Multiplication of Double-digit Numbers with Single-digit Numbers

What is Double-Digit Multiplication?

We’ve learned how to multiply small numbers. Now let’s learn something exciting – multiplying bigger numbers!

Double-digit numbers are numbers from 10 to 99. They have two digits (tens and ones).

Examples of double-digit numbers: 12, 25, 34, 48, 67, 85, 99

In this chapter, we’ll learn to multiply double-digit numbers by small numbers (1, 2, 3, 4, and 5).

Example:

23 × 2 = ?
14 × 3 = ?
32 × 4 = ?

Don’t worry! It’s easier than it looks! 😊

Understanding Place Value First

Before we multiply, let’s remember place value:

Example: The number 24

Tens  |  Ones
  2   |   4

2 is in the tens place = 2 tens = 20
4 is in the ones place = 4 ones = 4
So, 24 = 20 + 4

Example: The number 35

Tens  |  Ones
  3   |   5

3 is in the tens place = 3 tens = 30
5 is in the ones place = 5 ones = 5
So, 35 = 30 + 5

This is very important for multiplication!

The Multiplication Symbol

We use the multiplication sign (×) to show multiplication.

Different ways to write multiplication:

Horizontal format: 12 × 3 = 36
Vertical format:
```
  12
×  3
----
  36
----
```
Using a dot: 12 • 3 = 36
In words: “12 times 3 equals 36”

For now, we’ll focus on horizontal and vertical formats!

Method 1: Using Multiplication Tables

Multiplication tables help us multiply quickly!

Let’s Learn the Basic Tables First

×2 Table (Multiply by 2):

1 × 2 = 2
2 × 2 = 4
3 × 2 = 6
4 × 2 = 8
5 × 2 = 10
6 × 2 = 12
7 × 2 = 14
8 × 2 = 16
9 × 2 = 18
10 × 2 = 20

×3 Table (Multiply by 3):

1 × 3 = 3
2 × 3 = 6
3 × 3 = 9
4 × 3 = 12
5 × 3 = 15
6 × 3 = 18
7 × 3 = 21
8 × 3 = 24
9 × 3 = 27
10 × 3 = 30

×4 Table (Multiply by 4):

1 × 4 = 4
2 × 4 = 8
3 × 4 = 12
4 × 4 = 16
5 × 4 = 20
6 × 4 = 24
7 × 4 = 28
8 × 4 = 32
9 × 4 = 36
10 × 4 = 40

×5 Table (Multiply by 5):

1 × 5 = 5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25
6 × 5 = 30
7 × 5 = 35
8 × 5 = 40
9 × 5 = 45
10 × 5 = 50

Method 2: Vertical Multiplication (Step-by-Step)

This is the most important method! Let’s learn it carefully.

Example 1: 12 × 3 = ?

Step 1: Write the numbers vertically (one below the other)

    12   ← This is the number we're multiplying (bigger number on top)
  ×  3   ← This is what we're multiplying by (smaller number below)
  ----

Step 2: Start with the ONES place (right side)

Multiply 2 × 3 = 6

    12
  ×  3
  ----
     6   ← Write 6 in the ones place

Step 3: Now multiply the TENS place

Multiply 1 × 3 = 3 (Remember: 1 in tens place means 10, so it’s really 10 × 3 = 30)

    12
  ×  3
  ----
    36   ← Write 3 in the tens place

Answer: 12 × 3 = 36 ✓

Let’s check with pictures:

🟦 is tens
🟩 is ones

12 × 3 means “3 groups of 12”

Group 1: 🟦 🟩🟩 (1 ten + 2 ones = 12) Group 2: 🟦 🟩🟩 (1 ten + 2 ones = 12) Group 3: 🟦 🟩🟩 (1 ten + 2 ones = 12)

Total: 🟦🟦🟦 🟩🟩🟩🟩🟩🟩 = 3 tens + 6 ones = 36 ✓

Example 2: 21 × 4 = ?

Step 1: Write vertically

    21
  ×  4
  ----

Step 2: Multiply ONES place

1 × 4 = 4

Step 3: Multiply TENS place

2 × 4 = 8 (2 tens × 4 = 8 tens = 80)

Answer: 21 × 4 = 84 ✓

Example 3: 33 × 2 = ?

Step-by-step:

Step 1: Write it        Step 2: Multiply ones    Step 3: Multiply tens
    33                      33                       33
  ×  2                    ×  2                     ×  2
  ----                    ----                     ----
                             6  (3 × 2 = 6)         66  (3 × 2 = 6)

Answer: 33 × 2 = 66 ✓

Example 4: 14 × 5 = ?

Step-by-step:

    14
  ×  5
  ----

Ones: 4 × 5 = 20 (Write 0 in ones place, carry 2 to tens) Tens: 1 × 5 = 5, plus 2 (carried) = 7

     ²14  ← Small 2 shows we carried
  ×   5
  -----
     70

Wait! Let’s learn about carrying in the next section!

Understanding “Carrying” in Multiplication

Sometimes when we multiply, the answer in the ones place is 10 or more. When this happens, we need to carry to the tens place!

Example 1: 14 × 5 = ? (With Carrying)

Step 1: Write vertically

    14
  ×  5
  ----

Step 2: Multiply ONES place

4 × 5 = 20

But wait! 20 is bigger than 9, so:

Write 0 in the ones place
Carry the 2 to the tens place (write it small above the tens)

     ²1    ← Carry the 2 here
    14
  ×  5
  ----
     0    ← Write 0 in ones place

Step 3: Multiply TENS place and add the carried number

1 × 5 = 5 Then add the carried 2: 5 + 2 = 7

Answer: 14 × 5 = 70 ✓

Example 2: 19 × 3 = ? (With Carrying)

Step 1: Write vertically

    19
  ×  3
  ----

Step 2: Multiply ONES

9 × 3 = 27

Write 7 in ones place
Carry 2 to tens place

Step 3: Multiply TENS and add carried number

1 × 3 = 3 Add carried 2: 3 + 2 = 5

Answer: 19 × 3 = 57 ✓

Example 3: 26 × 4 = ? (With Carrying)

Step 1: Write it         Step 2: Multiply ones     Step 3: Multiply tens + carry
    26                       ²2                        ²2
  ×  4                      26                        26
  ----                    ×  4                      ×  4
                          ----                      ----
                             4  (6×4=24, write 4)    104  (2×4=8, +2=10)
                                (carry 2)

Answer: 26 × 4 = 104 ✓

Method 3: Breaking Numbers Apart (Expanded Form)

This method helps you understand what’s really happening!

Example 1: 23 × 2 = ?

Step 1: Break 23 into tens and ones

23 = 20 + 3

Step 2: Multiply each part by 2

20 × 2 = 40
 3 × 2 =  6

Step 3: Add the results

40 + 6 = 46

Answer: 23 × 2 = 46 ✓

Visual representation:

23 × 2 means:

(20 + 3) × 2 = (20 × 2) + (3 × 2)
             = 40 + 6
             = 46

Example 2: 34 × 3 = ?

Step 1: Break 34 apart

34 = 30 + 4

Step 2: Multiply each part

30 × 3 = 90
 4 × 3 = 12

Step 3: Add

90 + 12 = 102

Answer: 34 × 3 = 102 ✓

Example 3: 42 × 4 = ?

Break it apart:

42 = 40 + 2

40 × 4 = 160
 2 × 4 =   8

160 + 8 = 168

Answer: 42 × 4 = 168 ✓

Method 4: Using Arrays and Groups (Visual Method)

This method is great for understanding smaller double-digit numbers!

Example 1: 12 × 3 = ?

Think: 3 groups of 12

We can show 12 as 1 ten + 2 ones:

Group 1: [🟦] [🟩🟩]  = 12
Group 2: [🟦] [🟩🟩]  = 12
Group 3: [🟦] [🟩🟩]  = 12
         ----  ------
Total:   3 tens + 6 ones = 30 + 6 = 36

Answer: 12 × 3 = 36 ✓

Example 2: 11 × 4 = ?

Think: 4 groups of 11

Group 1: [🟦] [🟩]  = 11
Group 2: [🟦] [🟩]  = 11
Group 3: [🟦] [🟩]  = 11
Group 4: [🟦] [🟩]  = 11
         ----  ----
Total:   4 tens + 4 ones = 40 + 4 = 44

Answer: 11 × 4 = 44 ✓

Example 3: 21 × 2 = ?

Array format:

Row 1: 🟦🟦 🟩  (21 = 2 tens + 1 one)
Row 2: 🟦🟦 🟩  (21 = 2 tens + 1 one)
       ----  --
Total: 4 tens + 2 ones = 40 + 2 = 42

Answer: 21 × 2 = 42 ✓

Tips and Tricks for Success! 🌟

Tip 1: Master Your Basic Tables First

Before multiplying double-digit numbers, make sure you know these tables by heart:

×2 table (2, 4, 6, 8, 10, 12, 14, 16, 18, 20)
×3 table (3, 6, 9, 12, 15, 18, 21, 24, 27, 30)
×4 table (4, 8, 12, 16, 20, 24, 28, 32, 36, 40)
×5 table (5, 10, 15, 20, 25, 30, 35, 40, 45, 50)

Practice these every day!

Tip 2: Always Start from the ONES Place

Remember: In vertical multiplication, always multiply from right to left!

    25     ← Start here (ones)
  ×  3     ← Then move here (tens)
  ----

This is the rule! Don’t start from the left.

Tip 3: Use “Carrying” Carefully

When the answer is 10 or more:

Write the ones digit in the answer
Write the tens digit small above the next column
Don’t forget to add it in the next step!

Example:

     ²1    ← Don't forget this carried number!
    16
  ×  5
  ----
    80

Tip 4: Check Your Answer with Addition

You can always check multiplication by using repeated addition!

Example: Is 12 × 3 = 36 correct?

Check: 12 + 12 + 12 = 36 ✓

Yes, it’s correct!

Tip 5: Look for Patterns with ×5

When multiplying by 5, the answer always ends in 0 or 5!

11 × 5 = 55  (ends in 5)
12 × 5 = 60  (ends in 0)
13 × 5 = 65  (ends in 5)
14 × 5 = 70  (ends in 0)

Pattern: If the ones digit is even, answer ends in 0. If odd, answer ends in 5!

Tip 6: Doubling Trick for ×2

Multiplying by 2 is the same as doubling!

23 × 2 = 23 + 23 = 46
31 × 2 = 31 + 31 = 62

Think: “What’s double of this number?”

Tip 7: Use the “Double-Double” for ×4

To multiply by 4, double the number twice!

Example: 12 × 4 = ?

Step 1: Double 12 = 24
Step 2: Double 24 = 48

So, 12 × 4 = 48

Tip 8: Break Big Problems into Small Ones

If a problem looks hard, break it into easier parts!

Example: 45 × 3 = ?

Instead of doing it all at once:

Think: 45 = 40 + 5

40 × 3 = 120  (Easy! 4 × 3 = 12, add a zero)
 5 × 3 =  15  (Easy! From your ×3 table)

120 + 15 = 135

Tip 9: Practice with Real Objects

Use real things to understand:

Egg cartons: 12 eggs × 2 cartons = 24 eggs
Pencil boxes: 24 pencils × 3 boxes = 72 pencils
Coin groups: 25 cents × 4 = 100 cents = $1

Tip 10: Write Neatly and Line Up Columns

Good:

Bad (messy):

  23
 × 4
 ---
 92

Keep your columns straight so you don’t make mistakes!

Special Patterns to Remember! 🎯

Pattern 1: Multiplying by 1

Any number × 1 = that same number

23 × 1 = 23
45 × 1 = 45
99 × 1 = 99

Pattern 2: Multiplying by 10

When multiplying by 10, just add a zero!

12 × 10 = 120
25 × 10 = 250
48 × 10 = 480

Why? Because 10 = 1 ten and 0 ones!

Pattern 3: Numbers Ending in 0

If a number ends in 0, multiply is easier!

Example: 20 × 3 = ?

Think: 2 × 3 = 6
Add the zero: 60

So, 20 × 3 = 60

Example: 30 × 4 = ?

Think: 3 × 4 = 12
Add the zero: 120

So, 30 × 4 = 120

Pattern 4: Multiples of 11

Multiplying 11 is fun!

11 × 2 = 22  (2 and 2)
11 × 3 = 33  (3 and 3)
11 × 4 = 44  (4 and 4)
11 × 5 = 55  (5 and 5)

Pattern: The answer has the same digit repeated!

Common Mistakes to Avoid! ⚠️

Mistake 1: Forgetting to Carry

Wrong:

    16
  ×  5
  ----
    50  ❌ (Forgot about 6 × 5 = 30)

Right:

Mistake 2: Starting from the Wrong Side

Wrong: Starting from the tens place

Right: Always start from the ones place!

Mistake 3: Not Lining Up Columns

Wrong:

Right:

Keep everything neat and lined up!

Mistake 4: Forgetting Place Value

Remember: The 2 in 23 means 20, not just 2!

    23
  ×  3
  ----

Ones: 3 × 3 = 9
Tens: 2 × 3 = 6 (really 20 × 3 = 60)

Answer: 69

Real-Life Examples

Example 1: The Candy Store 🍬

A candy costs 12 rupees. Mom buys 4 candies. How much does she pay?

Answer: 48 rupees ✓

Example 2: The Book Fair 📚

Each book has 25 pages. You have 3 books. How many pages in total?

Answer: 75 pages ✓

Example 3: The Garden 🌻

A garden has 14 rows. Each row has 5 flowers. How many flowers in total?

Answer: 70 flowers ✓

Example 4: The Toy Store 🚗

A box has 32 toy cars. The store has 2 boxes. How many toy cars?

Answer: 64 toy cars ✓

Example 5: The Classroom ✏️

Each student gets 13 pencils. There are 4 students. How many pencils in total?

Answer: 52 pencils ✓

Remember! 📝

✓ Place value is important (tens and ones) ✓ Always start from the ones place (right side) ✓ Carry when the answer is 10 or more ✓ Line up your columns neatly ✓ Practice your basic tables every day ✓ Check your answer by adding repeatedly ✓ Use real-life examples to understand better

You’re becoming a multiplication expert! Keep practicing! 🎉

Multiplication Table Reference Chart

Keep this handy while you practice!

×  | 1  | 2  | 3  | 4  | 5  
---|----|----|----|----|----
1  | 1  | 2  | 3  | 4  | 5  
2  | 2  | 4  | 6  | 8  | 10 
3  | 3  | 6  | 9  | 12 | 15 
4  | 4  | 8  | 12 | 16 | 20 
5  | 5  | 10 | 15 | 20 | 25 
6  | 6  | 12 | 18 | 24 | 30 
7  | 7  | 14 | 21 | 28 | 35 
8  | 8  | 16 | 24 | 32 | 40 
9  | 9  | 18 | 27 | 36 | 45 
10 | 10 | 20 | 30 | 40 | 50

Use this chart to help you solve problems! 📊

Image by freepik

Worksheet on Multiplication of Double-digit Numbers with Single-digit Numbers