Now we’ll simplify expressions that use all four operations–addition, subtraction, multiplication, and division–with integers. Remember to follow the order of operations.
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] |
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.
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.
| [latex]<\left(-2\right)>^[/latex] | |
| Write in expanded form. | [latex]\left(-2\right)\left(-2\right)\left(-2\right)\left(-2\right)[/latex] |
| Multiply. | [latex]4\left(-2\right)\left(-2\right)[/latex] |
| Multiply. | [latex]-8\left(-2\right)[/latex] |
| Multiply. | [latex]16[/latex] |
2. The exponent is [latex]4[/latex] and the base is [latex]2[/latex]. We raise [latex]2[/latex] to the fourth power and then take the opposite.
| [latex]-^[/latex] | |
| Write in expanded form. | [latex]-\left(2\cdot 2\cdot 2\cdot 2\right)[/latex] |
| Multiply. | [latex]-\left(4\cdot 2\cdot 2\right)[/latex] |
| Multiply. | [latex]-\left(8\cdot 2\right)[/latex] |
| Multiply. | [latex]-16[/latex] |