Solved Exercises on Multiplication and Division Word Problem Vocabulary in Grade 4

Master multiplication and division word problem vocabulary: key terms, phrases, and concepts through these 5 detailed exercises.

Word Problem Vocabulary: Complete Guide
Core Concepts & Definitions

Word Problem Vocabulary: Specific words and phrases that indicate which mathematical operation to use.

Multiplication Keywords: Words that signal you need to multiply (times, each, total, product, groups of).

Division Keywords: Words that signal you need to divide (share, split, each, per, distribute, equal groups).

Problem Context: Understanding the situation described in the word problem.

🔍
Identify
❓
Meaning
⚙️
Apply
✅
Check
Multiplication Terms

• Total

• Times

• Product

• Each

• Per

• Groups of

Division Terms

• Share

• Split

• Each

• Equal groups

• Per

• Distributed

Problem Types

• Equal groups

• Area problems

• Rate problems

• Sharing problems

• Comparison problems

Multiplication Clues
Words that indicate multiplication: total, times, product, each, per, groups of, area, how many in all.
Division Clues
Words that indicate division: share, split, each, equal groups, per, distributed, how many in each group.
Context Clues
Understanding the situation: arranging items, distributing resources, calculating rates.
Comparison Words
Words showing relationships: more than, less than, twice as many, half of.
Step-by-Step Vocabulary Recognition Process
  1. Read the problem carefully: Identify what is being asked
  2. Circle key words: Look for multiplication or division indicators
  3. Identify the operation: Determine if you need to multiply or divide
  4. Understand the context: What real-world situation is described?
  5. Set up the equation: Write the mathematical expression
  6. Solve the problem: Perform the calculation
  7. Check your answer: Does it make sense in the context?
Multiplication Patterns

• Finding totals

• Area of rectangles

• Comparing quantities

• Scaling up

Division Patterns

• Sharing equally

• Finding group size

• Finding number of groups

• Scaling down

Tips for Vocabulary Success
  • Read the entire problem before starting
  • Identify what the question is asking for
  • Circle or highlight important words
  • Look for key operation words
  • Draw pictures to visualize the problem
  • Estimate your answer first
  • Check if your answer makes sense
  • Always include units in your answer
Vocabulary Exercises: 1 to 3
1 Multiplication vocabulary identification
Exercise 1
"Sarah has 6 bags of marbles. Each bag contains 8 marbles. How many marbles does Sarah have in total?"
Definition:

Vocabulary identification: Recognizing words that indicate multiplication in word problems

Vocabulary method:
  1. Read the problem completely
  2. Identify key words that indicate multiplication
  3. Look for words like "each," "total," "groups of"
  4. Determine the operation needed
Problem
6 bags × 8 marbles each
Solution
48 marbles
Step 1: Identify key words

"Each bag contains" indicates multiplication

Step 2: Identify the operation

"How many... in total?" suggests finding the total amount

Step 3: Set up the equation

6 bags × 8 marbles per bag = ? total marbles

Step 4: Calculate

6 × 8 = 48

Step 5: Check the answer

Estimate: 6 × 8 = 48, which seems reasonable

6 × 8 = 48
Final answer:

Sarah has 48 marbles in total.

Applied rules:

• Vocabulary clue: "Each bag contains" indicates multiplication

• Problem type: Finding total of equal groups

• Verification: 48 ÷ 6 = 8 ✓

🎒
Bags
6
➡️
×
×
marble
Per Bag
8
🟰
Total
48
2 Division vocabulary identification
Exercise 2
"A teacher has 36 students and wants to divide them equally into 4 groups. How many students will be in each group?"
Definition:

Vocabulary identification: Recognizing words that indicate division in word problems

Problem
36 students ÷ 4 groups
Solution
9 students/group
Step 1: Identify key words

"Divide equally into" indicates division

Step 2: Identify the operation

"How many... in each group?" suggests finding group size

Step 3: Set up the equation

36 students ÷ 4 groups = ? students per group

Step 4: Calculate

36 ÷ 4 = 9

Step 5: Check the answer

9 × 4 = 36 ✓

36 ÷ 4 = 9
Final answer:

There will be 9 students in each group.

Applied rules:

• Vocabulary clue: "Divide equally" indicates division

• Problem type: Finding group size

• Verification: 9 × 4 = 36 ✓

👤
Total Students
36
➡️
÷
÷
👥
Groups
4
🟰
Per Group
9
3 Multi-step vocabulary identification
Exercise 3
"A farmer has 8 rows of apple trees. Each row has 12 trees. If each tree produces 6 apples, how many apples does the farmer get in total?"
Definition:

Multi-step vocabulary: Recognizing multiple operations needed in complex word problems

Problem
(8 rows × 12 trees) × 6 apples
Solution
576 apples
Step 1: Identify first operation

"Each row has" indicates first multiplication: 8 × 12

Step 2: Identify second operation

"How many... in total?" indicates second multiplication

Step 3: Set up the equation

(8 × 12) × 6 = ? total apples

Step 4: Calculate

96 × 6 = 576

Step 5: Check the answer

Estimate: 10 × 10 × 6 = 600, so 576 is reasonable

(8 × 12) × 6 = 576
Final answer:

The farmer gets 576 apples in total.

Applied rules:

• Vocabulary clues: "Each" and "total" indicate multiplication

• Problem type: Multi-step multiplication

• Verification: 576 ÷ 6 = 96, 96 ÷ 12 = 8 ✓

🍎
Rows
8
➡️
× Trees
× 12
➡️
× Apples
× 6
🟰
Total
576
Vocabulary Rules & Methods
Total = Rate × Time
Rate Problems
Multiplication
Total = Rate × Quantity
Equal groups
Division
Rate = Total ÷ Quantity
Equal sharing
Multi-Step
Multiple Operations
Complex problems
Key definitions:

Multiplication: Repeated addition of equal groups

Division: Sharing equally or finding group size

Rate: Amount per unit (per hour, per day, per item)

Unit: The measurement used (dollars, hours, items)

Complete methodology:
  1. Read and understand: What is being asked?
  2. Identify key vocabulary: Circle words indicating operations
  3. Choose operation: Based on vocabulary clues
  4. Plan the solution: What operations are needed?
  5. Solve: Perform calculations carefully
  6. Check: Does the answer make sense?
Tip 1: Look for key words that indicate multiplication or division.
Tip 2: Draw a picture to visualize the problem.
Tip 3: Estimate your answer first to check reasonableness.
Tip 4: Always include units in your final answer.
Common errors: Misreading vocabulary, choosing wrong operations, forgetting units.
Key notes: Vocabulary words guide you to the correct operation.
Important rules to remember:

• Multiplication: Use when finding totals of equal groups

• Division: Use when sharing equally or finding group size

• Keywords: Look for "each," "total," "share," "split"

• Units: Always include appropriate units in your answer

🔍
Identify
Find key words
⚙️
Apply
Choose operation
✅
Check
Verify solution
Vocabulary Exercises: 4 to 5
4 Real-world vocabulary problem
Exercise 4
"A bakery makes 15 batches of cookies each day. Each batch contains 24 cookies. How many cookies does the bakery make in 5 days?"
Definition:

Real-world vocabulary: Recognizing vocabulary in practical, everyday situations

Problem
(15 batches × 24 cookies) × 5 days
Solution
1800 cookies
Step 1: Identify key words

"Each batch contains" and "in 5 days" indicate multiplication

Step 2: Identify the operation

"How many... in 5 days?" suggests finding total amount

Step 3: Set up the equation

(15 × 24) × 5 = ? total cookies

Step 4: Calculate

360 × 5 = 1800

Step 5: Check the answer

Estimate: 15 × 25 × 5 = 1875, so 1800 is reasonable

(15 × 24) × 5 = 1800
Final answer:

The bakery makes 1800 cookies in 5 days.

Applied rules:

• Vocabulary clue: "Each batch contains" and "in 5 days" indicate multiplication

• Problem type: Multi-step multiplication

• Verification: 1800 ÷ 5 = 360, 360 ÷ 24 = 15 ✓

🍪
Batches/Day
15
➡️
× Cookies
× 24
➡️
× Days
× 5
🟰
Total
1800
5 Multi-step vocabulary problem
Exercise 5
"A school bought 120 books and wants to put them equally on 6 shelves. Then, each shelf is divided into 4 sections. How many books are in each section?"
Definition:

Multi-step vocabulary: Recognizing multiple operations in complex word problems

Problem
(120 ÷ 6) ÷ 4
Solution
5 books/section
Step 1: Identify first operation

"Put them equally" indicates first division: 120 ÷ 6

Step 2: Identify second operation

"Each shelf is divided into" indicates second division

Step 3: Set up the equation

(120 ÷ 6) ÷ 4 = ? books per section

Step 4: Calculate

20 ÷ 4 = 5

Step 5: Check the answer

5 × 4 × 6 = 120 ✓

(120 ÷ 6) ÷ 4 = 5
Final answer:

There are 5 books in each section.

Applied rules:

• Vocabulary clues: "Equally" and "divided into" indicate division

• Problem type: Multi-step division

• Verification: 5 × 24 = 120 ✓

📚
Total Books
120
➡️
÷ Shelves
÷ 6
➡️
÷ Sections
÷ 4
🟰
Per Section
5

Questions & Answers

Question: How do I know if I need to multiply or divide in a word problem?

Answer: Look for key words and think about what the problem is asking:

  • Multiply when: You need to find a total of equal groups ("each," "times," "product," "area")
  • Divide when: You need to share equally or find how many groups ("share," "split," "each," "per," "distribute")

For example: "There are 4 apples in each basket and 5 baskets" → Multiply (4 × 5)

"Share 20 apples equally among 4 children" → Divide (20 ÷ 4)

Question: My child has trouble recognizing the vocabulary words. How can I help them practice?

Answer: Here are strategies to help with vocabulary recognition:

  • Create flashcards with key words and their meanings
  • Practice reading word problems together and highlighting key words
  • Play games where you identify whether words indicate multiplication or division
  • Make lists of key words and practice sorting them
  • Work on word problems regularly to build familiarity
  • Encourage your child to read the entire problem before deciding

Consistent practice will build confidence!

Question: What if a word problem has words that could mean both multiplication and division?

Answer: This can happen! Here's what to do:

  • Read the entire problem carefully to understand the context
  • Look for other words that clarify the situation
  • Think about what the question is asking for
  • Draw a picture to visualize the problem
  • Try both operations and see which makes more sense
  • Check if your answer is reasonable in the context

For example, "each" can appear in both types of problems, but the overall context determines the operation.