## 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.

### example

$\text{Simplify: }7\left(-2\right)+4\left(-7\right)-6$

Solution:
We use the order of operations. Multiply first and then add and subtract from left to right.

 $7\left(-2\right)+4\left(-7\right)-6$ Multiply first. $-14+\left(-28\right)-6$ Add. $-42 - 6$ Subtract. $-48$

### 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:

1.  ${\left(-2\right)}^{4}$
2.  ${-2}^{4}$

Now you try it.

### example

$\text{Simplify: }12 - 3\left(9 - 12\right)$

### example

Simplify: $8\left(-9\right)\div {\left(-2\right)}^{3}$

### example

$\text{Simplify:}-30\div 2+\left(-3\right)\left(-7\right)$

### 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

$\text{Evaluate }2{x}^{2}-3x+8\text{ when }x=-4$

### example

$\text{Evaluate }3x+4y - 6\text{ when }x=-1\text{ and }y=2$.

### try it

In the following video we show more examples of how to substitute integers into variable expressions.