Apply Order of Operations
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What you will learn
- 1State the order of operations: parentheses, multiplication and division, then addition and subtraction
- 2Evaluate expressions with two or more operations using the correct order
- 3Identify errors caused by applying operations in the wrong order
- 4Write and solve expressions using parentheses to change the value
Mini Lesson
When an expression contains more than one operation, the order in which you calculate matters. Mathematicians follow a set of rules — the order of operations — so that everyone gets the same answer. For Grade 4, the rule is: parentheses first, then multiplication and division left to right, then addition and subtraction left to right.
The Order of Operations Rule
- Parentheses first — calculate whatever is inside the parentheses before anything else.
- Multiplication and division next — work left to right.
- Addition and subtraction last — work left to right.
Without Parentheses
- 3 + 4 × 2: multiply first → 4 × 2 = 8, then add → 3 + 8 = 11.
- If you added first instead: 3 + 4 = 7, then 7 × 2 = 14 — that is wrong.
- The correct answer is 11, not 14.
With Parentheses
- (3 + 4) × 2: parentheses first → 3 + 4 = 7, then multiply → 7 × 2 = 14.
- Parentheses change the value of the expression.
- 3 + 4 × 2 = 11, but (3 + 4) × 2 = 14 — different results!
Real-Life Example
- You buy 2 books at $5 each and 3 pens at $3 each.
- Correct: 2 × $5 + 3 × $3 = $10 + $9 = $19.
- Wrong: (2 + 3) × ($5 + $3) = 5 × $8 = $40 — this ignores the separate prices.
Words to know
Order of operations
A set of rules that says which operation to do first in a math expression
e.g. Order of operations: parentheses, then × and ÷, then + and −.
Parentheses
The symbols ( ) that group operations to be done first
e.g. The parentheses in (2 + 3) × 4 mean add first.
Expression
A math statement made of numbers and operations, with no equals sign
e.g. 5 + 2 × 3 is an expression.
Evaluate
To work out the value of an expression by following the rules in order
e.g. Evaluate 5 + 2 × 3 = 11.
Operation
One of the four actions: add, subtract, multiply, or divide
e.g. Multiplication is the operation done before addition.
Tip: always scan the expression for parentheses first, then look for × and ÷ before doing any + or −.
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