SME
Grade 5 Math · Problem type
Evaluate expressions with grouping symbols
Use this for “2 × [5 + (3 × 4)]”: work from the inside out.
Diagram
2 groups of 17
34 in all
This is an example. Type your own values to start a new problem.
Multiplier
×
[
Number in the brackets
+
(
First factor
×
Second factor
)]
=
Result
Product in the parentheses
worked out (not typed)
Value in the brackets
worked out (not typed)
Formulas
3 × 4 = 12
First factor × second factor = product in the parentheses
5 + 12 = 17
Number in the brackets + product in the parentheses = value in the brackets
2 × 17 = 34
Multiplier × value in the brackets = result
Assumptions
•
Parentheses first, then the brackets around them: work from the inside out.
•
So 2 × [5 + (3 × 4)] = 2 × [5 + 12] = 2 × 17 = 34.
•
Factors and the multiplier to 10, the number in the brackets to 50.
Step-by-step
WE KNOW
Multiplier: 2
Number in the brackets: 5
First factor: 3
Second factor: 4
FIND
product in the parentheses, value in the brackets, result
Step 1 · Find product in the parentheses
3 × 4 = ?
First factor × second factor = product in the parentheses
Parentheses first: multiply inside them.
Product in the parentheses = 12
Step 2 · Find value in the brackets
5 + 12 = ?
Number in the brackets + product in the parentheses = value in the brackets
Then the brackets: add the product to the number there.
Value in the brackets = 17
Step 3 · Find result
2 × 17 = ?
Multiplier × value in the brackets = result
Last, multiply the value in the brackets.
2 × 10 = 20 and 2 × 7 = 14
20 + 14 = 34
Result = 34
Check
Put the numbers back in. Both sides should match.
3 × 4 = 12 ✓
5 + 12 = 17 ✓
2 × 17 = 34 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Numerical expressions and order of operations
Main lesson
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.
Write numerical expressions
Use this for “Which expression matches the words?” with parentheses.