1.1: Order of Operations and Sign Rules | Algebra 1 Honors

How it works

Evaluate powers before multiplication and division, then addition and subtraction. Operations at the same level are evaluated from left to right. Parentheses can make a negative number the base of a power; without them, an initial minus sign is applied after exponentiation.

-(a^2)\ne(-a)^2\quad(a\ne0)

Worked examples

Example 1

Evaluate $\displaystyle -3^2+2(5-1)$ .

The power is evaluated first: $\displaystyle -3^2=-9$ . The parentheses give $\displaystyle 4$ , so the value is $\displaystyle -9+8=-1$ .

Example 2

Simplify $\displaystyle -2(3x-4)+5x$ .

Distribute to both terms: $\displaystyle -6x+8+5x=-x+8$ . The negative factor changes both signs.

Problems

Problem 1.1.1

Evaluate $\displaystyle 18\div3\cdot2-5$ .

Show worked solution

Division and multiplication have equal precedence: $\displaystyle 18\div3=6$ , then $\displaystyle 6\cdot2=12$ . The result is $\displaystyle 12-5=7$ .

Problem 1.1.2

Simplify $\displaystyle 4(2x-3)-3(x+1)$ .

Show worked solution

Distribute: $\displaystyle 8x-12-3x-3=5x-15$ .

Problem 1.1.3

Evaluate $\displaystyle (-4)^2-4^2$ .

Show worked solution

The first term is $\displaystyle 16$ and the second is $\displaystyle 16$ , so the difference is $\displaystyle 0$ .

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 1.1.1

Problem 1.1.2

Problem 1.1.3

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