Writing Numerical Expressions from Word Problems Worksheets - Complete Practice Set for 4th Grade

Master writing numerical expressions from word problems: addition, subtraction, multiplication, division with detailed examples and practice exercises.

Worksheet: Exercises 1 to 3
1 Addition word problems
Exercise 1
Sarah has 15 apples. Her friend gives her 8 more apples. Write a numerical expression to represent the total number of apples Sarah has.
Definition:

Numerical expression: A mathematical phrase that uses numbers and operation symbols (+, -, ×, ÷) to represent a calculation.

Problem Analysis:
Starting amount: 15 apples
Added amount: 8 more apples
Operation word: "more" indicates addition
Expression Building:
1
Identify the starting amount: 15
2
Identify the operation: "more" means addition (+)
3
Identify the amount being added: 8
4
Combine: 15 + 8
Numerical Expression: 15 + 8
Applied rules:

• Keywords for addition: "more", "total", "altogether", "sum", "increased by", "combined"

• Structure: Starting amount + Added amount

• No equals sign: An expression shows the calculation, not the result

Final answer:

15 + 8

2 Subtraction word problems
Exercise 2
Tom had 24 stickers. He gave 9 stickers to his sister. Write a numerical expression to represent how many stickers Tom has left.
Problem Analysis:
Starting amount: 24 stickers
Amount taken away: 9 stickers
Operation word: "gave" indicates subtraction
Expression Building:
1
Identify the starting amount: 24
2
Identify the operation: "gave" means subtraction (-)
3
Identify the amount being subtracted: 9
4
Combine: 24 - 9
Numerical Expression: 24 - 9
Applied rules:

• Keywords for subtraction: "gave", "left", "remaining", "difference", "decreased by", "less than"

• Structure: Starting amount - Amount taken away

• Order matters: The first number is always the starting amount

Final answer:

24 - 9

3 Multiplication word problems
Exercise 3
A bakery has 6 boxes of cookies. Each box contains 12 cookies. Write a numerical expression to represent the total number of cookies.
Problem Analysis:
Number of groups: 6 boxes
Items per group: 12 cookies per box
Operation word: "each" indicates multiplication
Expression Building:
1
Identify the number of groups: 6
2
Identify the operation: "each" means multiplication (×)
3
Identify the amount per group: 12
4
Combine: 6 × 12
Numerical Expression: 6 × 12
Applied rules:

• Keywords for multiplication: "each", "per", "times", "groups of", "product", "multiplied by"

• Structure: Number of groups × Items per group

• Equal groups: Multiplication represents repeated addition of equal groups

Final answer:

6 × 12

Keyword Guide: Operations and Their Signs
Operation Keywords
Addition, Subtraction, Multiplication, Division
Addition (+)
more, total, altogether, sum, increased by
plus, combined, added to, in all
Subtraction (-)
less, fewer, left, remaining, difference
decreased by, take away, gave away
Multiplication (×)
each, per, times, groups of, product
multiplied by, rows of, columns of
Key definitions:

Numerical expression: A combination of numbers and operation symbols that shows a calculation without solving it.

Operation: A mathematical action (addition, subtraction, multiplication, division).

Variable: A symbol (usually a letter) that represents an unknown number (not used in 4th grade).

Step-by-step process:
  1. Read carefully: Understand what the problem is asking
  2. Find key information: Identify the numbers and important details
  3. Look for operation words: Find words that indicate the operation needed
  4. Identify the order: Determine which number comes first
  5. Write the expression: Put the numbers and operation symbol together
Tip 1: Circle or underline the numbers in the word problem.
Tip 2: Look for clue words that tell you which operation to use.
Tip 3: Don't solve the expression - just write it!
Tip 4: Check if your expression makes sense with the story.
Expression vs. Equation: An expression shows the calculation (2 + 3), an equation shows the answer (2 + 3 = 5)
Order matters: In subtraction and division, the order of numbers changes the result
Essential rules:

• No equals sign: Numerical expressions don't have equals signs or answers

• Operation words: Learn to recognize key words that indicate operations

• Context matters: Make sure your expression fits the story

• Number order: Pay attention to which number comes first in subtraction/division

Worksheet: Exercises 4 to 5
4 Division word problems
Exercise 4
Emma has 36 candies that she wants to share equally among 4 friends. Write a numerical expression to represent how many candies each friend will get.
Problem Analysis:
Total amount: 36 candies
Number of groups: 4 friends
Operation word: "share equally" indicates division
Expression Building:
1
Identify the total amount: 36
2
Identify the operation: "share equally" means division (÷)
3
Identify the number of groups: 4
4
Combine: 36 ÷ 4
Numerical Expression: 36 ÷ 4
Applied rules:

• Keywords for division: "share equally", "divide", "per", "split", "groups of", "how many in each"

• Structure: Total amount ÷ Number of groups

• Equal sharing: Division represents fair sharing into equal groups

Final answer:

36 ÷ 4

5 Multi-step word problems
Exercise 5
A school bought 5 packages of markers. Each package has 8 markers. Then 12 markers were given to the art room. Write a numerical expression to represent how many markers are left for the classrooms.
Problem Analysis:
Number of packages: 5 packages
Markers per package: 8 markers
Markers given away: 12 markers
First operation: "packages of" means multiplication
Second operation: "given to" means subtraction
Expression Building:
1
Calculate total markers: 5 × 8
2
Subtract markers given away: - 12
3
Combine: (5 × 8) - 12
4
Note: Parentheses show which operation happens first
Numerical Expression: (5 × 8) - 12
Applied rules:

• Multi-step problems: May require more than one operation

• Parentheses: Show which operation should be done first

• Order of operations: Multiplication/division before addition/subtraction

Final answer:

(5 × 8) - 12

Complete Guide: Writing Numerical Expressions
Expression Patterns
Recognizing Mathematical Structures
Core definitions:

Numerical expression: A mathematical phrase containing numbers and operation symbols (+, -, ×, ÷) without an equals sign.

Operation: A mathematical action that combines numbers (addition, subtraction, multiplication, division).

Term: Each number in an expression (in 3 + 5, the terms are 3 and 5).

Result: The answer when you evaluate (solve) an expression.

Complete problem-solving method:
  1. Read the entire problem to understand the situation
  2. Identify and circle all numbers in the problem
  3. Look for operation clue words that indicate the operation needed
  4. Determine the order of numbers (especially important for subtraction and division)
  5. Write the numerical expression using numbers and operation symbols
  6. Check if your expression makes sense in the context of the problem
Tip 1: Underline clue words that tell you which operation to use.
Tip 2: Draw pictures or models to visualize the problem.
Tip 3: Remember: expressions don't have equals signs or answers.
Tip 4: Practice reading problems multiple times to catch all details.
Addition patterns: Combining amounts, finding totals, increasing quantities
Subtraction patterns: Taking away, finding differences, remaining amounts
Multiplication patterns: Equal groups, repeated addition, area calculations
Division patterns: Sharing equally, grouping, finding unit rates
Complete rules reference:

• Addition words: more, total, altogether, sum, increased by, combined, plus

• Subtraction words: less, fewer, left, remaining, difference, decreased by, take away

• Multiplication words: each, per, times, groups of, product, multiplied by, rows of

• Division words: share equally, divide, per, split, how many in each, distributed

• Order matters: In subtraction and division, the order of numbers affects the result

Additional Practice Worksheet

Instructions: Write a numerical expression for each word problem. Do not solve the expression.
Problem 1: Maria collected 25 seashells at the beach. She found 13 more seashells later in the day. Write an expression for the total number of seashells.
Answer: 25 + 13
Problem 2: A farmer has 48 eggs. He puts 6 eggs in each carton. Write an expression to find how many cartons he needs.
Answer: 48 ÷ 6
Problem 3: Jake read 3 books last week. Each book had 150 pages. Write an expression to find the total number of pages he read.
Answer: 3 × 150
Problem 4: Sarah had 60 dollars. She spent 25 dollars on a new shirt. Write an expression to find how much money she has left.
Answer: 60 - 25
Problem 5: A store received 7 boxes of pencils. Each box contained 24 pencils. Then 35 pencils were sold. Write an expression to find how many pencils are left.
Answer: (7 × 24) - 35

Comprehensive Summary: Writing Numerical Expressions from Word Problems

Definitions and Concepts
Numerical Expression: A mathematical phrase that uses numbers and operation symbols (+, -, ×, ÷) to represent a calculation without solving it. For example: 5 + 3, 12 - 7, 4 × 6.
Operation: A mathematical action: addition (+), subtraction (-), multiplication (×), or division (÷).
Clue Words: Specific words in word problems that indicate which operation to use.
Terms: The individual numbers in an expression (in 8 + 5, the terms are 8 and 5).
Multi-step Problems: Word problems that require more than one operation to solve.
Core Rules and Principles
No Equals Sign Rule: Numerical expressions do not contain equals signs (=) or answers. They only show the calculation.
Operation Words: Learn to recognize clue words that indicate operations (more = addition, left = subtraction, each = multiplication, share = division).
Order Matters: In subtraction and division, changing the order of numbers changes the result (10 - 3 ≠ 3 - 10).
Context Verification: Your expression should make logical sense within the word problem's story.
Parentheses Priority: In multi-step expressions, parentheses show which operation should be done first.
Step-by-Step Method
Step 1: Read the entire word problem carefully to understand the situation.
Step 2: Identify and circle all the numbers mentioned in the problem.
Step 3: Look for clue words that indicate which operation to use.
Step 4: Determine the order of numbers (especially important for subtraction and division).
Step 5: Write the numerical expression using numbers and operation symbols.
Step 6: Check if your expression makes sense in the context of the problem.
Examples (Simple to Advanced)
Simple Addition: "Tom has 5 apples and gets 3 more" → 5 + 3
Simple Subtraction: "Sarah had 10 cookies and ate 4" → 10 - 4
Simple Multiplication: "There are 4 boxes with 6 toys each" → 4 × 6
Simple Division: "Share 15 candies among 3 children" → 15 ÷ 3
Multi-step: "Buy 3 packs of 10 stickers, give away 8" → (3 × 10) - 8
Tips and Tricks
Circle Numbers: Visually mark all numbers in the word problem to avoid missing any.
Underline Clues: Highlight operation words to help identify the correct operation.
Draw Pictures: Sketch simple diagrams to visualize the problem situation.
Check Context: Make sure your expression fits logically with the story.
Practice Patterns: Recognize common problem structures and their corresponding expressions.
Common Pitfalls and Solutions
Pitfall: Including equals signs or answers in expressions. Solution: Remember expressions only show the calculation, not the result.
Pitfall: Wrong order in subtraction/division. Solution: Identify the starting amount first.
Pitfall: Missing numbers in multi-step problems. Solution: Read the problem multiple times.
Pitfall: Confusing similar operation words. Solution: Create a reference list of clue words.
Pitfall: Not using parentheses when needed. Solution: Use parentheses to show order of operations.
Key Takeaways for Memorization
Addition Clues: "more", "total", "altogether", "sum", "combined", "increased by"
Subtraction Clues: "left", "remaining", "difference", "take away", "gave", "fewer"
Multiplication Clues: "each", "per", "times", "groups of", "product", "rows of"
Division Clues: "share equally", "divide", "per", "split", "how many in each"
Expression Rule: Numbers + Operation symbols, NO equals sign or answer!

Questions & Answers

Question: How do I know whether to add or multiply when I see the word "more"? Sometimes it seems like both could work.

Answer: Great observation! The word "more" typically indicates addition, but context is crucial:

  • Simple addition: "Sarah has 5 apples and gets 3 more" → 5 + 3
  • Multiplication context: Be careful with phrases like "3 times more" which can be ambiguous, but in 4th grade, focus on "gets more" as addition
  • Key distinction: "More" usually means adding to what you already have

Always look at the full sentence to understand the relationship. If someone "has" something and "gets more," it's addition. If you see "times" with "more," pay extra attention to the exact wording.

Question: I sometimes get confused about the order of numbers in subtraction problems. How do I know which number goes first?

Answer: This is a common challenge! Here's the key principle:

  • Start with what you have: The first number in a subtraction expression is always the starting amount
  • Subtract what's taken away: The second number is what gets subtracted
  • Example: "Jake had 15 marbles and lost 6" → Start with 15, lose 6 → 15 - 6
  • Keywords: "had", "started with", "beginning" usually indicate the first number

Think: "I started with this much, then this amount was taken away."

Question: When do I need to use parentheses in my expressions? Some problems seem to need them and others don't.

Answer: Parentheses are used to show which operation should be done first. In 4th grade, you'll mainly use them in multi-step problems:

  • When you multiply first, then add/subtract: "Buy 3 packs of 10 stickers, then give away 8" → (3 × 10) - 8
  • When you add/subtract first, then multiply/divide: "Combine 5 and 3, then multiply by 2" → (5 + 3) × 2
  • Simple problems don't need parentheses: 5 + 3 or 12 ÷ 4

Parentheses help clarify the order of operations and make your mathematical thinking clear.