SME
Grade 5 Math · Problem type
Interpret numerical expressions
Use this to compare (3 + 5) × 4 and 3 + 5 × 4.
Diagram
The difference: 32 − 23 = 9.
This is an example. Type your own values to start a new problem.
(
First number
+
Second number
)
×
Multiplier
=
With parentheses
First number
+
Second number
×
Multiplier
=
Without parentheses
Difference
worked out (not typed)
Formulas
(3 + 5) × 4 = 32
(First number + second number) × multiplier = with parentheses
3 + 5 × 4 = 23
First number + second number × multiplier = without parentheses
32 − 23 = 9
With parentheses − without parentheses = difference
Assumptions
•
With parentheses, add first: (3 + 5) × 4 = 8 × 4 = 32.
•
Without them, multiply first: 3 + 5 × 4 = 3 + 20 = 23.
•
Numbers to 20, the multiplier to 10.
Step-by-step
WE KNOW
First number: 3
Second number: 5
Multiplier: 4
FIND
with parentheses, without parentheses, difference
Step 1 · Find with parentheses
(3 + 5) × 4 = ?
(First number + second number) × multiplier = with parentheses
Parentheses first: add, then multiply.
3 + 5 = 8
8 × 4 = 32
With parentheses = 32
Step 2 · Find without parentheses
3 + 5 × 4 = ?
First number + second number × multiplier = without parentheses
No parentheses: multiply first, then add.
5 × 4 = 20 (multiply first)
3 + 20 = 23
Without parentheses = 23
Step 3 · Find difference
32 − 23 = ?
With parentheses − without parentheses = difference
Compare the two answers.
Difference = 9
Check
Put the numbers back in. Both sides should match.
(3 + 5) × 4 = 32 ✓
3 + 5 × 4 = 23 ✓
32 − 23 = 9 ✓
Topic check
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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.
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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.