5th Grade Numerical Expressions and Order of Operations Worksheets with Answers (Free PDF)

5th grade order of operations worksheet – Maths PDF

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This 5th grade order of operations worksheet covers numerical expressions and order of operations (Common Core 5.OA.A.1, 5.OA.A.2), with a free PDF to print.

Key takeaway: This worksheet helps fifth grade students practice evaluating numerical expressions with parentheses, brackets, and braces, and writing expressions from words.

Topic: Numerical Expressions and Order of Operations (5th grade)
Content: 20 worksheet problems, from easy to challenging
Standards: 5.OA.A.1, 5.OA.A.2
Answers: On a separate page, so you can try every worksheet problem first
Format: Free printable PDF, US Letter, black and white

This worksheet helps fifth grade students practice evaluating numerical expressions with parentheses, brackets, and braces, and writing expressions from words. Also, real situations such as shopping, trading cards, and baking show how one expression can describe a whole story.

There are 20 problems. The first five evaluate expressions with two operations, and the next six use grouping symbols, including three layers. Then, one problem compares expressions without calculating, two write expressions, and the last seven are word problems and a mistake to find. Also, allow about 30 minutes, and rewrite the expression after each step.

These 20 problems build your skill with the order of operations. You will evaluate expressions with parentheses, brackets and braces, write expressions from words, and compare an expression to its parts without calculating (Common Core 5.OA.A.1 and 5.OA.A.2).

The first problems are quick one-step checks. The last six are word problems that need one expression and more than one operation. Show every step on paper before you look at the answer key.

Grade 5 · Common Core State Standards: 5.OA.A.1, 5.OA.A.2

5th grade order of operations worksheet: worksheet problems 1 to 10

1 – Multiply before adding

First, evaluate $8+4\times3$.

2 – Divide before subtracting

Next, evaluate $20-6\div2$.

3 – Parentheses first

Then, evaluate $(9+5)\times2$. The picture shows two groups of $9+5$.

Two groups of 9 + 5.

4 – Dividing by a sum

Now, evaluate $36\div(2+4)$.

5 – Two products

Also, evaluate $5\times6-4\times3$.

6 – Left to right

First, evaluate $48\div8\times3$.

7 – Parentheses, then multiply

Next, evaluate $7+(12-4)\times2$.

8 – Brackets and parentheses

Then, evaluate $2\times[5+(8-3)]$.

9 – Three layers of grouping

Now, evaluate $60-3\times[2+(10-6)]$. The picture shows the groups inside each other.

The green group is innermost, so it is first.

10 – Braces

Also, evaluate $\{4+[18\div(3\times3)]\}\times5$.

Worksheet problems 11 and up

11 – Parentheses then subtract

First, evaluate $3\times(14+6)-10$.

12 – Compare without calculating

Without calculating, tell which is greater: $6\times(417+389)$ or $417+389$. Then tell how many times as large the greater one is.

Top: one group. Bottom: six groups.

13 – Write: add, then multiply

Then, write an expression for this phrase. Do not evaluate it: add 9 and 6, then multiply by 4.

Four groups of 9 and 6.

14 – Write: subtract, then divide

Now, write an expression for this phrase. Do not evaluate it: subtract 5 from 20, then divide by 3.

15 – School store

Maya buys 5 notebooks that cost $\$4$ each and 1 pencil case that costs $\$6$. Write one expression for the total cost, then find the total.

Price tags at the school store.

16 – Trading cards

Jamal has 3 packs of 24 trading cards. He gives 18 cards to his cousin. Write one expression and find how many cards Jamal has left.

17 – Bake sale cookies

Sofia bakes 4 trays with 12 cookies on each tray. She sets aside 6 cookies for the teachers. She shares the rest equally among 6 volunteers. Write one expression and find how many cookies each volunteer gets.

4 trays, 12 cookies on each tray.

Worksheet problem 18 and after

18 – Sticker rows

Ethan has 18 stickers and gets 7 more. He puts all of them in 5 equal rows. Write one expression and find how many stickers are in each row.

19 – Twice the sum

Priya writes the number sentence: twice the sum of 15 and 9, minus 8. Write it as one expression and evaluate it.

20 – Find Diego's mistake

Diego evaluates $6+4\times5$ and gets 50. Explain his mistake and find the correct value.

Diego’s work.

Key facts behind this 5th grade order of operations worksheet

Key facts

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.

Common mistakes with this 5th grade order of operations worksheet

Students add before they multiply in an expression such as 3 plus 5 times 2. Multiply first, then add.
Students work left to right in a division and multiplication expression and then switch the order. Always go left to right for those two operations.
Students ignore the innermost grouping symbol. Work from the inside out through every layer. Slow down at that step and check it twice.
Students write several separate calculations for a story. Write one expression that shows the whole story, then evaluate it.

Tips before you start the worksheet problems

Circle the operation you do first on each line. This habit prevents skipped steps. Repeat this habit on every problem for the best results.
Rewrite the whole expression with the result of each step. The shorter expression is easier to read. Repeat this habit on every problem for the best results.
Teachers can ask students to explain a mistake in words, naming the operation that should have come first.

Download the 5th grade order of operations worksheet as a PDF with the button below and keep it with your notes.

5th grade order of operations worksheet: frequently asked questions

How do you evaluate an expression with three layers of grouping?

Start with the innermost symbols and work outward. In 10 minus 2 times [3 plus (8 minus 4)], first compute 8 minus 4, then 3 plus 4, then multiply by 2, and finally subtract from 10.

How do you write one expression for a shopping story?

Show each action in order, with parentheses for the part done first. Four items at 3 dollars plus one item at 5 dollars becomes 4 times 3 plus 5. Then evaluate to find the total.

How do you explain a classmate’s mistake with the order of operations?

Say which operation the classmate did first and which should come first. If someone adds before multiplying, state that multiplication comes before addition. Then show the correct value. A quick check like this takes only a few seconds and prevents most errors.

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