Subtraction Property
Subtracting a number is the same as adding it's opposite.
[latex]a-b=a+(-b)[/latex]
Look at these two examples.
example
Simplify: [latex]-74-\left(-58\right)[/latex].
Answer:
Solution:
We are taking [latex]58[/latex] negatives away from [latex]74[/latex] negatives. |
[latex]-74-\left(-58\right)[/latex] |
Subtract. |
[latex]-16[/latex] |
Now you can try a similar problem.
In the following video we show another example of subtracting two digit integers.
https://youtu.be/IfiN-mJZu2E
Now let's increase the complexity of the examples a little bit. We will use the order of operations to simplify terms in parentheses before we subtract from left to right.
example
Simplify: [latex]7-\left(-4 - 3\right)-9[/latex].
Answer:
Solution:
We use the order of operations to simplify this expression, performing operations inside the parentheses first. Then we subtract from left to right.
Simplify inside the parentheses first. |
[latex]7-\left(-4 - 3\right)-9[/latex] |
Subtract from left to right. |
[latex]7-\left(-7\right)-9[/latex] |
Subtract. |
[latex]14--9[/latex] |
|
[latex]5[/latex] |
Now you try it.
Watch the following video to see more examples of simplifying integer expressions that involve subtraction.
https://youtu.be/mDkSpz0BPPc
Now we will add another operation to an expression. Because multiplication and division come before addition and subtraction, we will multiply, then subtract.
example
Simplify: [latex]3\cdot 7 - 4\cdot 7 - 5\cdot 8[/latex].
Answer:
Solution:
We use the order of operations to simplify this expression. First we multiply, and then subtract from left to right.
Multiply first. |
[latex]3\cdot 7 - 4\cdot 7 - 5\cdot 8[/latex] |
Subtract from left to right. |
[latex]21--28--40[/latex] |
Subtract. |
[latex]--7--40[/latex] |
|
[latex]--47[/latex] |
Now you try.
Watch the following video to see another example of simplifying an integer expression involving multiplication and subtraction.
https://youtu.be/42Su4r5UmoE
example
Evaluate [latex]x - 4\text{ when}[/latex]
- [latex]x=3[/latex]
- [latex]x=-6[/latex].
Answer:
Solution:
1. To evaluate [latex]x - 4[/latex] when [latex]x=3[/latex] , substitute [latex]3[/latex] for [latex]x[/latex] in the expression.
|
[latex]x--4[/latex] |
[latex]\text{Substitute }\color{red}{3}\text{ for }x[/latex] |
[latex]\color{red}{3}--4[/latex] |
Subtract. |
[latex]--1[/latex] |
2. To evaluate [latex]x - 4[/latex] when [latex]x=-6[/latex], substitute [latex]-6[/latex] for [latex]x[/latex] in the expression.
|
[latex]x--4[/latex] |
[latex]\text{Substitute }\color{red}{--6}\text{ for }x[/latex] |
[latex]\color{red}{--6}--4[/latex] |
Subtract. |
[latex]--10[/latex] |
Now you try.
In the next example, we will subtract a positive and a negative.
example
Evaluate [latex]20-z\text{ when}[/latex]
- [latex]z=12[/latex]
- [latex]z=-12[/latex]
Answer:
Solution:
1. To evaluate [latex]20-z\text{ when }z=12[/latex], substitute [latex]12[/latex] for [latex]z[/latex] in the expression.
|
[latex]20--z[/latex] |
[latex]\text{Substitute }\color{red}{12}\text{ for }z[/latex] |
[latex]20--\color{red}{12}[/latex] |
Subtract. |
[latex]8[/latex] |
2. To evaluate [latex]20-z\text{ when }z=-12,\text{ substitute }-12\text{ for }z\text{in the expression.}[/latex]
|
[latex]20--z[/latex] |
[latex]\text{Substitute }\color{red}{--12}\text{ for }z[/latex] |
[latex]20--(\color{red}{--12})[/latex] |
Subtract. |
[latex]32[/latex] |
Now you try.