We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

Study Guides > Prealgebra

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

Simplify: 7(−2)+4(−7)−6\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(−2)+4(−7)−67\left(-2\right)+4\left(-7\right)-6
Multiply first. −14+(−28)−6-14+\left(-28\right)-6
Add. −42−6-42 - 6
Subtract. −48-48
 

try it

#145337
In teh following example we provide an explanation for the difference between (−3)2(-3)^2 and −32-3^2. https://youtu.be/qB5PZzmjenI

example

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

Answer: Solution: According to the order of operations, we simplify inside parentheses first. Then we will multiply and finally we will subtract.

12−3(9−12)12 - 3\left(9 - 12\right)
Subtract the parentheses first. 12−3(−3)12 - 3\left(-3\right)
Multiply. 12−(−9)12-\left(-9\right)
Subtract. 21\text{21}

 

try it

#145345
 

example

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

Answer: Solution: First we will multiply and divide from left to right. Then we will add.

−30÷2+(−3)(−7)-30\div 2+\left(-3\right)\left(-7\right)
Divide. −15+(−3)(−7)-15+\left(-3\right)\left(-7\right)
Multiply. −15+21-15+21
Add. 6\text{6}

 

try it

#145352
 

example

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

Answer: Solution:

3x+4y−−63x+4y--6
Substitute x=−1x=-1 and y=2y=2 . 3(−−1)+4(2)−−63(\color{red}{--1})+4(\color{blue}{2})--6
Multiply. −−3+8−−6--3+8--6
Simplify. −−1--1

 

try it

#145353
In teh following video we show more examples of how to substitute integers into variable expressions. https://youtu.be/dkFIVfJTG9E

Licenses & Attributions