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### Course: 7th grade (Illustrative Mathematics)>Unit 5

Lesson 9: Lesson 9: Multiplying rational numbers

# 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 can be a shortcut for adding equal groups of the same size. For example, we can show $5$ groups of $7$ these ways:
• $7+7+7+7+7$
• $5×7$
We can make equal groups with negative values, too.
Rewrite the expression $3\left(-4\right)$ as repeated addition.
$3\left(-4\right)=$

Evaluate.
$3\left(-4\right)=$

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 $6\left(-10\right)$.
Fill each blank with a number to keep both sides of the equation equivalent.
$6\left($
$\right)$
$=$$0$
$6\left($
$+\left(-10\right)\right)$
$=$$0$
$60+6\left(-10\right)$$=$$0$
$60+$
$=$$0$

Evaluate.
$6\left(-10\right)=$

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

## Want to join the conversation?

• why am I doing this if this ant for a grade im not doing this
• Frrrr thank you
• Idk why we need to read this
• the fact that some of us just do these to read the comments ;)
• that is so fr
• What is the product of 10(-10)?
• 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 :)
• why is negative numbers important
?
• Negative numbers often represent losses, things below the surface, etc. For instance, in a bank, negative numbers are used to represent withdrawals. I hope this helps!
• Im not getting a grade for this sooooo im not doing it.