Order of Operations

Grade 5 · mathematics · 100 practice problems · read aloud

🔊 Listen to this explanation

Order of Operations

This is the set of rules that tells us the correct sequence to solve a math problem with multiple operations (like +, -, ×, ÷). Without these rules, everyone could get a different answer for the same problem!

How to Solve: PEMDAS

Remember the acronym PEMDAS to know what order to follow:

  1. Parentheses - Do everything inside parentheses first.
  2. Exponents - Solve any exponents (like 3²).
  3. Multiplication and Division - Do these from left to right.
  4. Addition and Subtraction - Do these from left to right.

Worked Examples

Example 1: 12 ÷ 3 × 2 + (5 - 2)

  1. Parentheses: (5 - 2) = 3 → Now we have: 12 ÷ 3 × 2 + 3
  2. Division/Multiplication (left to right): 12 ÷ 3 = 4 → 4 × 2 = 8 → Now we have: 8 + 3
  3. Addition: 8 + 3 = 11 ✅

Example 2: 5 + 2 × 3²

  1. Exponents: 3² = 9 → Now we have: 5 + 2 × 9
  2. Multiplication: 2 × 9 = 18 → Now we have: 5 + 18
  3. Addition: 5 + 18 = 23 ✅

⚠️ Common Mistakes

  • Going left to right without PEMDAS: For 10 - 3 + 2, you do go left to right (7 + 2 = 9). But for 10 - 3 × 2, multiplication comes first! (3 × 2 = 6, then 10 - 6 = 4).
  • Thinking "M" always comes before "D": Multiplication and Division have equal priority, so you solve them from left to right. 8 ÷ 4 × 2 = 2 × 2 = 4 (not 8 ÷ 8 = 1).

🎯 Tips & Tricks

  • Remember PEMDAS as: "Please Excuse My Dear Aunt Sally"
  • Underline or highlight the operation you are about to do next in the problem.
  • Rewrite the problem after each step so you don't get lost.

How to Practice

Try creating your own problems! Start simple like 4 × (2 + 5). Then, make them more complex. Ask a friend to solve it and see if you get the same answer. You can also find lots of practice worksheets online. ✏️

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 (24 + 16) ÷ 8 = ?

Hint: Remember to perform the operation inside the grouping symbols first before dealing with the division.

Show the answer

Answer: 5

  1. First, look at the problem: (24 + 16) ÷ 8 We must follow the order of operations, which says to calculate what is inside the parentheses first.
  2. Calculate inside the parentheses: 24 + 16 = 40 So now the problem becomes: 40 ÷ 8
  3. Perform the division: 40 ÷ 8 = 5
  4. Therefore, the final answer is 5.

2 (12 + 8) × 3 - 15 = ?

Hint: Remember to perform operations inside grouping symbols first before moving to multiplication or division.

Show the answer

Answer: 45

  1. Perform the operation inside the parentheses** 12 + 8 = 20 Now the expression becomes: 20 × 3 - 15 **
  2. Perform multiplication** 20 × 3 = 60 Now the expression becomes: 60 - 15 **
  3. Perform subtraction** 60 - 15 = 45 **Final Answer:** 45

Let's solve the problem step by step. We have: (12 + 8) × 3 - 15 **

3 (15 + 5) × 3 - 10 = ?

Hint: Remember to perform operations inside grouping symbols first before moving to multiplication or division, then addition or subtraction.

Show the answer

Answer: 50

  1. Calculate inside the parentheses. (15 + 5) = 20 Now the expression becomes: 20 × 3 - 10
  2. Perform multiplication. 20 × 3 = 60 Now the expression becomes: 60 - 10
  3. Perform subtraction. 60 - 10 = 50 Final answer: 50

We follow the order of operations (PEMDAS/BODMAS): parentheses first, then multiplication/division from left to right, then addition/subtraction from left to right.

4 (18 + 6) × 3 - 15 = ?

Hint: Remember to perform operations inside grouping symbols first before moving to multiplication or division, then addition or subtraction.

Show the answer

Answer: 57

  1. First, handle the parentheses. (18 + 6) = 24 Now the expression becomes: 24 × 3 - 15
  2. Next, perform multiplication. 24 × 3 = 72 Now the expression becomes: 72 - 15
  3. Finally, perform subtraction. 72 - 15 = 57 So the final answer is 57.

Let's solve the problem step-by-step using the order of operations (PEMDAS/BODMAS).

5 (12 × 4) - (15 ÷ 3) = ?

Hint: Remember to perform operations inside parentheses first before combining results.

Show the answer

Answer: 43

  1. Handle the multiplication inside the first parentheses. 12 × 4 = 48 So now we have: 48 - (15 ÷ 3)
  2. Handle the division inside the second parentheses. 15 ÷ 3 = 5 So now we have: 48 - 5
  3. Perform the subtraction. 48 - 5 = 43 Final answer: 43

Let's solve the problem step by step. We have: (12 × 4) - (15 ÷ 3)

6 (18 + 12) ÷ (5 × 2) = ?

Hint: Remember to perform operations inside grouping symbols first before moving to other operations.

Show the answer

Answer: 3

  1. First, handle the parentheses from left to right. Start with the left parentheses: 18 + 12 = 30 So now we have: 30 ÷ (5 × 2)
  2. Handle the parentheses on the right: 5 × 2 = 10 So now we have: 30 ÷ 10
  3. Perform the division: 30 ÷ 10 = 3 Final answer: 3

Let's solve step by step. We have: (18 + 12) ÷ (5 × 2)

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