Simplifying and Evaluating Expressions With Integers That Use all Four Operations
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.
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]
Show Solution
Solution:
The exponent tells how many times to multiply the base.
1. The exponent is [latex]4[/latex] and the base is [latex]-2[/latex]. We raise [latex]-2[/latex] to the fourth power.
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]
Show Solution
Solution:
[latex]2{x}^{2}-3x+8[/latex]
[latex]\text{Substitute}\color{red}{-4}\text{ for }x[/latex]
Keep in mind that when we substitute [latex]-4[/latex] for [latex]x[/latex], we use parentheses to show the multiplication. Without parentheses, it would look like [latex]2\cdot {-4}^{2}-3\cdot -4+8[/latex].
try it
example
[latex]\text{Evaluate }3x+4y - 6\text{ when }x=-1\text{ and }y=2[/latex].
Show Solution
Solution:
[latex]3x+4y-6[/latex]
Substitute [latex]x=-1[/latex] and [latex]y=2[/latex] .
In the following video we show more examples of how to substitute integers into variable expressions.
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Revision and Adaptation. Provided by: Lumen Learning. License: CC BY: Attribution
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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
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
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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