When we multiply two negative numbers, the answer is always a positive number.
As an example, let's calculate the product
Here, we have a product of two negative numbers, and The product will be positive. You can think of it as though the two minus signs cancel each other out:
So we have Now, to compute the number in the box, we multiply by without any signs: . Therefore,
Calculate
We have a product of two negative numbers, and So the product will be positive: Now, to compute the number that goes in the box, we multiply and without any signs: So, we get
What is the value of
Let's start by multiplying the first two numbers. We have the product of two negatives, which gives a positive: So we now have
Then, we work out this remaining product using the fact that a positive times a negative gives a negative:
$(-8) \cdot4 \cdot1=$
|
a
|
$32$ |
|
b
|
$-24$ |
|
c
|
$24$ |
|
d
|
$-32$ |
|
e
|
$-36$ |
$(-2) \cdot(-5) \cdot(- 4)=$
|
a
|
$40$ |
|
b
|
$-50$ |
|
c
|
$60$ |
|
d
|
$-40$ |
|
e
|
$50$ |
Calculate
We have a product of two negative numbers, so the product will be positive, and we can drop the minus signs as follows:
Now, we multiply the fractions by multiplying the numerators and denominators separately:
$\left(-\dfrac{2}{5}\right) \cdot \left( -\dfrac{1}{3} \right)=$
|
a
|
$-\dfrac{2}{15}$ |
|
b
|
$-\dfrac{15}{2}$ |
|
c
|
$-\dfrac{6}{5}$ |
|
d
|
$\dfrac{6}{5}$ |
|
e
|
$\dfrac{2}{15}$ |
$\left(-\dfrac{1}{2}\right) \cdot \dfrac{5}{3}=$
|
a
|
$-\dfrac{3}{10}$ |
|
b
|
$-\dfrac{5}{6}$ |
|
c
|
$\dfrac{5}{6}$ |
|
d
|
$-\dfrac{3}{5}$ |
|
e
|
$\dfrac{3}{10}$ |
What is
We have the product of a negative number and a positive number, which gives a negative number.
$(-4.2) \cdot (-3.6)=$
|
a
|
$15.12$ |
|
b
|
$-15.12$ |
|
c
|
$15.36$ |
|
d
|
$14.82$ |
|
e
|
$-14.82$ |
Here, we will prove that the product of two negative numbers is positive. Please don't worry if you don't fully understand all the details. Just follow along as best you can. You can circle back later if needed.
To explain why the product of two negatives is positive, we need to state some properties of numbers that we use regularly:
Subtracting a number is the same as adding its opposite: For example,
The commutative law: For any numbers and we have: For example,
The distributive law: For any numbers and we have: For example,
Let's now prove the following result:
We start with the following true equation:
This is true because any number multiplied by zero equals zero.
Now, since we can write the zero on the left-hand side as follows:
Subtracting a positive is the same as adding a negative. Therefore:
We now apply the distributive law:
Applying the commutative law to the first term on the left-hand side gives:
The number equals since this just means one copy of Therefore:
Finally, adding to both sides of the equation, we finally arrive at: