Solved Exercises on Multiplying and Dividing by 10s Worksheet in Grade 3

Master multiplying and dividing by 10s through comprehensive worksheet practice: patterns, applications, and mixed operations.

Solution: Exercises 1 to 3
1 Multiplication practice
Exercise 1
Complete the multiplication table: \(2 \times 10\), \(5 \times 10\), \(8 \times 10\), \(9 \times 10\), \(4 \times 10\)
Definition:

Multiplication by 10: Each digit moves one place value position to the left

Worksheet Instructions:

Apply the rule: When multiplying by 10, add a zero to the end of the number

\(2 \times 10\)
20
\(5 \times 10\)
50
\(8 \times 10\)
80
\(9 \times 10\)
90
\(4 \times 10\)
40
Pattern Recognition
2 → 20
5 → 50
8 → 80
Step 1: Identify the pattern

Each number is being multiplied by 10

Step 2: Apply the multiply by 10 rule

Add a zero to the end of each number

Step 3: Verify each answer

Check that each result is 10 times the original number

20, 50, 80, 90, 40
Final answer:

\(2 \times 10 = 20\), \(5 \times 10 = 50\), \(8 \times 10 = 80\), \(9 \times 10 = 90\), \(4 \times 10 = 40\)

Applied rules:

• Zero rule: Add a zero to the end of the number when multiplying by 10

• Pattern recognition: Each result is 10 times the original number

• Place value: Digits move one place to the left

2 Division practice
Exercise 2
Complete the division table: \(60 \div 10\), \(30 \div 10\), \(90 \div 10\), \(70 \div 10\), \(100 \div 10\)
Definition:

Division by 10: Each digit moves one place value position to the right

Worksheet Instructions:

Apply the rule: When dividing by 10, remove a zero from the end of the number

\(60 \div 10\)
6
\(30 \div 10\)
3
\(90 \div 10\)
9
\(70 \div 10\)
7
\(100 \div 10\)
10
Pattern Recognition
60 → 6
30 → 3
90 → 9
Step 1: Identify the pattern

Each number is being divided by 10

Step 2: Apply the divide by 10 rule

Remove one zero from the end of each number

Step 3: Verify each answer

Check that each result is 1/10 of the original number

6, 3, 9, 7, 10
Final answer:

\(60 \div 10 = 6\), \(30 \div 10 = 3\), \(90 \div 10 = 9\), \(70 \div 10 = 7\), \(100 \div 10 = 10\)

Applied rules:

• Zero removal: Remove a zero from the end of the number when dividing by 10

• Pattern recognition: Each result is 1/10 of the original number

• Place value: Digits move one place to the right

3 Mixed operations
Exercise 3
Complete the mixed operations: \(4 \times 10\), then divide the result by 10. Repeat for: \(7 \times 10\), then divide by 10.
Definition:

Inverse operations: Multiplication and division are opposite operations that undo each other

Worksheet Instructions:

Complete each operation pair and observe the relationship between multiplication and division by 10

\(4 \times 10 = 40\)
\(40 \div 10 = 4\)
\(7 \times 10 = 70\)
\(70 \div 10 = 7\)
Inverse Operations
4 → 40 → 4
7 → 70 → 7
Step 1: Complete the multiplication

\(4 \times 10 = 40\), \(7 \times 10 = 70\)

Step 2: Complete the division

\(40 \div 10 = 4\), \(70 \div 10 = 7\)

Step 3: Observe the pattern

We end up with the same number we started with!

\(4 \rightarrow 40 \rightarrow 4\), \(7 \rightarrow 70 \rightarrow 7\)
Final answer:

Multiplication by 10 and division by 10 are inverse operations

Applied rules:

• Inverse operations: One operation undoes the other

• Verification: Starting number equals ending number

• Relationship: Multiplication and division by 10 are opposites

Worksheet Practice Problems
Multiplication Problems
\(1 \times 10\)
10
\(3 \times 10\)
30
\(6 \times 10\)
60
\(8 \times 10\)
80
Division Problems
\(20 \div 10\)
2
\(50 \div 10\)
5
\(80 \div 10\)
8
\(100 \div 10\)
10
Mixed Problems
\(9 \times 10 = ?\)
90
\(90 \div 10 = ?\)
9
\(10 \times 10 = ?\)
100
\(100 \div 10 = ?\)
10
Key definitions:

Worksheet: A set of practice problems designed to reinforce mathematical concepts

Inverse operations: Operations that undo each other (multiplication and division)

Pattern recognition: Identifying consistent relationships between numbers

Worksheet completion strategy:
  1. Read instructions: Understand what is being asked
  2. Identify operation: Determine if multiplying or dividing by 10
  3. Apply rule: Use the appropriate rule for the operation
  4. Check answers: Verify each answer makes sense
Tip 1: Work through problems systematically from top to bottom.
Tip 2: Check your work by using the inverse operation.
Tip 3: Look for patterns to help with recall.
Tip 4: Practice regularly to build fluency.
Key insight: Worksheets provide structured practice to build math fluency.
Common error: Mixing up multiplication and division rules. Pay attention to the operation symbol!
Patterns and Relationships
\(n \times 10 = n0\)
Multiply by 10
\(n0 \div 10 = n\)
Divide by 10
Multiplication Patterns
1 → 10
2 → 20
3 → 30
4 → 40
5 → 50
Division Patterns
10 → 1
20 → 2
30 → 3
40 → 4
50 → 5
Inverse Relationships
2 → 20 → 2
5 → 50 → 5
7 → 70 → 7
9 → 90 → 9

Pattern Recognition Tips:

  • Multiplying by 10 adds a zero to the end
  • Dividing by 10 removes a zero from the end
  • The operations are opposites (inverses)
  • Patterns help with memorization
Worksheet Completion Tips
\(\text{Worksheet Success} = \text{Understanding} + \text{Practice} + \text{Verification}\)
Success Formula
Key concepts:

Math fluency: The ability to solve problems quickly and accurately

Pattern recognition: Identifying consistent relationships between numbers

Self-checking: Using inverse operations to verify answers

Effective worksheet strategies:
  1. Scan first: Look over the entire worksheet before starting
  2. Start easy: Complete simpler problems first to build confidence
  3. Check as you go: Verify answers using inverse operations
  4. Review: Go back and double-check your work
Tip 1: Circle or highlight the operation symbols to avoid confusion.
Tip 2: Use scratch paper if needed to work out problems.
Tip 3: Take breaks if you feel overwhelmed.
Tip 4: Ask for help when needed.
Common mistake: Rushing through worksheets without checking work.
Success strategy: Take your time and use patterns to help with recall.
Important worksheet facts to remember:

• Always read the instructions carefully before starting

• Multiplying by 10 adds a zero to the end of the number

• Dividing by 10 removes a zero from the end of the number

• These operations are inverses of each other

• Check your work by using the inverse operation

Questions & Answers

Question: Why do we need to do so many problems on worksheets? Isn't it boring?

Answer: Worksheets may seem repetitive, but they're very important for building math skills:

  • Practice makes permanent: Repetition helps move facts from short-term to long-term memory
  • Pattern recognition: Doing multiple problems helps you see patterns and relationships
  • Confidence building: Success with practice builds confidence for more complex problems

Think of it like practicing piano scales - repetition builds skill and muscle memory!

Question: How can I help my child stay focused while completing multiplication and division worksheets?

Answer: Here are effective strategies to maintain focus:

  • Set a timer: Work in short, focused bursts (10-15 minutes)
  • Provide incentives: Small rewards for completing sections
  • Make it visual: Use manipulatives or drawings to represent problems
  • Connect to real life: Show how these skills apply to everyday situations

Break longer worksheets into smaller chunks and celebrate progress along the way!

Question: What if I make a mistake on my worksheet? Should I erase it and start over?

Answer: Making mistakes is completely normal and part of learning! Here's what to do:

  • Don't panic: Mistakes help your brain learn
  • Circle the problem: Come back to it after completing others
  • Check your work: Use the inverse operation to verify answers
  • Learn from it: Understand why the mistake happened

Erasing isn't necessary - just correct the mistake and move on. Teachers appreciate seeing your thinking process!

Detailed Summary: Multiplying and Dividing by 10s Worksheet

Definitions of Key Concepts

  • Worksheet: A structured set of math problems designed for practice and reinforcement
  • Multiplication by 10: A mathematical operation that increases a number by a factor of 10
  • Division by 10: A mathematical operation that decreases a number by a factor of 10
  • Inverse Operations: Operations that undo each other (multiplication and division)
  • Pattern Recognition: Identifying consistent relationships between numbers and operations

Core Rules and Principles

  • Multiplication Rule: When multiplying by 10, add one zero to the end of the number
  • Division Rule: When dividing by 10, remove one zero from the end of the number
  • Inverse Relationship: Multiplying by 10 and dividing by 10 are opposite operations
  • Place Value: Multiplication moves digits left, division moves digits right
  • Worksheet Strategy: Approach problems systematically and check work as you go

Step-by-Step Methods and Procedures

  1. Worksheet Preparation:
    • Read all instructions carefully
    • Identify the type of problems (multiplication or division)
    • Gather necessary materials (pencil, eraser, scratch paper)
  2. Problem Solving:
    • Identify the operation needed (×10 or ÷10)
    • Apply the appropriate rule (add/remove zero)
    • Write the answer in the designated space
  3. Verification:
    • Use inverse operations to check answers
    • Ensure each answer makes logical sense
    • Review completed problems periodically

Concrete Examples (Simple to Advanced)

  • Simple Multiplication: \(1 \times 10 = 10\), \(3 \times 10 = 30\), \(5 \times 10 = 50\)
  • Simple Division: \(10 \div 10 = 1\), \(30 \div 10 = 3\), \(50 \div 10 = 5\)
  • Moderate Multiplication: \(12 \times 10 = 120\), \(25 \times 10 = 250\), \(47 \times 10 = 470\)
  • Moderate Division: \(120 \div 10 = 12\), \(250 \div 10 = 25\), \(470 \div 10 = 47\)
  • Advanced Mixed Operations: \(8 \times 10 = 80\), \(80 \div 10 = 8\); \(15 \times 10 = 150\), \(150 \div 10 = 15\)

Tips, Tricks, and Common Pitfalls

  • Tip 1: Circle or highlight operation symbols to avoid confusion
  • Tip 2: Use scratch paper to work out problems if needed
  • Tip 3: Look for patterns to help with recall and verification
  • Common Pitfall: Confusing multiplication and division symbols
  • Common Mistake: Forgetting to remove zeros when dividing by 10

Key Notes for Memorization

  • Rhyme: "To multiply by 10, add a zero at the end!"
  • Rhyme: "To divide by 10, take a zero off the end!"
  • Memory Aid: Multiplication makes numbers bigger, division makes them smaller
  • Pattern: These operations are opposites that undo each other

Explanation for Students

Worksheets are like practice fields for your brain! When you multiply by 10, you're making the number 10 times bigger by adding a zero. When you divide by 10, you're making it 10 times smaller by removing a zero. These operations are like opposites - if you multiply by 10 and then divide by 10, you get back to where you started! The more you practice with worksheets, the more automatic these operations become. Don't worry about making mistakes - they help your brain learn. Just take your time, look for patterns, and check your work using the opposite operation.