Grade 5 (age 10-11)

grade 5 Mixed Operations

Mixed Operations

Mixed operations combine +, −, ×, ÷ and brackets in one expression. Ignore the order and 3 + 4 × 2 changes the answer: brackets first, then × and ÷, then + and −. Operations of the same rank go left to right. Pick an expression and step the slider one stage at a time, and the part that is calculated first appears.

Why does order matter?

🤔 3 + 4 × 2 = ?

①Left to right: 3+4=7, 7×2=14 → wrong!

②Multiplication first: 4×2=8, 3+8=11 → correct!

③Math has a strict order of operations

④Without it, the same expression can have different answers

Order of Operations Rules

💡 Just remember 3 rules

①Brackets ( ) come first

②Then × and ÷

③Last, + and −

④Same priority → left to right!

Step-by-step Practice

Solution step0

✅ Practice this way!

①First check if there are brackets

②Underline ×÷ parts

③Calculate underlined parts first

④Finally do +−

⑤When brackets and division meet, as in 24÷(8−2)+5, do 8−2=6 first, then 24÷6=4, then 4+5=9

Summary

Order of Operations

Brackets ( ) → × ÷ → + −

Same-priority ops go left to right

Wrong Example

3 + 4 × 2 ≠ 14

Going left to right is wrong! Multiplication first

Correct Example

3 + 4 × 2 = 3 + 8 = 11

Multiply (4×2=8) first, then add

🎯 Key Points

①Brackets are top priority

②× ÷ before + −

③Same priority: left → right

④Mark which part to calculate first

⑤The mnemonic is brackets → ×÷ → +−. Division ranks with multiplication; subtraction ranks with addition

Examples and Unit Test

Example 1

Calculate 3 + 4 × 2.

Do multiplication before addition: 4 × 2 = 8.

Then add: 3 + 8 = 11.

▸ 11

Multiplication and division come before addition and subtraction.

Example 2

Calculate (3 + 4) × 2. Is the answer the same as Example 1?

Do the brackets first: 3 + 4 = 7.

Then multiply: 7 × 2 = 14. The brackets change the answer!

▸ 14

Brackets change the order of calculation and so change the answer.

Unit Test

What is the value of 20 − 12 ÷ 4?

①2

②17

③8

④11

▸ ② 17

Do the division first: 12 ÷ 4 = 3.

Then subtract: 20 − 3 = 17.

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Mixed Number Operations

Congruence & Symmetry