Introduction

Multiplying with negative numbers can be summed up by two simple rules.

The first rule says that when we multiply a negative number by a positive number, the result (product) is a negative number. We can picture this multiplication rule as \begin{align*} \mathbf{\color{red}(-)} \:\mathbf{\cdot}\: \mathbf{\color{blue}(+)} \:=\: \mathbf{\color{red}(-)} \qquad\textrm{or}\qquad \mathbf{\color{blue}(+)} \:\mathbf{\cdot}\: \mathbf{\color{red}(-)} \:=\: \mathbf{\color{red}(-)}. \end{align*}

For instance, let's find out the value of (-3) \cdot 10. Here, we have a product of a negative number \color{red}(-3) and a positive one {\color{blue}(10)}. So the product will be negative: {\color{red}(-3)} \cdot {\color{blue}10} = {\color{red} \mathbf{-} \fbox{[math]\phantom{30}[/math]} } Now, to compute the number that goes in the box, we multiply 3 by 10 without any signs: 3 \cdot 10 = 30. So, we get {\color{red}(-3)} \cdot {\color{blue}10} = {\color{red} -30 }.

Note that multiplication is commutative, meaning it doesn't matter in what order we multiply two numbers. Commutativity means that we're allowed to swap the numbers, which gives

{\color{red}(-3)} \cdot {\color{blue}10} = {\color{blue}10}\cdot {\color{red}(-3)} = {\color{red} -30 }.

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Example: Multiplying a Positive Number by a Negative Number

Find the value of (-5) \cdot 2.

EXPLANATION

We have a product of a negative number ({\color{red}-5}) and a positive number ({\color{blue}2}). So the product will be negative: {\color{red}(-5)} \cdot {\color{blue}2} = {\color{red}\mathbf{-} \fbox{[math]\phantom{10}[/math]} }

Now, to compute the number that goes in the box, we multiply 5 by 2 without any signs: 5 \cdot 2 = 10. So, we get

{\color{red}(-5)} \cdot {\color{blue}2} = {\color{red}-10}.

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Practice: Multiplying a Positive Number by a Negative Number

$10 \cdot(-2)=$

a
 $5$
b
 $-5$
c
 $-20$
d
 $8$
e
 $20$
Practice: Multiplying a Positive Number by a Negative Number

$(-3) \cdot2=$

a
 $-1$
b
 $-5$
c
 $6$
d
 $5$
e
 $-6$
Example: Multiplying a Positive Number by a Negative Number With Decimals

What is (-20) \cdot 1.2?

EXPLANATION

We have a product of a negative number ({\color{red}-20}) and a positive number ({\color{blue}1.2}) . So the product will be negative: {\color{red}(-20)} \cdot {\color{blue}1.2} = {\color{red}\mathbf{-} \fbox{[math]\phantom{24}[/math]} }

Now, to compute the number that goes in the box, we multiply 20 by 1.2 without any signs: 20 \cdot 1.2 = 24. So, we get

{\color{red}(-20)} \cdot {\color{blue}1.2} = {\color{red}-24}.

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Practice: Multiplying a Positive Number by a Negative Number With Decimals

$10 \cdot (-0.7)=$

a
 $7$
b
 $70$
c
 $-70$
d
 $-7$
e
 $-7.7$
Practice: Multiplying a Positive Number by a Negative Number With Decimals

$(0.4) \cdot (-15 ) =$

a
 $14.6$
b
 $15.4$
c
 $-6$
d
 $6$
e
 $-15.4$
Practice: Multiplying a Positive Number by a Negative Number With Decimals

$(- 1.5)\cdot 6=$

a
 $7.5$
b
 $4.5$
c
 $-4.5$
d
 $-9$
e
 $9$
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