5th Grade Numerical Expressions and Order of Operations Worksheet Solutions (PDF)
This answer key shows every step for the 20 order of operations problems. Each solution follows the same order: grouping symbols first, then multiplication and division from left to right, then addition and subtraction from left to right. Compare your steps, not only your final answers.
Grade 5 · Common Core State Standards: 5.OA.A.1, 5.OA.A.2
Exercise 1 – Multiply before adding
Multiply first: \(4\times3=12\).
Then add: \(8+12=20\).
Answer: 20
Exercise 2 – Divide before subtracting
Divide first: \(6\div2=3\).
Then subtract: \(20-3=17\).
Answer: 17
Exercise 3 – Parentheses first
Parentheses first: \(9+5=14\).
Then multiply: \(14\times2=28\).
Answer: 28
Exercise 4 – Dividing by a sum
Parentheses first: \(2+4=6\).
Then divide: \(36\div6=6\).
Answer: 6
Exercise 5 – Two products
Multiply from left to right: \(5\times6=30\) and \(4\times3=12\).
Then subtract: \(30-12=18\).
Answer: 18
Exercise 6 – Left to right
Multiplication and division are on the same level, so go from left to right.
\(48\div8=6\), then \(6\times3=18\).
Answer: 18
Exercise 7 – Parentheses, then multiply
Parentheses first: \(12-4=8\).
Multiply: \(8\times2=16\).
Add: \(7+16=23\).
Answer: 23
Exercise 8 – Brackets and parentheses
Innermost group: \(8-3=5\), so the brackets hold \(5+5=10\).
Multiply: \(2\times10=20\).
Answer: 20
Exercise 9 – Three layers of grouping
Innermost: \(10-6=4\). Brackets: \(2+4=6\).
Multiply: \(3\times6=18\).
Subtract: \(60-18=42\).
Answer: 42
Exercise 10 – Braces
Parentheses: \(3\times3=9\). Brackets: \(18\div9=2\).
Braces: \(4+2=6\).
Multiply: \(6\times5=30\).
Answer: 30
Exercise 11 – Parentheses then subtract
Parentheses: \(14+6=20\).
Multiply: \(3\times20=60\).
Subtract: \(60-10=50\).
Answer: 50
Exercise 12 – Compare without calculating
The first expression is six groups of \(417+389\), and the second is one group.
So \(6\times(417+389)\) is greater. It is 6 times as large.
Exercise 13 – Write: add, then multiply
The addition happens first, so it goes in parentheses: \((9+6)\).
Then multiply by 4.
Expression: \(4\times(9+6)\) (or \((9+6)\times4\))
Exercise 14 – Write: subtract, then divide
The subtraction happens first, so it goes in parentheses: \((20-5)\).
Then divide by 3.
Expression: \((20-5)\div3\)
Exercise 15 – School store
Expression: \(5\times4+6\).
Multiply first: \(5\times4=20\). Then add: \(20+6=26\).
Maya pays \(\$26\).
Exercise 16 – Trading cards
Expression: \(3\times24-18\).
Multiply: \(3\times24=72\). Subtract: \(72-18=54\).
Jamal has 54 cards left.
Exercise 17 – Bake sale cookies
Expression: \((4\times12-6)\div6\).
Parentheses: \(4\times12=48\), then \(48-6=42\).
Divide: \(42\div6=7\).
Each volunteer gets 7 cookies.
Exercise 18 – Sticker rows
Expression: \((18+7)\div5\).
Add: \(18+7=25\). Divide: \(25\div5=5\).
Each row has 5 stickers.
Exercise 19 – Twice the sum
Expression: \(2\times(15+9)-8\).
Parentheses: \(15+9=24\). Multiply: \(2\times24=48\). Subtract: \(48-8=40\).
Answer: 40
Exercise 20 – Find Diego's mistake
Diego added \(6+4\) first. But multiplication comes before addition.
Correct work: \(4\times5=20\), then \(6+20=26\).
Correct value: 26
All Grade 5 chapters: Grade 5 math.
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