There are two ways to add a positive number to a negative number. Let's work out the value of using both methods.
Method 1 - Picturing a Number Line
When we add, we move to the right on the number line.
So, to add to we start at on a number line and move spaces to the right.
When we do this, we land at Therefore,
Method 2 - Subtraction in Reverse
Adding a positive number to a negative number is like subtraction in reverse. To turn the addition into a subtraction, we must switch the numbers around.
So, to work out we can switch the numbers around to get
We're allowed to swap the numbers because addition is commutative, which means the order in which we add two numbers does not matter.
What is the value of
Method 1 - Picturing a Number Line
To add to we start at on a number line and move spaces to the right.
We end up at So,
Method 2 - Subtraction in Reverse
We can swap the order of the numbers and then compute the resulting subtraction:
$-39 + 14=$
|
a
|
$-27$ |
|
b
|
$-23$ |
|
c
|
$23$ |
|
d
|
$-25$ |
|
e
|
$25$ |
What is
We can swap the order of the numbers and then compute the resulting subtraction:
$-2+4.5=$
|
a
|
$1.5$ |
|
b
|
$2.3$ |
|
c
|
$2.5$ |
|
d
|
$-1.4$ |
|
e
|
$-3.1$ |
$-9.5+3.5=$
|
a
|
$-5$ |
|
b
|
$7$ |
|
c
|
$-4$ |
|
d
|
$4$ |
|
e
|
$-6$ |
$-5.09 + 4.3=$
|
a
|
$-0.87$ |
|
b
|
$-0.71$ |
|
c
|
$-1.21$ |
|
d
|
$-1.09$ |
|
e
|
$-0.79$ |
Suppose that we want to calculate
Since both fractions have a common denominator of we can combine them to form one fraction:
To compute the numerator, we can use either method that we've learned.
Method 1 - Picturing a Number Line
To add to we start at on a number line and move spaces to the right.
We end up at So and therefore
Method 2 - Subtraction in Reverse
We can swap the order of the numbers in the numerator and then compute the resulting subtraction:
So, we conclude that
Note: If two fractions have different denominators, we need to put them over a common denominator first and then subtract!
Find the value of
We put both fractions over a common denominator of and then add the numerators. This gives
To compute the numerator, we can use either Method 1 or Method 2, shown below.
Method 1 - Picturing a Number Line
To add to we start at on a number line and move spaces to the right.
So, Therefore,
Method 2 - Subtraction in Reverse
We can swap the order of the numbers in the numerator, and we get
So, we conclude that
$-\dfrac{1}{5}+\dfrac{4}{5}=$
|
a
|
$\dfrac65$ |
|
b
|
$-\dfrac35$ |
|
c
|
$-1$ |
|
d
|
$1$ |
|
e
|
$\dfrac35$ |
$-\dfrac3 8 + \dfrac 5 4=$
|
a
|
$-\dfrac78$ |
|
b
|
$-\dfrac12$ |
|
c
|
$\dfrac12$ |
|
d
|
$\dfrac14$ |
|
e
|
$\dfrac78$ |
$-\dfrac{3}{4} + \dfrac{2}{3} =$
|
a
|
$-\dfrac{1}{12}$ |
|
b
|
$-\dfrac{7}{12}$ |
|
c
|
$\dfrac{1}{6}$ |
|
d
|
$-\dfrac{5}{6}$ |
|
e
|
$\dfrac{5}{12}$ |
