SME
Grade 5 Math · Operations & Algebraic Thinking
Numerical expressions and order of operations
Use this for “Find the value of (2 + 6) × 5 − 9.”
Diagram
(3 + 5) × 4 = 32.
Subtract 7: 25.
Result: 25
This is an example. Type your own values to start a new problem.
(
First number inside
+
Second number inside
)
×
Multiplier
−
Number taken away
=
Result
Value inside the parentheses
worked out (not typed)
Product
worked out (not typed)
Formulas
3 + 5 = 8
First number inside + second number inside = value inside the parentheses
8 × 4 = 32
Value inside the parentheses × multiplier = product
32 − 7 = 25
Product − number taken away = result
Assumptions
•
Parentheses first: work inside them, then multiply, then subtract.
•
Then multiply or divide, then add or subtract.
•
The tape shows the value inside as equal groups, with the last number taken off the end.
•
Numbers inside the parentheses to 20, the multiplier to 10.
Step-by-step
WE KNOW
First number inside: 3
Second number inside: 5
Multiplier: 4
Number taken away: 7
FIND
value inside the parentheses, product, result
Step 1 · Find value inside the parentheses
3 + 5 = ?
First number inside + second number inside = value inside the parentheses
Parentheses first: add the two numbers inside.
Value inside the parentheses = 8
Step 2 · Find product
8 × 4 = ?
Value inside the parentheses × multiplier = product
Multiply next: the value inside times the multiplier.
Product = 32
Step 3 · Find result
32 − 7 = ?
Product − number taken away = result
Subtract last: the product minus the last number.
Result = 25
Check
Put the numbers back in. Both sides should match.
3 + 5 = 8 ✓
8 × 4 = 32 ✓
32 − 7 = 25 ✓
Topic check
See what you know: 5 questions on this topic
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More problem types
Evaluate expressions with parentheses
Use this for “(18 + 6) ÷ 4 =” and other parentheses before dividing.
Interpret numerical expressions
Use this to compare (3 + 5) × 4 and 3 + 5 × 4.
Order of operations
Use this for “6 + 12 ÷ 4 − 2 × 3 =”: multiply and divide first.
Evaluate expressions with grouping symbols
Use this for “2 × [5 + (3 × 4)]”: work from the inside out.
Write numerical expressions
Use this for “Which expression matches the words?” with parentheses.