a negative number

Discover what it means to multiply by negative numbers by using repeated addition and using the distributive property.

## Extending multiplication to more numbers

Whether we use whole numbers, fractions, or integers, multiplication still has the same meanings.

Let's explore how different properties of multiplication help us make sense of multiplication with negative numbers.

## Multiplication as repeated addition

Multiplication can be a shortcut for adding equal groups of the same size. For example, we can show $5$ groups of $7$ these ways:

$7+7+7+7+7$ $5\times 7$

We can make equal groups with negative values, too.

This makes sense on a number line, too.

Starting from $0$ , taking $3$ steps of $4$ units each in the negative direction leads us to $-12$ .

## Multiplication with the distributive property: positive times negative

The properties of multiplication work the same with negatives as with positive numbers and $0$ . Let's use the distributive property to convince ourselves of the value of $6(-10)$ .

**Describe a general pattern for when we multiply a positive number times a negative number.**

## Want to join the conversation?

- Idk why we need to read this(10 votes)
- why am I doing this if this ant for a grade im not doing this(8 votes)
- why so much khan!?(7 votes)
- i couldnt think for a sec. lol(6 votes)
- Are any of you doing this in 6th grade as well?

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^^(6 votes) - What is the product of 10(-10)?(3 votes)
- It's -100 (negative 100)

I'll explain

multiplying with numbers of different signs is just basically regular multiplication with different signs.

A positive number times a negative number is negative.

This is because as multiplication is basically repeated addition, here you are adding -10 to itself a bunch.

In other words, subtracting regularly.

Also multiplying two numbers of the same sign is positive (example -5 x -5 = 25, 5 x 5 = 25)

And it's the opposite with two numbers of different signs.

I hope I helped :)(4 votes)

- these comments are crazy(4 votes)
- how did I get them all correct? I LITERALLY GUESSED ALL OF THEM.(3 votes)
- bombastic side eye(0 votes)

- hello i am so smart heeheehhehhhhe(2 votes)
- so not smart smart people say ha ha ha ha ha ha ha ha ha ha ha(1 vote)

- (\_/)

('.')

(>?<)

^ ^

A better version(2 votes)