Multiplication

In multiplication we know how to multiply a one, two or three-digit number by another 1 or 2-digit number. We also know how to multiply a four-digit number by a 2-digit number. We also know the different methods of multiplication. Here, we shall make use of the methods and procedures learnt previously in multiplying larger numbers.

The numbers that are being multiplied are called factors.

The answer of a multiplication operation is called a product.

Let us recall the properties of multiplication:

I. The product does not change when the order of the numbers is changed.

5 × 4 = 4 × 5

6 × 3 = 3 × 6


II. The product does not change when the grouping of numbers is changed.

(6 × 7) × 4 = 6 × (7 × 4)

2 × (5 × 3) = (2 × 5) × 3


III. The product of a number and 1 is the number itself.

96 × 1 = 96

72 × 1 = 72


IV. The product of a number and 0 is 0.

754 × 0 = 0

316 × 0 = 0

For examples:

40 × 5 = 200

400 × 5 = 2000

4000 × 5 = 20000



Now, we will recall how to do multiplication of a number by a 1-digit number.


Examples on Expanded Notation Method:

1. Use expanded notation to multiply 64 and 8.

Expanded notation



4 × 8   =    32

60 × 8 = + 480
          =    512

Answer: 512

3 and 4 digit numbers can also be multiplied by a 1 digit number using the expanded notation method.

2. Use expanded notation to multiply 413 by 5.

Expanded Notation to Multiply





3 × 5    =        15
10 × 5  =        50
400 × 5 = + 2000
            =   2065

Answer: 2065

3. Use expanded notation to multiply 1246 by 3.

Expanded Notation to Multiply





6 × 3      =       18
40 × 3    =       50
200 × 3  =      600
1000 × 3 = + 3000
             =    3738

Answer: 3738

4. Use expanded notation to find the product of 1409 and 5.

Expanded Notation





9 × 5     =       45
0 × 5     =         0
400 × 5  =    2000
1000 × 5 = + 5000
             =    7045

Answer: 7045


Let us first revise the process of multiplication. 


Consider the following:

1. Multiply 215 by 7

Solution:

(i) (Expanded notation method)

215 × 7 = (200 + 10 + 5) × 7          1 4 0 0

= 200 × 7 + 10 × 7 + 5 × 7        +        7 0

= 1400 + 70 + 35                       +        3 5

= 1505                                            1 5 0 5


(ii) (Column method)

Column Method

Product = 1505

(i) 5 ones × 7 = 35 = 3 tens + 5 ones

5 is written under one column, 3 ten is carried over

(ii) 1 ten × 7 = 7 tens,

7 tens + 3 tens = 10 tens = 1 H + 0 ten.

0 is written under ten-column,

1 hundred is carried over

(iii) 2 hundreds × 7 = 14 hundreds

14 hundreds + 1 hundred = 15H

15H = 1Th + 5H. 1 is written under

Th-column and 5H is placed under H-column

So, 215 × 7 = 1505


2. Multiply 6103 by 8

Solution:

(i) (Expanded notation method)

6103 × 8 = (6000 + 100 + 0 + 3) × 8          4 8 0 0 0

= 48000 + 800 + 0 + 24                         +        8 0 0

= 48824                                                  +             0

                                                              +          2 4
                                                                  4 8 8 2 4


(ii) (Column method)

Multiplication

Product = 4 8 8 2 4

(i) 3 one × 8 = 24 ones = 2 tens + 4 ones

4 is placed under ones, 2 tens is carried over

(ii) 0 ten × 8 = 0, 0 + 2 = 2 tens, placed
under ten's

(iii) 1H × 8 = 8 hundreds, 8H is placed under H

(iv) 6Th × 8 = 48 thousands. It is placed under
Th.

So, 6103 × 8 = 48824



3. Find the product of 2113 and 3 using column method.

Solution:

multiply 4 digit numbers by a 1 digit number

Answer: 8452

3 × 4 = 12 ONES

Regroup as 1 TEN 2 ONES.

Related Concept

Addition

Word Problems on Addition

Subtraction

Check for Subtraction and Addition

Word Problems Involving Addition and Subtraction

Estimating Sums and Differences

Find the Missing Digits

Multiplication

Multiply a Number by a 2-Digit Number

Multiplication of a Number by a 3-Digit Number

Multiply a Number

Estimating Products

Word Problems on Multiplication

Multiplication and Division

Terms Used in Division

Division of Two-Digit by a One-Digit Numbers

Division of Four-Digit by a One-Digit Numbers

Division by 10 and 100 and 1000

Dividing Numbers

Estimating the Quotient

Division by Two-Digit Numbers

Word Problems on Division



4th Grade Math Activities

From Multiplication to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Relation between Diameter Radius and Circumference |Problems |Examples

    Apr 22, 24 05:19 PM

    Relation between Radius and Diameter of a Circle
    Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

    Read More

  2. Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

    Apr 22, 24 01:35 PM

    Circle using a Compass
    In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

    Read More

  3. Preschool Math Activities | Colorful Preschool Worksheets | Lesson

    Apr 21, 24 10:57 AM

    Preschool Math Activities
    Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

    Read More

  4. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Apr 20, 24 05:39 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  5. What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

    Apr 20, 24 05:29 PM

    Examples of Parallel Lines
    In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

    Read More