# Multiplying Whole Numbers

In this post we will discuss multiplication of whole numbers.

Here we will understand multiplication by two methods.
(a) Multiplication in parts
(b) Multiplication by column

After the concept we will move on to solve some related Grade 5 Math Questions

## Multi digit Multiplication

We will understand the concept with the help of examples.

### Multiply 3 digit with 1 digit number

Example 01
498 x 5

Method 01 (Multiplication in Parts)

Using Distributive Property of Multiplication which says:
a (b + c) = ab + ac

498 x 5 can be written as:
⟹ (400 + 90 + 8 ) x 5

Using Distributive Property of Multiplication
⟹ (400 x 5) + (90 x 5) + (8 x 5)
⟹ (2000) + (450) + (40)
⟹ 2490

Method 2 (Multiplication in Columns)

(a) Place Values

⟹ Find Place values of given numbers
⟹ Arrange number vertically such that digit with same place values are in same line

(b) Multiply Numbers

⟹ Multiply 5 with 8
5 x 8 = 40
We will write 0 and 4 will be carried to Tens Place

⟹ Multiply 5 with 9
5 x 5 = 45
And we also add the number 4 in carry
45 + 4 = 49
we will write 9 and 4 will be carried to Hundred Place

⟹ Multiply 5 with 4
5 x 4 = 20
And we also add the number 4 in carry
20 + 4 = 24
we will write 24 in the result

2490 is the solution

Example 02
640 x 7

Method 01 (Multiplication in Parts)

640 x 7 can be written as

⟹ (600 + 40) x 7
⟹ (600 x 7) + (40 x 7)
⟹ (4200) + (280)
⟹ 4480

Method 2 (Multiplication in Columns)

(a) Place Value
⟹ Find Place values of given numbers
⟹ Arrange the number in column so digit with same place value are in same vertical line

(b) Multiply Numbers

⟹ Multiply 7 with 0
7 x 0 = 0
we write 0 in the main solution

Multiply 7 with 4
7 x 4 = 28
we write 8 in main solution and 2 is carried over to Hundred Place

Multiply 7 with 6
7 x 6 = 42
Add the number 2 in carry
42 + 2 = 44
Write 44 in part of main solution

Now lets move on to solve some difficult questions which involves multi digit numbers

### Multiply 3 digit and 2 digit number

Example 01
453 x 36

We will solve this question using column method

(a) Place Value
Find Place Value of given numbers
Arrange them vertically such that digit with same place value are in same line

(b) Multiply Numbers

One’s Column Multiplication

⟹ Multiply 6 with 3
6 x 3 = 18
we write 8 in the solution and 1 is carried over to Tens Place

⟹ Multiply 6 with 5
6 x 5 = 30
Now add number 1 present in carry
30 + 1 = 31
we write 1 in the main solution and 3 is carried over to Hundred Place

⟹ Multiply 6 with 4
6 x 4 = 24
Now add number 3 present in carry
24 + 3 = 27
we write 27 in the main solution

Here Multiplication with One’s Column is completed.

Now move on to Ten’s Column calculation. Before than mark ” X ” (which is 0) in one’s column

Ten’s Column Multiplication

⟹ Multiply 3 with 3
3 x 3 = 9
write 9 in main solution

⟹Multiply 3 with 5
3 x 5 = 15
write 5 in main solution and 1 is carried over to hundred place

⟹Multiply 3 with 4
3 x 4 = 12
Also add 1 present in carry
12 + 1 = 13
write 13 in main solution

Here Multiplication of Ten’s Column is completed

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Example 02
721 x 48

Solving the question using column method

(a) Place Value
Find Place Value and arrange the numbers vertically

(b) Multiply Numbers

One’s Column Multiplication

⟹ Multiply 8 with 1
8 x 1 = 8
Write 8 in the main solution

⟹ Multiply 8 with 2
8 x 2 = 16
Write 6 in the main solution and 1 is carried over to Hundred Place

⟹ Multiply 8 with 7
8 x 7 = 56
Add 1 which is present in carry
56 + 1 = 57
Write 57 in the main solution

Ten’s Column Multiplication

Mark “X” in One column

⟹ Multiply 4 with 1
4 x 1 = 4
Write 4 in main solution

⟹ Multiply 4 with 2
4 x 2 = 8
Write 8 in main solution

⟹ Multiply 4 with 7
4 x 7 = 28
Write 28 in main solution

34608 is the solution

### Multiply 4 digit with 2 digit

Example 01
6583 x 62

(a) Place Value
Find place value of numbers and arrange them vertically such that number with same place value are in same line

(b) Multiply Numbers

One’s Column Multiplication

⟹ Multiply 2 with 3
2 x 3 = 6
Write 6 in main solution

⟹ Multiply 2 with 8
2 x 8 = 16
Write 6 in main solution and 1 is carried over to Hundred Place

⟹ Multiply 2 with 5
2 x 5 = 10
Also add 1 present in carry
10 + 1 = 11
Write 1 in main solution and 1 is carried over to Thousand Place

⟹ Multiply 2 with 6
2 x 6 = 12
Also add 1 present in carry
12 + 1 = 13
Write 13 in main solution

We are done with One’s column multiplication

Ten’s column multiplication

Mark X in One’s column

⟹ Multiply 6 with 3
6 x 3 = 18
Write 8 in the solution and 1 is carried over to Tens Place

⟹ Multiply 6 with 8
6 x 8 = 48
1 + 48 = 49
Write 9 in main solution and 4 is carried over to Hundred’s Place

⟹ Multiply 6 with 5
6 x 5 = 30
30 + 4 = 34

Write 4 in main solution and 3 is carried over to Thousand Place

⟹ Multiply 6 with 6
6 x 6 = 36
36 + 3 = 39

write 39 in main solution

408146 is the solution

### Multiply 3 digit by 3 digit number

Example 01
726 x 654

(a) Place value
Find Place Value and arrange the number vertically

(b) Ones Column Multiplication

⟹ Multiply 4 with 6
4 x 6 = 24
write number 4 in solution and carry 2 on Tens Place

⟹ Multiply 4 with 2
4 x 2 = 8
8 + 2 = 10
write number 0 in solution and carry 1 on Hundred Place

⟹ Multiply 4 with 7
4 x 7 = 28
28 + 1 = 29
write number 29 in solution

(c) Tens Column Multiplication

Mark X in Ones Column

⟹ Multiply 5 with 6
5 x 6 = 30
Write 0 in solution and 3 is carried over to Tens Place

⟹ Multiply 5 with 2
5 x 2 = 10
10 + 3 = 13
write number 3 in solution and 1 is carried over to Hundred Place

⟹ Multiply 5 with 7
5 x 7 = 35
35 + 1 = 36
write 36 in solution

(d) Hundred Column Multiplication

Mark X in Ones and Tens Column

⟹ Multiply 6 with 6
6 x 6 = 36
Write 6 in solution and 3 is carried over to Tens Place

⟹ Multiply 6 with 2
6 x 2 = 12
12 + 3 = 15
write number 5 in solution and 1 is carried over to Hundred Place

⟹ Multiply 6 with 7
6 x 7 = 42
42 + 1 = 43
write 43 in solution

Add all the numbers in solution column

474804 is the solution

Example 02
Multiply 443 x 120

(a) Ones Column multiplication

⟹ Multiply 0 with 3
0 x 3 = 0
Write 0 in solution

⟹ Multiply 0 with 4
0 x 4 = 0
Write 0 in solution

⟹ Multiply 0 with 4
0 x 4 = 0
Write 0 in solution

(b) Tens Column multiplication

Put X in the ones column

⟹ Multiply 2 with 3
2 x 3 = 6
Write 6 in solution

⟹ Multiply 2 with 4
2 x 4 = 8
Write 8 in solution

⟹ Multiply 2 with 4
2 x 4 = 8
Write 8 in solution

(c) Hundreds Column multiplication

Put X in the Ones and Tens column

⟹ Multiply 1 with 3
1 x 3 = 3
Write 3 in solution

⟹ Multiply 1 with 4
1 x 4 = 4
Write 4 in solution

⟹ Multiply 1 with 4
1 x 4 = 4
Write 4 in solution

(d) Add all the numbers in solution

53160 is the solution

Here we will discuss some important multiplication problems.

All the questions are to the standard of Grade 5

Explanation/Solution are also provided for each question

### Basic Multiplication

Here two numbers are given in the question.

You have to multiply the numbers and find the solution

(01) Multiply 517 x 82

(02) Multiply 65 x 74

4810 is the solution

(03) Multiply 748 x 27

20196 is the solution

(04) Multiply 617 and 315

194355 is the solution

(05) Multiply 403 x 414

166842 is the solution

(06) Multiply 855 x 93

79515 is the solution

(07) Multiply 942 x 27

25434 is the solution

(08) Multiply 322 x 638

205436 is the solution

(09) Multiply 69 x 92

6348 is the solution

(10) Multiply 66 x 42

2772 is the solution

(11) Multiply 44 x 67

2948 is the solution

(12) Multiply 717 x 342

245214 is the solution

(13) Multiply 450 x 72

32400 is the solution

(14) Multiply 141 x 144

20304 is the solution

(15) Multiply 547 x 809

442523 is the solution

### Missing digits in Multiplication

Given below are the images of multiplication with empty boxes.

You have to complete the multiplication and fill up the empty boxes.

(01) 371 x 93

(02) 145 x 69

(03) 653 x 55

(04) 456 x 139

(05) 632 x 731

(6) Multiply and find the missing digits in below image

(07) Multiply 225 x 79 and find the missing boxes

(08) Fill up the empty boxes

(09) Do the multiplication and fill up the missing digits

(10) Find the missing digits in below multiplication