Simplifying Expressions with Integers
Simplifying Expressions with Integers
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
\(\text{Simplify:}\phantom{\rule{0.2em}{0ex}}7\left(-2\right)+4\left(-7\right)-6.\)
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. | \(-48\) |
Example
Simplify:
- \((−2)^4\)
- \(\phantom{\rule{0.2em}{0ex}}{-2}^{4}\)
Solution
The exponent tells how many times to multiply the base.
The exponent is \(4\) and the base is \(-2.\) We raise \(-2\) to the fourth power.
| \({\left(-2\right)}^{4}\) | |
| Write in expanded form. | \(\left(-2\right)\left(-2\right)\left(-2\right)\left(-2\right)\) |
| Multiply. | \(4\left(-2\right)\left(-2\right)\) |
| Multiply. | \(-8\left(-2\right)\) |
| Multiply. | \(16\) |
The exponent is \(4\) and the base is \(2.\) We raise \(2\) to the fourth power and then take the opposite.
| \(-{2}^{4}\) | |
| Write in expanded form. | \(-\left(2\cdot 2\cdot 2\cdot 2\right)\) |
| Multiply. | \(-\left(4\cdot 2\cdot 2\right)\) |
| Multiply. | \(-\left(8\cdot 2\right)\) |
| Multiply. | \(-16\) |
Example
\(\text{Simplify:}\phantom{\rule{0.2em}{0ex}}12-3\left(9-12\right).\)
Solution
According to the order of operations, we simplify inside parentheses first. Then we will multiply and finally we will subtract.
| \(12-3\left(9-12\right)\) | |
| Subtract the parentheses first. | \(12-3\left(-3\right)\) |
| Multiply. | \(12-\left(-9\right)\) |
| Subtract. | \(\text{21}\) |
Example
Simplify: \(8\left(-9\right)÷{\left(-2\right)}^{3}.\)
Solution
We simplify the exponent first, then multiply and divide.
| \(8\left(-9\right)÷{\left(-2\right)}^{3}\) | |
| Simplify the exponent. | \(8\left(-9\right)÷\left(-8\right)\) |
| Multiply. | \(-72÷\left(-8\right)\) |
| Divide. | \(\text{9}\) |
Example
\(\text{Simplify:}\phantom{\rule{0.2em}{0ex}}-30÷2+\left(-3\right)\left(-7\right).\)
Solution
First we will multiply and divide from left to right. Then we will add.
| \(-30÷2+\left(-3\right)\left(-7\right)\) | |
| Divide. | \(-15+\left(-3\right)\left(-7\right)\) |
| Multiply. | \(-15+21\) |
| Add. | \(\text{6}\) |
Optional Video: Multiplying and Dividing Signed Numbers
This lesson is part of:
Introducing Integers