Whenever we add a negative number, we write parentheses around the negative number so that it's easier to read.
For example, instead of
which is difficult to read, we write
Adding a negative number is the same as subtracting a positive number. Therefore, we can drop the addition sign and the parentheses in the above expression, which gives
Carrying out the addition, as usual, we get
Calculate the value of
We drop the parentheses and the addition sign to give
Then, we move spaces to the left of on a number line.
We end up at Therefore,
What is the value of
First, we drop the parentheses and the addition sign, which gives
Then, we carry out the subtraction as usual. This gives
What is the value of $2 + (- 1.5)?$
|
a
|
$-1.5$ |
|
b
|
$-2.5$ |
|
c
|
$-0.5$ |
|
d
|
$0.5$ |
|
e
|
$1.5$ |
What is the value of $1.2 + (- 2.6)?$
|
a
|
$-1.4$ |
|
b
|
$-1.6$ |
|
c
|
$1.2$ |
|
d
|
$1$ |
|
e
|
$-1.8$ |
We can add a negative fraction using the same method. To demonstrate, let's find the value of
First, we eliminate the parentheses and obtain
Now, since both fractions have a common denominator of we can combine the numerators, which gives
Next, we work out using our number line.
We find that So, we get
If two fractions have different denominators, we need to put them over a common denominator first and then subtract! Let's see an example.
Find the value of
First, we drop the parentheses and the addition sign, which gives
Now, we need to convert the fractions to have the same denominator. To convert to have a denominator of we multiply the numerator and denominator by as follows:
Now, the subtraction problem is Because the two fractions now have the same denominator, we can combine the numerators:
Next, we work out using our number line.
We find that So, we get
What is the value of $\ -\dfrac 5 3 + \left(-\dfrac 2 3\right)?$
|
a
|
$-1$ |
|
b
|
$-\dfrac{7}{3}$ |
|
c
|
$-\dfrac 8 3$ |
|
d
|
$\dfrac{2}{3}$ |
|
e
|
$-\dfrac{2}{3}$ |
$1 + \left(-\dfrac 5 2\right) = $
|
a
|
$\dfrac 5 2$ |
|
b
|
$-\dfrac 5 2$ |
|
c
|
$\dfrac 3 2$ |
|
d
|
$\dfrac 1 2$ |
|
e
|
$-\dfrac 3 2$ |
