Solved Exercises on How to Explain Multiples in Grade 4

Master how to explain multiples: definition, identification, and patterns through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 What Are Multiples?
Exercise 1
Explain what multiples are and list the first 5 multiples of 2.
Definition:

Multiple: A number that can be divided evenly by another number. Multiples of 2 are: 2×1, 2×2, 2×3, etc.

Explanation Method:
  1. Define what a multiple is in simple terms
  2. Show how multiples are created by multiplication
  3. List the first few multiples in order
  4. Identify the pattern in the multiples

Explanation: A multiple is a number you get when you multiply another number by a whole number (1, 2, 3, 4...). For example, multiples of 2 are the answers to: 2×1, 2×2, 2×3, 2×4, 2×5...

Step 1: Multiply by 1

2 × 1 = 2

Step 2: Multiply by 2

2 × 2 = 4

Step 3: Multiply by 3

2 × 3 = 6

Step 4: Multiply by 4

2 × 4 = 8

Step 5: Multiply by 5

2 × 5 = 10

2
4
6
8
10
↑ Pattern: Add 2 each time ↑
First 5 multiples of 2: 2, 4, 6, 8, 10
Final answer:

Multiples of 2: 2, 4, 6, 8, 10

Applied rules:

• Multiplication: Base number × whole number = multiple

• Pattern: Each multiple is the previous + base number

• Division: Every multiple ÷ base number = whole number

2 Identifying Multiples
Exercise 2
Explain how to identify if a number is a multiple of 4. Check if 16, 22, and 24 are multiples of 4.
Definition:

Multiple Check: A number is a multiple of 4 if it can be divided by 4 with no remainder.

Explanation: To check if a number is a multiple of 4, divide it by 4. If there's no remainder, it's a multiple of 4. Multiples of 4 always end in 0, 2, 4, 6, or 8 (even digits).

16 ÷ 4 = 4 ✓
22 ÷ 4 = 5.5 ✗
24 ÷ 4 = 6 ✓
Step 1: Check 16

16 ÷ 4 = 4 (no remainder)

Yes, 16 is a multiple of 4

Step 2: Check 22

22 ÷ 4 = 5 remainder 2

No, 22 is not a multiple of 4

Step 3: Check 24

24 ÷ 4 = 6 (no remainder)

Yes, 24 is a multiple of 4

Step 4: Verify with multiplication

4 × 4 = 16 ✓

4 × 6 = 24 ✓

Multiples: 16, 24
Not multiples: 22
Multiples of 4: 16, 24 | Not multiples: 22
Final answer:

16 and 24 are multiples of 4, 22 is not

Applied rules:

• Division test: Multiple ÷ base = whole number

• Pattern: Multiples of 4 are always even

• Quick check: Last 2 digits divisible by 4

3 Multiples Pattern
Exercise 3
Explain the pattern in multiples of 5 and list the first 6 multiples.
Definition:

Pattern: A consistent rule that governs how multiples behave.

Explanation: Multiples of 5 always end in 0 or 5. This is because 5×1=5, 5×2=10, 5×3=15, etc. The pattern is: 5, 10, 15, 20, 25, 30...

5×1=5
5×2=10
5×3=15
5×4=20
5×5=25
5×6=30
Step 1: Multiply by 1

5 × 1 = 5

Step 2: Multiply by 2

5 × 2 = 10

Step 3: Multiply by 3

5 × 3 = 15

Step 4: Multiply by 4

5 × 4 = 20

Step 5: Multiply by 5

5 × 5 = 25

Step 6: Multiply by 6

5 × 6 = 30

↑ Pattern: Ends in 0 or 5 ↑
5
10
15
20
25
30
First 6 multiples of 5: 5, 10, 15, 20, 25, 30
Final answer:

Multiples of 5: 5, 10, 15, 20, 25, 30

Applied rules:

• Pattern recognition: Multiples of 5 end in 0 or 5

• Multiplication: Base number × whole number = multiple

• Consistency: Pattern holds for all multiples

Multiples Rules and Methods
Multiple = Base × Whole\ Number
Multiple Definition
Rule 1
n × 1 = n
Any number is a multiple of itself
Rule 2
n × 0 = 0
0 is a multiple of every number
Rule 3
n × m = mn
Multiplication creates multiples
Key definitions:

Multiple: A number that can be divided evenly by another number

Pattern: A consistent rule that governs how multiples behave

Common Multiple: A number that is a multiple of two or more numbers

Complete methodology:
  1. Define the concept: Explain what a multiple is in simple terms
  2. Identify the base number: Determine which number's multiples you need
  3. Apply multiplication: Multiply by 1, 2, 3, 4, etc.
  4. Check divisibility: Verify each result ÷ base = whole number
  5. Find patterns: Look for sequences and relationships
Tip 1: Multiples always increase by the base number.
Tip 2: Even numbers have only even multiples.
Tip 3: Use multiplication tables to find multiples quickly.
Tip 4: Patterns help predict future multiples.
Patterns to remember: Multiples of 5 end in 0 or 5, multiples of 10 end in 0.
Key insight: Every number has infinite multiples, starting from itself.
Multiples Rules:

• Multiple of n = n × k (where k is any whole number)

• First multiple of any number = the number itself

• Zero is a multiple of every number

• Multiples form arithmetic sequences

Solution: Exercises 4 to 5
4 Common Multiples
Exercise 4
Explain how to find common multiples of 3 and 4. Find the first 3.
Definition:

Common Multiple: A number that is a multiple of two or more numbers.

Explanation: To find common multiples, list the multiples of each number and find which numbers appear in both lists. The first common multiple is called the Least Common Multiple (LCM).

Multiples of 3: 3,6,9,12,15,18,21,24,27,30,33,36
Multiples of 4: 4,8,12,16,20,24,28,32,36
Step 1: List multiples of 3

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36...

Step 2: List multiples of 4

4, 8, 12, 16, 20, 24, 28, 32, 36...

Step 3: Find common numbers

Compare lists: 12 appears in both

Next: 24 appears in both

Then: 36 appears in both

Step 4: Verify

12 ÷ 3 = 4 ✓ and 12 ÷ 4 = 3 ✓

24 ÷ 3 = 8 ✓ and 24 ÷ 4 = 6 ✓

36 ÷ 3 = 12 ✓ and 36 ÷ 4 = 9 ✓

12
24
36
First 3 common multiples: 12, 24, 36
Final answer:

12, 24, 36

Applied rules:

• Listing method: Write multiples of each number

• Comparison: Find numbers appearing in both lists

• Verification: Check divisibility by both numbers

5 Real-world Application
Exercise 5
Explain how multiples are used in real life. Give an example with packaging.
Definition:

Real-world application: Using multiples to solve practical problems involving grouping and packaging.

Explanation: Multiples are used in everyday life for organizing items into groups. For example, eggs come in cartons of 12 (multiples of 12: 12, 24, 36, 48...), and cookies might come in packages of 6 (multiples of 6: 6, 12, 18, 24...).

Eggs: 12,24,36,48...
Cookies: 6,12,18,24...
Cans: 4,8,12,16...
Step 1: Identify the packaging unit

If cookies come in packages of 6, the possible quantities are multiples of 6

Step 2: Apply the concept

You can buy 6, 12, 18, 24, 30, 36... cookies, but not 7, 13, or 19

Step 3: Find real-world examples

Pens come in packs of 5: 5, 10, 15, 20...

Donuts come in dozens: 12, 24, 36, 48...

Step 4: Connect to math

These are all examples of multiples in action!

Packaging: 6,12,18...
Counting: 5,10,15...
Organizing: 10,20,30...
Multiples in real life: packaging, counting, organizing
Final answer:

Multiples help organize items into equal groups in real life

Applied rules:

• Problem solving: Translate words to mathematical operations

• Real-world connection: Link math to everyday situations

• Pattern recognition: Identify how multiples are used practically

Multiples Complete Guide
Multiple = Factor × Whole\ Number
Multiples Formula
Key definitions:

Multiple: A number that can be divided by another number without remainder

Pattern: A consistent rule that governs how multiples behave

Common Multiple: A number that is a multiple of two or more numbers

Explaining Multiples Methods:
  1. Define clearly: Explain what a multiple is in simple terms
  2. Use examples: Show how multiples are created by multiplication
  3. Identify patterns: Point out consistent behaviors
  4. Provide verification: Show how to check if a number is a multiple
  5. Connect to real life: Demonstrate practical applications
Tip 1: Multiples of 2 are always even numbers.
Tip 2: Multiples of 5 end in 0 or 5.
Tip 3: Multiples of 10 always end in 0.
Tip 4: Sum of digits of multiples of 3 is also a multiple of 3.
Tip 5: Every number is a multiple of its factors.
Multiples patterns: They form arithmetic sequences with common difference equal to the base number.
Number relationships: If A is a multiple of B, then B is a factor of A.
Important Properties:

• Every number is a multiple of 1

• Every number is a multiple of itself

• 0 is a multiple of every number

• Multiples are always ≥ the base number (except 0)

• There are infinitely many multiples of any number

Multiples Patterns Infographic
📊
Multiples of 2
Pattern: Even numbers
2
4
6
8
10
Multiples of 3
Pattern: Sum of digits ÷ 3
3
6
9
12
15
Multiples of 5
Pattern: End in 0 or 5
5
10
15
20
25
How to Explain Multiples
1
Define
2
Show examples
3
Find patterns
4
Apply
Multiples Relationships
Every multiple of 6 is also a multiple of 2 and 3
Common multiples of 2 and 3: 6, 12, 18, 24...
Remember: Multiples Always Increase!

Questions & Answers

Question: How can I explain multiples to someone who doesn't understand them?

Answer: Here's how to explain multiples simply:

  • Start with counting: Multiples are numbers you get when you count by a number
  • Use examples: Counting by 3s: 3, 6, 9, 12... these are multiples of 3
  • Show multiplication: Multiples come from multiplication (3×1=3, 3×2=6, 3×3=9...)
  • Use real objects: Eggs in cartons of 12, cookies in packages of 6

Say: "Multiples are the answers when you multiply a number by 1, 2, 3, 4..."

For example: Multiples of 4 are: 4, 8, 12, 16, 20... because those are the answers to 4×1, 4×2, 4×3, 4×4, 4×5...

Question: How do I know if a big number like 144 is a multiple of 12?

Answer: There are several ways to check:

  • Division test: 144 ÷ 12 = 12 (whole number, so yes!)
  • Factor breakdown: 12 = 3×4, so 144 must be divisible by both 3 and 4
  • Pattern check: Since 12 = 3×4, check if 144 follows both patterns

For 144: It ends in 44, and 44÷4=11 (so divisible by 4). Sum of digits: 1+4+4=9, and 9÷3=3 (so divisible by 3). Since it's divisible by both 3 and 4, it's divisible by 12.

Therefore, 144 is a multiple of 12: 12×12=144.

Question: What should I do if I get confused about multiples?

Answer: Here's what to do when confused about multiples:

  1. Go back to basics: Remember multiples come from multiplication
  2. Write them out: List the first few multiples to see the pattern
  3. Check with division: Divide to see if there's a remainder
  4. Use smaller numbers: Practice with easier examples first
  5. Look for patterns: Notice how multiples behave

For example, if you're confused about multiples of 7, write them out: 7, 14, 21, 28, 35... You'll see they increase by 7 each time.

Practice with small numbers first, then work up to larger ones!