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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 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.