{"id":65169,"date":"2026-07-22T11:01:20","date_gmt":"2026-07-22T10:01:20","guid":{"rendered":"https:\/\/blog-admin.thethinkacademy.com\/?p=65169"},"modified":"2026-07-22T11:01:23","modified_gmt":"2026-07-22T10:01:23","slug":"math-order-of-operations-guide","status":"publish","type":"post","link":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/07\/22\/math-order-of-operations-guide\/","title":{"rendered":"Order of Operations Explained: Rules, Examples and Practice"},"content":{"rendered":"\n

The math order of operations is one of the most important \u2014 and most misunderstood \u2014 concepts in elementary and middle school mathematics. It appears in Grades 5 through 9 across Canada, affects everything from basic arithmetic to algebra, and is the source of some of the most common errors students make when they start secondary school mathematics.<\/p>\n\n\n\n

This guide explains the math order of operations clearly, with step-by-step examples, common mistakes, and practice problems at the end. If your child is confused by BEDMAS or keeps getting different answers to the same expression, this is the right place to start.<\/p>\n\n\n

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\"math<\/a><\/figure>\n<\/div>\n\n\n
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What Is the Math Order of Operations?<\/h2>\n\n\n\n

The math order of operations is a set of rules that tells you which part of a mathematical expression to calculate first when there are multiple operations involved.<\/p>\n\n\n\n

Without a consistent order of operations, the same expression could produce different answers depending on which operation you did first. That would make mathematics unreliable \u2014 which is why mathematicians agreed on a universal rule.<\/p>\n\n\n\n

In Canada, the math order of operations is taught using the acronym BEDMAS<\/strong>:<\/p>\n\n\n\n

Letter<\/th>Stands For<\/th>Example<\/th><\/tr><\/thead>
B<\/strong><\/td>Brackets<\/td>(3 + 4)<\/td><\/tr>
E<\/strong><\/td>Exponents<\/td>2\u00b3<\/td><\/tr>
D<\/strong><\/td>Division<\/td>20 \u00f7 4<\/td><\/tr>
M<\/strong><\/td>Multiplication<\/td>5 \u00d7 3<\/td><\/tr>
A<\/strong><\/td>Addition<\/td>8 + 6<\/td><\/tr>
S<\/strong><\/td>Subtraction<\/td>12 \u2212 5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The rule:<\/strong> Always work through a mathematical expression in this order \u2014 Brackets first, then Exponents, then Division and Multiplication (left to right), then Addition and Subtraction (left to right).<\/p>\n\n\n\n

You may also see PEMDAS (used in the US, where P stands for Parentheses) or BODMAS (used in the UK, where O stands for Orders). These are all the same rule, just with different acronyms.<\/p>\n\n\n\n

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Why the Math Order of Operations Matters<\/h2>\n\n\n\n

Here is the classic example that shows why math order of operations rules exist:<\/p>\n\n\n\n

What is 2 + 3 \u00d7 4?<\/strong><\/p>\n\n\n\n

If you go left to right without the math order of operations: 2 + 3 = 5, then 5 \u00d7 4 = 20<\/strong> \u2717<\/p>\n\n\n\n

If you apply the math order of operations (multiplication before addition): 3 \u00d7 4 = 12, then 2 + 12 = 14<\/strong> \u2713<\/p>\n\n\n\n

The correct answer is 14<\/strong> \u2014 and anyone who learned the math order of operations will get the same answer every time.<\/p>\n\n\n\n

This is not a trick question. It is the core reason the math order of operations was established: to ensure that mathematical expressions have exactly one correct interpretation, regardless of who is reading them.<\/p>\n\n\n\n

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BEDMAS Explained Step by Step<\/h2>\n\n\n\n

Step 1: Brackets First<\/h3>\n\n\n\n

Always calculate everything inside brackets before anything outside them.<\/p>\n\n\n\n

Example:<\/strong> (5 + 3) \u00d7 4 \u2192 First: 5 + 3 = 8 \u2192 Then: 8 \u00d7 4 = 32<\/strong><\/p>\n\n\n\n

Compare to: 5 + 3 \u00d7 4 (no brackets) \u2192 First: 3 \u00d7 4 = 12 (multiplication before addition) \u2192 Then: 5 + 12 = 17<\/strong><\/p>\n\n\n\n

The brackets completely change the answer. This is exactly what they are designed to do \u2014 they override the default math order of operations.<\/p>\n\n\n\n

Nested brackets:<\/strong> When brackets appear inside other brackets, always work from the innermost set outward.<\/p>\n\n\n\n

Example:<\/strong> ((2 + 3) \u00d7 4) \u2212 6 \u2192 Innermost: 2 + 3 = 5 \u2192 Next bracket: 5 \u00d7 4 = 20 \u2192 Final: 20 \u2212 6 = 14<\/strong><\/p>\n\n\n\n

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Step 2: Exponents<\/h3>\n\n\n\n

After brackets, evaluate any exponents (powers).<\/p>\n\n\n\n

Example:<\/strong> 3 + 2\u00b3 \u00d7 4 \u2192 First: 2\u00b3 = 8 \u2192 Then: 8 \u00d7 4 = 32 (multiplication before addition) \u2192 Final: 3 + 32 = 35<\/strong><\/p>\n\n\n\n

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Step 3: Division and Multiplication (Left to Right)<\/h3>\n\n\n\n

Division and multiplication have equal priority in the math order of operations. When both appear in an expression, work from left to right \u2014 whichever comes first gets done first.<\/p>\n\n\n\n

Example:<\/strong> 20 \u00f7 4 \u00d7 3 \u2192 Left to right: 20 \u00f7 4 = 5, then 5 \u00d7 3 = 15<\/strong> \u2713<\/p>\n\n\n\n

Common mistake:<\/strong> Doing multiplication before division because M comes before D in BEDMAS. \u2192 20 \u00f7 (4 \u00d7 3) = 20 \u00f7 12 \u2248 1.67 \u2717<\/p>\n\n\n\n

The left-to-right rule is critical. DM are equal partners \u2014 neither comes before the other. The one that appears first in the expression gets done first.<\/p>\n\n\n\n

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Step 4: Addition and Subtraction (Left to Right)<\/h3>\n\n\n\n

Exactly like multiplication and division, addition and subtraction have equal priority. Work left to right.<\/p>\n\n\n\n

Example:<\/strong> 15 \u2212 6 + 4 \u2192 Left to right: 15 \u2212 6 = 9, then 9 + 4 = 13<\/strong> \u2713<\/p>\n\n\n\n

Common mistake:<\/strong> Always adding before subtracting. \u2192 15 \u2212 (6 + 4) = 15 \u2212 10 = 5 \u2717<\/p>\n\n\n\n

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Worked Examples: Math Order of Operations in Action<\/h2>\n\n\n\n

Example 1 (Grade 5 level):<\/strong> 4 + 6 \u00f7 2<\/p>\n\n\n\n

Step 1: Division first \u2192 6 \u00f7 2 = 3 Step 2: Addition \u2192 4 + 3 = 7<\/strong><\/p>\n\n\n\n

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Example 2 (Grade 6 level):<\/strong> 3 \u00d7 (8 \u2212 5) + 2\u00b2<\/p>\n\n\n\n

Step 1: Brackets \u2192 8 \u2212 5 = 3 Step 2: Exponents \u2192 2\u00b2 = 4 Step 3: Multiplication \u2192 3 \u00d7 3 = 9 Step 4: Addition \u2192 9 + 4 = 13<\/strong><\/p>\n\n\n\n

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Example 3 (Grade 7 level):<\/strong> 18 \u00f7 3 + 4 \u00d7 2 \u2212 5<\/p>\n\n\n\n

Step 1: Division \u2192 18 \u00f7 3 = 6 Step 2: Multiplication \u2192 4 \u00d7 2 = 8 Step 3: Left to right (addition then subtraction) \u2192 6 + 8 = 14, then 14 \u2212 5 = 9<\/strong><\/p>\n\n\n\n

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Example 4 (Grade 8 level):<\/strong> (2\u00b3 + 4) \u00f7 3 \u2212 1<\/p>\n\n\n\n

Step 1: Brackets (exponent inside) \u2192 2\u00b3 = 8, then 8 + 4 = 12 Step 2: Division \u2192 12 \u00f7 3 = 4 Step 3: Subtraction \u2192 4 \u2212 1 = 3<\/strong><\/p>\n\n\n\n

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Example 5 (Grade 9 challenge):<\/strong> 5 + 2 \u00d7 (3\u00b2 \u2212 1) \u00f7 4<\/p>\n\n\n\n

Step 1: Brackets (exponent inside) \u2192 3\u00b2 = 9, then 9 \u2212 1 = 8 Step 2: Left to right (multiplication before division, left to right) \u2192 2 \u00d7 8 = 16, then 16 \u00f7 4 = 4 Step 3: Addition \u2192 5 + 4 = 9<\/strong><\/p>\n\n\n\n

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The Most Common Math Order of Operations Mistakes<\/h2>\n\n\n\n

Students who understand BEDMAS in principle still make predictable errors. Knowing the common mistakes in advance helps avoid them.<\/p>\n\n\n\n

Mistake 1: Ignoring left-to-right for division and multiplication.<\/strong> Thinking M always comes before D is the single most common math order of operations error at the Grade 6\u20137 level. Remember: D and M are equal. Work left to right.<\/p>\n\n\n\n

Mistake 2: Ignoring left-to-right for addition and subtraction.<\/strong> Same principle as above. A and S are equal \u2014 left to right always.<\/p>\n\n\n\n

Mistake 3: Forgetting to apply BEDMAS inside brackets.<\/strong> The math order of operations applies inside brackets too. (2 + 3 \u00d7 4) is not (2 + 3) \u00d7 4 \u2014 you still do multiplication before addition inside the brackets.<\/p>\n\n\n\n

Mistake 4: Treating negative numbers carelessly.<\/strong> Expressions involving negative numbers and operations need particular care. \u22123\u00b2 means \u2212(3\u00b2) = \u22129, not (\u22123)\u00b2 = 9. The exponent applies to 3, not to \u22123, unless there are brackets.<\/p>\n\n\n\n

Mistake 5: Rushing through multi-step expressions.<\/strong> The math order of operations requires working through an expression in stages, rewriting after each step. Students who try to do it all mentally or skip rewriting intermediate steps make significantly more errors than those who work through it methodically, one step at a time.<\/p>\n\n\n\n

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Math Order of Operations Practice Problems<\/h2>\n\n\n\n

Work through these problems applying BEDMAS. Answers are at the bottom \u2014 try them before checking.<\/p>\n\n\n\n

Set A \u2014 Grade 5\/6 Level<\/strong><\/p>\n\n\n\n

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  1. 5 + 3 \u00d7 2 = ___<\/li>\n\n\n\n
  2. (7 + 3) \u00d7 4 = ___<\/li>\n\n\n\n
  3. 24 \u00f7 6 + 5 = ___<\/li>\n\n\n\n
  4. 8 \u2212 2 + 5 = ___<\/li>\n\n\n\n
  5. 3 \u00d7 4 \u2212 8 \u00f7 2 = ___<\/li>\n\n\n\n
  6. (9 \u2212 3) \u00f7 2 \u00d7 4 = ___<\/li>\n<\/ol>\n\n\n\n

    Set B \u2014 Grade 7\/8 Level<\/strong><\/p>\n\n\n\n

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    1. 2\u00b3 + 4 \u00d7 3 = ___<\/li>\n\n\n\n
    2. (5 + 3) \u00d7 (8 \u2212 4) \u00f7 4 = ___<\/li>\n\n\n\n
    3. 36 \u00f7 4 \u2212 2 \u00d7 3 + 5 = ___<\/li>\n\n\n\n
    4. 3 \u00d7 (2 + 4\u00b2) \u2212 6 = ___<\/li>\n\n\n\n
    5. (8 \u2212 3)\u00b2 \u00f7 5 + 7 = ___<\/li>\n\n\n\n
    6. 4 + 6 \u00d7 2 \u2212 3\u00b2 \u00f7 3 = ___<\/li>\n<\/ol>\n\n\n\n

      Set C \u2014 Grade 9 Challenge<\/strong><\/p>\n\n\n\n

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      1. 2 + 3 \u00d7 (4\u00b2 \u2212 10) \u00f7 3 = ___<\/li>\n\n\n\n
      2. (5\u00b2 \u2212 4 \u00d7 3) \u00f7 (7 \u2212 2) \u00d7 2 = ___<\/li>\n\n\n\n
      3. 6 \u00d7 2 \u2212 (3 + 1)\u00b2 + 8 \u00f7 2 = ___<\/li>\n<\/ol>\n\n\n\n
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        Answers:<\/strong><\/p>\n\n\n\n

        Set A: 1) 11   2) 40   3) 9   4) 11   5) 8   6) 12<\/p>\n\n\n\n

        Set B: 7) 20   8) 8   9) 8   10) 48   11) 12   12) 13<\/p>\n\n\n\n

        Set C: 13) 8   14) 26\/5 = 5.2   15) 6<\/p>\n\n\n\n

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        Math Order of Operations in the Ontario Curriculum<\/h2>\n\n\n\n

        The math order of operations is first introduced formally in the Ontario curriculum in Grade 6<\/strong>, and is applied and extended through to Grade 9 and beyond<\/strong>. It underpins:<\/p>\n\n\n\n