Solved Exercises on Multiplying by 10 in Grade 3

Master multiplying by 10: place value patterns, mental math strategies, and real-world applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Place Value Pattern
Exercise 1
Show the pattern when multiplying by 10: 1 × 10, 2 × 10, 3 × 10, 4 × 10, 5 × 10
Definition:

Place Value Pattern: When multiplying any number by 10, the digits shift one place to the left and a zero is added to the right. This is because 10 is the base of our number system.

Method:
  1. Take the original number
  2. Multiply by 10
  3. Observe the pattern: digits shift left, zero appears on right
  4. Notice that each result is 10 times larger than the original
Original Number Multiplication Result Pattern 1 1 × 10 10 1 → 10 2 2 × 10 20 2 → 20 3 3 × 10 30 3 → 30 4 4 × 10 40 4 → 40 5 5 × 10 50 5 → 50
Ones
Tens
Hundreds
Thousands
4
Ones
→
4
Tens
→
0
Ones
Original
4
Multiply by 10
4 × 10
Result
40
Step 1: Take the original number

Start with 4 in the ones place

Step 2: Multiply by 10

4 × 10 shifts the digit one place to the left

Step 3: Add a zero

The ones place becomes 0, the tens place gets the original digit

Step 4: Verify the result

40 is ten times larger than 4

4 × 10 = 40
Final answer:

4 × 10 = 40, demonstrating the place value pattern of multiplying by 10

Applied rules:

• Place Value Rule: Each place value is 10 times the previous place value

• Shift Pattern: Digits move one place left when multiplied by 10

• Zero Addition: A zero is added to the right of the original number

2 Mental Math Strategy
Exercise 2
Use mental math to solve: 7 × 10, 9 × 10, 12 × 10, 25 × 10
Definition:

Mental Math Strategy: A quick method for multiplying by 10 by adding a zero to the end of the number. This works because multiplying by 10 shifts all digits one place to the left.

Mental Math Tip: To multiply any number by 10, simply add a zero to the end of the number!
7 × 10
70
9 × 10
90
12 × 10
120
Step 1: For 7 × 10

Add a zero to 7 → 70

Step 2: For 9 × 10

Add a zero to 9 → 90

Step 3: For 12 × 10

Add a zero to 12 → 120

Step 4: For 25 × 10

Add a zero to 25 → 250

2
25
5
25
0
250
0
250
25
Ones
→
25
Tens
→
0
Ones
7 × 10 = 70, 9 × 10 = 90, 12 × 10 = 120, 25 × 10 = 250
Final answer:

7 × 10 = 70, 9 × 10 = 90, 12 × 10 = 120, 25 × 10 = 250

Applied rules:

• Mental Math Rule: Add a zero to multiply by 10

• Place Value Shift: All digits move one place to the left

• Quick Calculation: This strategy speeds up computation

3 Real-World Application
Exercise 3
If a pack of pencils costs $3, how much would 10 packs cost? Use multiplying by 10 to solve.
Definition:

Real-World Application: Using multiplication by 10 to solve practical problems involving equal groups or scaling quantities by a factor of 10.

Real-World Connection: When buying 10 of something, you multiply the price by 10!
Price per pack
$3
Number of packs
10
Total cost
$30
Step 1: Identify the cost per unit

One pack costs $3

Step 2: Identify the number of units

You want 10 packs

Step 3: Set up the multiplication

Total cost = $3 × 10

Step 4: Apply the multiply by 10 rule

Add a zero to 3 → $30

3
$3
0
$30
$3
Cost
→
$30
Total Cost
$3 × 10 = $30
Final answer:

10 packs of pencils would cost $30 because $3 × 10 = $30

Applied rules:

• Real-World Rule: Multiply unit cost by quantity to find total cost

• Multiplication by 10: Quick method for scaling by 10

• Money Application: Same principle applies to currency

Multiplying by 10: Core Concepts
n × 10 = n0
Mental Math Rule
Rule 1
Add Zero
4 × 10 = 40
Rule 2
Place Value
4 moves from ones to tens
Rule 3
Ten Times
4 becomes ten times larger
Rule 4
Decimal Shift
Digits move one place left
Key definitions:

Place Value: The value of a digit based on its position in a number

Digit: A single symbol used to make numerals (0-9)

Base 10 System: Our number system where each place value is 10 times the previous

Mental Math: Calculating in your head without writing down steps

Mental Math Strategy:
  1. Look at the number: Identify the original number to multiply
  2. Add a zero: Put a zero at the end of the number
  3. Read the result: The new number is 10 times larger
  4. Verify: Count to ensure the result makes sense
Key Pattern: Every number multiplied by 10 ends in 0
Value Increase: The result is always 10 times the original number
Tip 1: Remember: multiplying by 10 makes numbers 10 times bigger.
Tip 2: Just add a zero to multiply by 10 - it's that simple!
Tip 3: This works for any whole number, big or small.
Solution: Exercises 4 to 5
4 Shopping Scenario
Exercise 4
A store sells notebooks for $6 each. If you buy 10 notebooks, how much will you spend? Explain using place value.
Definition:

Shopping Scenario: A real-world problem involving multiplication by 10 to calculate total cost when buying multiple identical items.

Shopping Tip: When buying 10 of something, just add a zero to the single-item price!
6
$6
0
$60
$6
Per Notebook
→
$60
Total Cost
Price per notebook
$6
Number of notebooks
10
Total cost
$60
Step 1: Identify the unit price

Each notebook costs $6

Step 2: Identify the quantity

You're buying 10 notebooks

Step 3: Apply multiplication by 10

$6 × 10 = $60

Step 4: Explain using place value

The 6 moves from the ones place to the tens place, and a 0 goes in the ones place

$6 × 10 = $60
Final answer:

You will spend $60 because $6 × 10 = $60, where the 6 moves from ones to tens place and 0 fills the ones place

Applied rules:

• Place Value Rule: Digits shift one place left when multiplied by 10

• Shopping Rule: Unit price × Quantity = Total cost

• Mental Math Rule: Add a zero to multiply by 10

5 Mixed Practice
Exercise 5
Solve these problems using multiplying by 10: (a) 15 × 10, (b) 8 × 10, (c) 32 × 10, (d) If one apple costs 40 cents, how much do 10 apples cost?
Definition:

Mixed Practice: Applying the multiplication by 10 rule to various problems including multi-digit numbers and word problems.

Part (a)
15 × 10 = 150
Part (b)
8 × 10 = 80
Part (c)
32 × 10 = 320
Part (d)
40¢ × 10 = 400¢ = $4.00
Step 1: Solve 15 × 10

Add a zero to 15 → 150

Step 2: Solve 8 × 10

Add a zero to 8 → 80

Step 3: Solve 32 × 10

Add a zero to 32 → 320

Step 4: Solve the word problem

40 cents × 10 = 400 cents = $4.00

3
32
2
32
0
320
32
Original
→
32
Tens
→
0
Ones
(a) 150, (b) 80, (c) 320, (d) $4.00
Final answer:

(a) 15 × 10 = 150, (b) 8 × 10 = 80, (c) 32 × 10 = 320, (d) 10 apples cost $4.00

Applied rules:

• Consistent Pattern: The rule works for single and multi-digit numbers

• Unit Conversion: 400 cents = $4.00 (divide by 100)

• Place Value Shift: All digits move one place left when multiplied by 10

Advanced Multiplying by 10 Concepts
abc × 10 = abc0
General Rule
Key definitions:

Base 10 System: Our decimal number system where each place value is 10 times the previous place value

Place Value: The value of a digit based on its position in a number (ones, tens, hundreds, etc.)

Multiplication Pattern: A consistent relationship that occurs when performing multiplication

Advanced Strategies:
  1. Recognize the pattern: Understand that multiplying by 10 always adds a zero
  2. Apply place value: Know that digits shift one place to the left
  3. Use mental math: Quickly calculate by adding zeros
  4. Verify results: Check that the answer is 10 times larger
  5. Extend to larger numbers: Apply the same principle to any size number
Tip 1: The multiply-by-10 rule works for any number, no matter how large.
Tip 2: This pattern helps with multiplying by 100 (add two zeros) and 1000 (add three zeros).
Tip 3: Understanding this concept prepares you for decimals and larger numbers.
Tip 4: This is a foundational skill that helps with many other math operations.
Pattern Recognition: Multiplying by 10 always increases the value by a factor of 10.
Place Value Understanding: This reinforces the structure of our number system.
Extended rules:

• General Rule: n × 10 = n followed by 0

• Place Value Shift: Each digit moves one place value higher

• Value Increase: The result is always 10 times the original number

• Universal Application: Works for any whole number

Single Digit
5 × 10 = 50
5 → 50
Two Digits
23 × 10 = 230
23 → 230
Three Digits
147 × 10 = 1470
147 → 1470
Four Digits
2563 × 10 = 25630
2563 → 25630

Questions & Answers

Question: Why does multiplying by 10 always add a zero? Why doesn't it work differently?

Answer: Great question! This happens because we use a base-10 number system. Here's why:

  • Our number system has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
  • Each place value is 10 times the previous: Ones, Tens, Hundreds, Thousands
  • When you multiply by 10: All digits move to the next higher place value
  • The ones place becomes empty: So we fill it with a 0

For example: 34 × 10

  • The 3 moves from tens to hundreds place
  • The 4 moves from ones to tens place
  • The ones place becomes empty, so we put 0 there
  • Result: 340

It's like shifting everything one spot to the left!

Question: Does this rule work for bigger numbers too, like 100 or 1000?

Answer: Yes! The same principle applies to larger powers of 10:

  • Multiplying by 10: Add 1 zero (3 × 10 = 30)
  • Multiplying by 100: Add 2 zeros (3 × 100 = 300)
  • Multiplying by 1000: Add 3 zeros (3 × 1000 = 3000)

The number of zeros you add matches the number of zeros in the multiplier:

  • 45 × 10 = 450 (added 1 zero)
  • 45 × 100 = 4500 (added 2 zeros)
  • 45 × 1000 = 45000 (added 3 zeros)

This is because 100 = 10 × 10 and 1000 = 10 × 10 × 10!

Question: What happens when we divide by 10? Is there a similar pattern?

Answer: Yes! Dividing by 10 is the opposite of multiplying by 10:

  • Multiplying by 10: Digits move one place to the left, add zero
  • Dividing by 10: Digits move one place to the right, remove last digit

Examples:

  • 50 ÷ 10 = 5 (50 loses its last digit 0, becomes 5)
  • 340 ÷ 10 = 34 (340 loses its last digit 0, becomes 34)
  • 700 ÷ 10 = 70 (700 loses its last digit 0, becomes 70)

It's like the reverse process - digits shift back one place to the right!