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Grade 4 (age 9-10)

grade 4 Order of Operations

When an expression mixes addition, subtraction, multiplication and division, you work it out in an agreed order. Work inside parentheses first, then multiplication and division, and finally addition and subtraction; operations of the same rank go from left to right. Because everyone uses the same order, an expression has only one answer, no matter who works it out. Change the three numbers to see how far apart the left-to-right answer, the multiply-first answer and the answer with parentheses can be.

Why Order Matters

⚠️ Same Expression, Different Answers?
①Working 5 + 3 × 4 from left to right gives 8 × 4 = 32
②Multiplying first gives 5 + 12 = 17
③Since we agree to multiply and divide first, the correct answer is 17
④3 × 4 means 3 groups of 4, so it is worked out as one piece before it is added to 5

Multiply and Divide First

5
3
4

Parentheses

🔑 Parentheses Come First
①Whatever is inside parentheses is worked out before anything else
②(5 + 3) × 4 means finding 5 + 3 = 8 first, then 8 × 4 = 32
③Parentheses let you make addition happen before multiplication
④Multiplication and division go from left to right, and so do addition and subtraction: 12 ÷ 6 × 2 = 2 × 2 = 4
⑤The same holds when division and subtraction are mixed: 12 − 6 ÷ 2 = 12 − 3 = 9

Summary

Order of Operations
① ( ) → ② ×, ÷ → ③ +, −
Parentheses, then multiplication and division, then addition and subtraction
Operations of the Same Rank
× with ÷, and + with −: left to right
Work them in order from left to right
Using Parentheses
(5 + 3) × 4 = 32 ≠ 5 + 3 × 4 = 17
Adding parentheses changes the order of work and the answer
🎯 Summary
①Work inside parentheses first
②Multiply and divide before you add and subtract
③Operations of the same rank go from left to right
④Put parentheses around any part you want done first
⑤Keep this order in mind even when you use a calculator

Examples and Unit Test

Example 1
Work out 5 + 3 × 4.
1
Multiply before adding: 3 × 4 = 12.
2
Then add: 5 + 12 = 17.
▸ 17
Working left to right would give 32, which is wrong.
Example 2
Work out (5 + 3) × 4. Is the answer the same as in Example 1?
1
Work inside the parentheses first: 5 + 3 = 8.
2
Then multiply: 8 × 4 = 32, which is different from the 17 in Example 1.
▸ 32
With the same numbers and signs, parentheses change the order and so the answer.
Unit Test
What is 12 − 6 ÷ 2?
①3
②9
③6
④12
▸ ② 9
1
Divide first: 6 ÷ 2 = 3.
2
Then subtract: 12 − 3 = 9.
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Understanding Decimals
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Estimation — Number Range

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