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Grade 4 (age 9-10)

grade 4 Order of Operations

Order of Operations

A mixed calculation is one expression that mixes addition, subtraction, multiplication, and division. You do multiplication and division before addition and subtraction, and anything inside brackets comes first. Skip that order and the answer changes, so the rule matters. Point through each part of the expression and the order of the operations appears.

Order of calculation matters!

⚠️ Same expression, different answer?
①5 + 3 × 4 from the front gives 32
②Multiplication first gives 17
③The answer is 17! Multiplication·division come first

Multiplication·Division First!

5
3
4

Power of Brackets

🔑 Brackets come first!
①Brackets ( ) are calculated first
②Use brackets to choose your order
③Order: brackets → ×÷ → +−
④Same rank goes left to right: 12 ÷ 6 × 2 = 4
⑤The picture shows a + b × c. Division and subtraction follow the same order. Example: 12 − 6 ÷ 2 = 9

Summary

Order of Operations
① ( ) → ② ×, ÷ → ③ +, −
Brackets first, then ×÷, then +−
Same Precedence
× = ÷, + = − → left to right
Equal-priority ops go in left-to-right order
Using Brackets
(5 + 3) × 4 = 32 ≠ 5 + 3 × 4 = 17
Brackets change the calculation order
🎯 Key Points
①( ) is always first!
②×, ÷ before +, −
③Equal priority: left to right
④Brackets let you set the order
⑤Same rule applies on calculators

Examples and Unit Test

Example 1
Calculate 5 + 3 × 4.
1
Do multiplication before addition: 3 × 4 = 12.
2
Then add: 5 + 12 = 17.
▸ 17
Multiplication and division come before addition and subtraction.
Example 2
Calculate (5 + 3) × 4. Is the answer the same as Example 1?
1
Do the brackets first: 5 + 3 = 8.
2
Then multiply: 8 × 4 = 32. The brackets change the answer!
▸ 32
Brackets change the order of calculation and so change the answer.
Unit Test
What is the value of 12 − 6 ÷ 2?
①3
②9
③6
④12
▸ ② 9
1
Do the division first: 6 ÷ 2 = 3.
2
Then subtract: 12 − 3 = 9.
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Understanding Decimals
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Estimation — Number Range