Learning Outcomes
- Use the order of operations to simplify expressions that involve integer multiplication, division, addition, and subtraction
- Evaluate integer expressions using the order of operations
Now we’ll simplify expressions that use all four operations–addition, subtraction, multiplication, and division–with integers. Remember to follow the order of operations.
example
[latex]\text{Simplify: }7\left(-2\right)+4\left(-7\right)-6[/latex]
Solution:
We use the order of operations. Multiply first and then add and subtract from left to right.
[latex]7\left(-2\right)+4\left(-7\right)-6[/latex] | |
Multiply first. | [latex]-14+\left(-28\right)-6[/latex] |
Add. | [latex]-42 - 6[/latex] |
Subtract. | [latex]-48[/latex] |
try it
Watch the following video to see another example of how to use the order of operations to simplify an expression that contains integers.
In our next example we will simplify expressions with integers that also contain exponents.
example
Simplify:
- [latex]{\left(-2\right)}^{4}[/latex]
- [latex]{-2}^{4}[/latex]
Now you try it.
try it
example
[latex]\text{Simplify: }12 - 3\left(9 - 12\right)[/latex]
try it
example
Simplify: [latex]8\left(-9\right)\div {\left(-2\right)}^{3}[/latex]
try it
example
[latex]\text{Simplify:}-30\div 2+\left(-3\right)\left(-7\right)[/latex]
try it
In the following video we show more examples of how to evaluate expressions with integers using the order of operations.
Evaluate Variable Expressions with Integers
Now we can evaluate expressions that include multiplication and division with integers. Remember that to evaluate an expression, substitute the numbers in place of the variables, and then simplify.
example
[latex]\text{Evaluate }2{x}^{2}-3x+8\text{ when }x=-4[/latex]
try it
example
[latex]\text{Evaluate }3x+4y - 6\text{ when }x=-1\text{ and }y=2[/latex].
try it
In the following video we show more examples of how to substitute integers into variable expressions.
Candela Citations
- Ex: Simplify an Expression With Integers Using the Order of Operations. Authored by: James Sousa (Mathispower4u.com). Located at: https://youtu.be/RJ7uU9HbdqA. License: CC BY: Attribution
- Ex 1: Order of Operations with Integers. Authored by: James Sousa (Mathispower4u.com). Located at: https://youtu.be/UlfXxzuJIfs. License: CC BY: Attribution
- Ex: Substitute and Evaluate Expressions x^2+3, (x+3)^2, x^2+2x+3. Authored by: James Sousa (Mathispower4u.com). Located at: https://youtu.be/dkFIVfJTG9E. License: Public Domain: No Known Copyright
- Ex: Evaluating Negative Numbers Raised to Powers. Authored by: James Sousa (Mathispower4u.com). Located at: https://youtu.be/qB5PZzmjenI. License: CC BY: Attribution
- Question ID: 145332, 145337, 145340, 145345, 145348, 145352, 145353. Authored by: Alyson Day. License: CC BY: Attribution. License Terms: IMathAS Community License CC-BY + GPL
- Prealgebra. Provided by: OpenStax. License: CC BY: Attribution. License Terms: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757