Mr. Alongi Math
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Rules & properties reference

Order of Operations

The order of operations tells us which part of a math problem to complete first, next, and last.

In simple words:First parentheses and brackets, then exponents, then multiply or divide from left to right, and finally add or subtract from left to right.
Problem6 + 2 × 5
Multiply first6 + 10 = 16
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Why should I care?

Without one shared order, people could get different answers to the same problem. The order of operations helps people and calculators read math the same way.

Quick-reference chart

The Rules

Read the rule, then study the example.

1. Parentheses and Brackets

Complete the math inside ( ) and [ ] first. If one is inside another, start with the inside set.

2[7 + (5 - 3)]First: 5 - 3 = 2Next: 7 + 2 = 9Then: 2 × 9 = 18

2. Exponents

Find the value of powers after parentheses and brackets.

4 + 2³First: 2³ = 8Then: 4 + 8 = 12

3. Multiply or Divide

These share a level. Move from left to right.

24 ÷ 6 × 2First: 24 ÷ 6 = 4Then: 4 × 2 = 8

4. Add or Subtract

These share a level. Move from left to right.

10 - 3 + 2First: 10 - 3 = 7Then: 7 + 2 = 9

PEMDAS Reminder

Use PEMDAS to remember the order, but remember that M and D share a step, and A and S share a step.

PEMDASParentheses → ExponentsMultiply/Divide → Add/Subtract

Fraction Bars

Finish the top and bottom of a fraction before dividing them.

8 + 45 - 212 ÷ 3Answer: 4

Follow the thinking

Worked Examples

18 - 2(3 + 1)²

  1. Parentheses: 3 + 1 = 4.
  2. Exponent: 4² = 16.
  3. Multiply: 2 × 16 = 32.
  4. Subtract: 18 - 32 = -14.
18 - 2(3 + 1)² = -14

30 ÷ 5 × 2 + 1

  1. No parentheses, brackets, or exponents.
  2. Move left to right: 30 ÷ 5 = 6.
  3. Continue left to right: 6 × 2 = 12.
  4. Add last: 12 + 1 = 13.
30 ÷ 5 × 2 + 1 = 13

Watch out

Common Mistakes

  • Multiplication does not always come before division. Move left to right.
  • Addition does not always come before subtraction. Move left to right.
  • Do not skip parentheses or brackets, even when the numbers outside look easier.

Check yourself

Quick Practice

1. 7 + 3 × 4

Multiply 3 × 4 first. The final answer is 19.

2. (9 - 5)² ÷ 2

Parentheses first, then exponent, then divide. The answer is 8.

3. 20 ÷ 4 × 5

Start on the left with 20 ÷ 4. The answer is 25.

Your turn

10-Question: What Comes Next?

Type the operation you should complete first or next. You may type the numbers and symbol, such as 2 × 5.

Find the mistake

Fix the Student’s Mistake

Choose the action that should have been taken.

1A student solved 18 ÷ 3 × 2 by multiplying 3 × 2 first.
2A student solved 10 - 4 + 2 by adding 4 + 2 first.
3A student solved 3 + 2² as 5².
4A student ignored the brackets in 2[6 - 1].

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