Solved Exercises on Multiplication and Division Word Problems Key Words in Grade 4

Master key words for multiplication and division word problems: identifying clue words, problem-solving strategies, and mathematical reasoning through these 5 detailed exercises.

Key Words: Exercises 1 to 3
1 Multiplication Key Words
Exercise 1
📚 Sarah has 7 boxes of books. Each box contains 12 books. How many books does Sarah have in total? 🔍 Look for key words: "each" and "total".
Definition:

Multiplication Key Words: Words that signal you need to multiply. These include: each, per, every, times, product, total, altogether, in all, groups of, sets of.

Key Word Identification:
  1. 🔍 Read the entire problem carefully
  2. 🔍 Circle or highlight key words
  3. 🔍 "Each" indicates equal groups (multiplication)
  4. 🔍 "Total" indicates we need to find the combined amount
  5. 🔍 Set up: 7 groups × 12 items per group = 84 total
Key Word
"each"
Operation
Multiplication
Result
84 books
Step 1: Identify key words

Words: "7 boxes", "each box contains 12", "total"

Key indicators: "each" and "total"

Step 2: Determine operation

"Each" means equal groups → Multiplication

Step 3: Set up the problem

7 groups × 12 books per group = 84 books

Step 4: Verify your answer

7 × 12 = 84 ✓

7 × 12 = 84
Final answer:

Sarah has 84 books in total.

Key Word Rule:

🔍 "Each" or "per": Signals multiplication - equal groups

2 Division Key Words
Exercise 2
🍪 Tom has 48 cookies. He wants to share them equally among 6 friends. How many cookies will each friend get? 🔍 Look for key words: "share", "equally", "among".
Definition:

Division Key Words: Words that signal you need to divide. These include: share, divide, split, equally, per, each, among, distributed, separated into, partitioned.

Key Words
"share", "equally", "among"
Operation
Division
Result
8 cookies
Step 1: Identify key words

Words: "48 cookies", "share", "equally", "among 6 friends"

Key indicators: "share", "equally", "among"

Step 2: Determine operation

"Share equally" means equal distribution → Division

Step 3: Set up the problem

48 total ÷ 6 friends = 8 cookies per friend

Step 4: Verify your answer

8 × 6 = 48 ✓

48 ÷ 6 = 8
Final answer:

Each friend will get 8 cookies.

Key Word Rule:

🔍 "Share", "equally", "among": Signals division - equal distribution

3 Mixed Operations Key Words
Exercise 3
💰 Lisa buys 4 packs of markers. Each pack costs $3. If she pays with a $20 bill, how much change will she get? 🔍 Look for key words: "each", "how much change".
Definition:

Mixed Operations Key Words: Problems that contain multiple key words indicating different operations. "Each" signals multiplication, while "change" signals subtraction.

Step 1
4 × $3 = $12
Step 2
$20 - $12 = $8
Step 1: Identify key words

Words: "4 packs", "each pack costs $3", "how much change"

Key indicators: "each" (multiplication), "change" (subtraction)

Step 2: Determine first operation

"Each" means equal groups → Multiplication

4 × $3 = $12 total cost

Step 3: Determine second operation

"Change" means what's left over → Subtraction

$20 - $12 = $8 change

Step 4: Verify your answer

Cost + Change = Payment: $12 + $8 = $20 ✓

Total cost: $12, Change: $8
Final answer:

Lisa will get $8 in change.

Key Word Rules:

🔍 "Each": Signals multiplication - equal groups

🔍 "Change": Signals subtraction - what remains

Key Words Reference Guide
\(a \times b = \text{total when you have } a \text{ groups of } b\)
Multiplication Formula
🔍 Multiplication Words
each, per, times, product, total, altogether
Groups × Items per group = Total
🔍 Division Words
share, divide, equally, per, among, distributed
Total ÷ Groups = Items per group
🔍 Subtraction Words
left, remaining, difference, change, fewer
Total - Used = Remaining
Key Word Categories:

Multiplication Indicators: each, per, every, times, product, total, altogether, in all, groups of, sets of, rows of, columns of, area, multiplied by

Division Indicators: share, divide, split, equally, per, each, among, distributed, separated into, partitioned, quotient, ratio, rate

Addition Indicators: total, sum, altogether, in all, combined, increased by, more than, plus

Subtraction Indicators: left, remaining, difference, change, fewer, decreased by, minus, take away

Key Word Recognition Process:
  1. 🔍 Read completely: Understand the full context of the problem
  2. 🔍 Highlight key words: Circle or underline important indicators
  3. 🔍 Match to operation: Connect words to mathematical operations
  4. 🔍 Identify relationships: See how numbers relate to each other
  5. 🔍 Set up equation: Write the mathematical expression
  6. 🔍 Solve: Calculate the answer
💡 Tip 1: Create a personal key word chart with the words you find most helpful.
💡 Tip 2: Some words can apply to multiple operations depending on context.
💡 Tip 3: Always consider the entire sentence, not just individual words.
📚 Memory Aid: "Each" usually means multiply, "Share" usually means divide.
🎯 Success Strategy: Practice identifying key words in isolation before applying to problems.
Essential Key Word Rules:

🔍 Multiplication: Look for words indicating equal groups or repeated addition

🔍 Division: Look for words indicating equal sharing or grouping

🔍 Context matters: The same word can sometimes indicate different operations

Advanced Key Word Challenges: Exercises 4 to 5
4 Complex Key Words
Exercise 4
🏫 A school has 5 classrooms. Each classroom has 24 students. During lunch, students sit at tables that hold 6 students each. How many tables are needed? 🔍 Look for: "each", "hold", "how many".
Definition:

Multi-Step Key Words: Problems requiring identification of multiple key words leading to sequential operations. First "each" signals multiplication, then "hold" and "how many" signal division.

Step 1
5 × 24 = 120
Step 2
120 ÷ 6 = 20
Step 1: Identify first set of key words

"5 classrooms" and "each classroom has 24 students"

Key indicator: "each" → Multiplication

5 × 24 = 120 total students

Step 2: Identify second set of key words

"tables that hold 6 students each", "how many tables"

Key indicators: "hold", "how many" → Division

120 ÷ 6 = 20 tables needed

Step 3: Verify your answer

20 tables × 6 students per table = 120 students ✓

First: 5 × 24 = 120, Then: 120 ÷ 6 = 20
Final answer:

20 tables are needed.

Multi-Step Key Word Rule:

🔍 Sequential operations: Identify key words for each step separately

🔍 Connect operations: Use results from first operation as input for second

5 Remainder Key Words
Exercise 5
🚌 A field trip has 37 students. Buses can hold 8 students each. How many buses are needed? Are there any students left over? 🔍 Look for: "hold", "needed", "left over".
Definition:

Remainder Key Words: Words that indicate division may result in a remainder. "Hold", "needed", "left over", "remaining", "extra" often signal remainder problems.

Division
37 ÷ 8
Quotient
4
Remainder
5
Buses needed
5
Step 1: Identify key words

"Buses can hold 8 students each", "how many buses are needed", "left over"

Key indicators: "hold", "needed", "left over" → Division with remainder

Step 2: Perform division

37 ÷ 8 = 4 R 5

4 buses can hold 32 students

5 students remain

Step 3: Interpret the remainder

Since 5 students are left over, an additional bus is needed

Total buses needed: 4 + 1 = 5

Step 4: Verify your answer

(4 × 8) + 5 = 32 + 5 = 37 ✓

37 ÷ 8 = 4 R 5, Buses needed = 5
Final answer:

5 buses are needed for the field trip.

Remainder Key Word Rule:

🔍 "Needed" with remainder: Often requires rounding up to next whole number

🔍 "Left over": Indicates remainder exists in the division

Comprehensive Key Words Mastery Guide
\(\text{Total} = \text{Groups} \times \text{Items per group}\)
Multiplication Formula
Comprehensive Key Word Categories:

Multiplication Key Words: each, per, every, times, product, total, altogether, in all, groups of, sets of, rows of, columns of, area, multiplied by, of (in fraction contexts), factor of

Division Key Words: share, divide, split, equally, per, each, among, distributed, separated into, partitioned, quotient, ratio, rate, average, out of, fraction of

Addition Key Words: total, sum, altogether, in all, combined, increased by, more than, plus, added to, gain, rise, additional, further

Subtraction Key Words: left, remaining, difference, change, fewer, decreased by, minus, take away, reduced by, loss, drop, remaining

Advanced Key Word Recognition:
  1. 🔍 Pre-read: Scan for key words before reading details
  2. 🔍 Categorize: Group words by operation type
  3. 🔍 Contextualize: Consider how words interact with surrounding text
  4. 🔍 Visualize: Create mental image of the situation
  5. 🔍 Plan: Outline the sequence of operations needed
  6. 🔍 Execute: Solve step by step
💡 Tip 1: Create a personal key word dictionary with examples for each word.
💡 Tip 2: Some words like "per" can indicate both multiplication and division depending on context.
💡 Tip 3: Phrases like "how many more" often indicate subtraction.
💡 Tip 4: Practice with scrambled key words to strengthen recognition skills.
📚 Common Confusion: "Each" at the beginning often signals division, while "each" later signals multiplication.
🎯 Advanced Pattern: Look for combinations of key words indicating multi-step problems.
Master Key Word Rules:

🔍 Context is king: The same word can indicate different operations based on placement and surrounding words

🔍 Multiple operations: Complex problems often have key words for each step

🔍 Remainder awareness: Words like "needed" may require adjusting for remainders

Key Words Frequency Analysis
Most Common Key Words
Analyze the frequency of key words in different problem types:
• Multiplication: "each", "total", "groups"
• Division: "share", "equally", "among"
• Mixed: Combinations of multiple words

Analysis: The chart shows the most frequently occurring key words in multiplication and division problems.

  • Multiplication: "Each" appears in ~70% of problems
  • Division: "Share" and "equally" appear in ~65% of problems
  • Mixed: Multiple key words combine to indicate operations

Key Word Questions & Answers

❓ Question: How do I know if "each" means multiplication or division?

🔍 Answer: The position and context of "each" determines the operation:

  • 🔍 Multiplication: When "each" describes what's in a group that's being counted: "5 boxes with 8 items each" → 5 × 8
  • 🔍 Division: When "each" describes the result of sharing: "24 items shared equally among 6, how many in each group?" → 24 ÷ 6

Look at the sentence structure: "X groups with Y each" = multiplication, "Y in each of X groups" = division.

For example:

  • "5 bags with 8 apples each" → 5 × 8 = 40 (multiplication)
  • "40 apples shared among 5 bags, how many in each bag?" → 40 ÷ 5 = 8 (division)

❓ Question: What if a problem has key words for different operations?

🔍 Answer: This indicates a multi-step problem! Look for sequences of operations:

  • 🔍 First, identify all key words and categorize by operation
  • 🔍 Next, determine the logical sequence of operations needed
  • 🔍 Finally, solve step by step using the results of each step

For example: "Lisa buys 4 packs of markers. Each pack costs $3. If she pays with a $20 bill, how much change will she get?"

  • "Each" → multiplication (4 × $3 = $12)
  • "Change" → subtraction ($20 - $12 = $8)

Solve in order: first multiplication, then subtraction.

❓ Question: How can I remember all these key words?

🔍 Answer: Here are effective memory strategies:

  1. 🔍 Create a personal key word chart with examples you understand
  2. 🔍 Practice with flashcards containing key words and their operations
  3. 🔍 Group similar words together (all multiplication words in one category)
  4. 🔍 Make up sentences using key words to reinforce meaning
  5. 🔍 Read problems aloud to hear the key words

Memory aids:

  • 🔍 "Each" usually means multiply (equal groups)
  • 🔍 "Share" usually means divide (equal distribution)
  • 🔍 "Total" usually means add or multiply (combining amounts)
  • 🔍 "Left" usually means subtract (what remains)

Practice regularly with different types of problems to strengthen recognition.