5th Grade Numerical Expressions and Order of Operations Worksheet Solutions (PDF)
This grade 5 expressions answers for 5th Grade covers numerical expressions and order of operations (Common Core 5.OA.A.1, 5.OA.A.2), with a free PDF to print.
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
Grade 5 expressions answers: exercises 1 to 10
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
Exercises 11 and up
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
Key facts behind this grade 5 expressions answers
- Do grouping symbols ( ), [ ] and { } first, from the inside out.
- Multiplication and division share one level: work left to right.
- Addition and subtraction share one level: work left to right.
- Words like add first, then multiply need parentheses when you write them as an expression.
- An expression like 3 × (5 + 7) is 3 times as large as 5 + 7.
How to use this grade 5 expressions answers
Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.
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5th Grade Numerical Expressions and Order of Operations Worksheet Solutions
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