**What is multiplication?**

The process of finding out the product between two or more numbers is called multiplication. The result thus obtained is called the **product**. Suppose, you bought 6 pens on one day and 6 pens on the next day. Total pens you bought are now 2 times 6 or 6 + 6 = 12.

This can also be written as 2 x 6 = 12

Note the symbol used for multiplication. The symbol (x) is generally used to represent multiplication. Other common symbols that are used for multiplication are the asterisk (*) and dot (.)

**What is meant by multiplication as a comparison?**

Multiplication, by comparison, means that you compare two quantities in such a manner that when one quantity is multiplied by a specific number the other quantity is produced. Let us take an example. Consider the sentence, “ Harry is twice as tall as Peter “. This means that if the age of Peter is “ p “ then, the age of Harry will be two times that of Peter, i.e. 2p.

Let us take another example.

**Example**

The length of the bench is 30 m. it is thrice as long as the length of the Stool. What is the length of the stool?

**Solution**

We have been given that, the length of the bench is 30 m. it is thrice as long as the length of the Stool. Now, let the length of the stool be “ s “. Therefore, we have,

3 s = 30

⇒ s = 10 m

Hence, the length of the stool is 30 m

**Representing Multiplication table as multiplication by comparison**

Let us now understand how to read some of the multiplication tables in the form of multiplication by comparison

**Multiplication as Comparison for Table of 2**

Multiplication Table | Multiplication as Comparison |

2 × 1 = 2 | 2 is one time as many as 2 and 2 times as many as one |

2 × 2 = 4 | 4 is two times as many as 2 |

2 × 3 = 6 | 6 is three times as many as 2 and 2 times as many as three |

2 × 4 = 8 | 8 is four times as many as 2 and 2 times as many as four |

2 × 5 = 10 | 10 is five times as many as 2 and 2 times as many as five |

2 × 6 = 12 | 12 is six times as many as 2 and 2 times as many as six |

2 × 7 = 14 | 14 is seven times as many as 2 and 2 times as many as seven |

2 × 8 = 16 | 16 is eight times as many as 2 and 2 times as many as eight |

2 × 9 = 18 | 18 is nine times as many as 2 and 2 times as many as nine |

2 × 10 = 20 | 20 is ten times as many as 2 and 2 times as many as ten |

2 x 11 = 22 | 22 is eleven times as many as 2 and 2 times as many as eleven |

2 x 12 = 24 | 24 is twelve times as many as 2 and 2 times as many as twelve |

2 x 13 = 26 | 26 is thirteen times as many as 2 and 2 times as many as thirteen |

2 x 14 = 28 | 28 is fourteen times as many as 2 and 2 times as many as fourteen |

2 x 15 = 30 | 30 is fifteen times as many as 2 and 2 times as many as fifteen |

2 x 16 = 32 | 32 is sixteen times as many as 2 and 2 times as many as sixteen |

2 x 17 = 34 | 34 is seventeen times as many as 2 and 2 times as many seventeen |

2 x 18 = 36 | 36 is eighteen times as many as 2 and 2 times as many as eighteen |

2 x 19 = 38 | 38 is nineteen times as many as 2 and 2 times as many as nineteen |

2 x 20 = 40 | 40 is twenty times as many as 2 and 2 times as many as twenty |

**Multiplication as Comparison for Table of 3**

Multiplication Table | Multiplication as Comparison |

3 × 1 = 3 | 3 is one time as many as 3 and 3 times as many as one |

3 × 2 = 6 | 6 is two times as many as 3 and 3 times as many as two |

3 × 3 = 9 | 3 is three times as many as 3 |

3 × 4 = 12 | 12 is four times as many as 3 and 3 times as many as four |

3 × 5 = 15 | 15 is five times as many as 3 and 3 times as many as five |

3 × 6 = 18 | 18 is six times as many as 3 and 3 times as many as six |

3 × 7 = 21 | 21 is seven times as many as 3 and 3 times as many as seven |

3 × 8 = 24 | 24 is eight times as many as 3 and 3 times as many as eight |

3 × 9 = 27 | 27 is nine times as many as 3 and 3 times as many as nine |

3 × 10 = 30 | 30 is ten times as many as 3 and 3 times as many as ten |

3 x 11 = 33 | 33 is eleven times as many as 3 and 3 times as many as eleven |

3 x 12 = 36 | 36 is twelve times as many as 3 and 3 times as many as twelve |

3 x 13 = 39 | 39 is thirteen times as many as 3 and 3 times as many as thirteen |

3 x 14 = 42 | 42 is fourteen times as many as 3 and 3 times as many as fourteen |

3 x 15 = 45 | 45 is fifteen times as many as 3 and 3 times as many as fifteen |

3 x 16 = 48 | 48 is sixteen times as many as 3 and 3 times as many as sixteen |

3 x 17 = 51 | 51 is seventeen times as many as 3 and 3 times as many seventeen |

3 x 18 = 54 | 54 is eighteen times as many as 3 and 3 times as many as eighteen |

3 x 19 = 57 | 57 is nineteen times as many as 3 and 3 times as many as nineteen |

3 x 20 = 60 | 60 is twenty times as many as 3 and 3 times as many as twenty |

**Multiplication as Comparison for Table of 4**

Multiplication Table | Multiplication as Comparison |

4 × 1 = 4 | 4 is one time as many as 4 and 4 times as many as one |

4 × 2 = 8 | 8 is two times as many as 4 and 4 times as many as two |

4 × 3 = 12 | 12 is three times as many as 4 and 4 times as many as three |

4 × 4 = 16 | 16 is four times as many as 4 |

4 × 5 = 20 | 20 is five times as many as 4 and 4 times as many as five |

4 × 6 = 24 | 24 is six times as many as 4 and 4 times as many as six |

4 × 7 = 28 | 28 is seven times as many as 4 and 4 times as many as seven |

4 × 8 = 32 | 32 is eight times as many as 4 and 4 times as many as eight |

4 × 9 = 36 | 36 is nine times as many as 4 and 4 times as many as nine |

4 × 10 = 40 | 40 is ten times as many as 4 and 4 times as many as ten |

4 x 11 = 44 | 44 is eleven times as many as and 4 times as many as eleven |

4 x 12 = 48 | 48 is twelve times as many as 4 and 4 times as many as twelve |

4 x 13 = 52 | 52 is thirteen times as many as 4 and 4 times as many as thirteen |

4 x 14 = 56 | 56 is fourteen times as many as 4 and 4 times as many as fourteen |

4 x 15 = 60 | 60 is fifteen times as many as 4 and 4 times as many as fifteen |

4 x 16 = 64 | 64 is sixteen times as many as 4 and 4 times as many as sixteen |

4 x 17 = 68 | 68 is seventeen times as many as 4 and 4 times as many seventeen |

4 x 18 = 72 | 72 is eighteen times as many as 4 and 4 times as many as eighteen |

4 x 19 = 76 | 76 is nineteen times as many as 4 and 4 times as many as nineteen |

4 x 20 = 80 | 80 is twenty times as many as 4 and 4 times as many as twenty |

**Multiplication as Comparison for Table of 5**

Multiplication Table | Multiplication as Comparison |

5 × 1 = 5 | 5 is one time as many as 5 and 5 times as many as one |

5 × 2 = 10 | 10 is two times as many as 5 and 5 times as many as two |

5 × 3 = 15 | 15 is three times as many as 5 and 5 times as many as three |

5 × 4 = 20 | 20 is four times as many as 5 and 5 times as many as four |

5 × 5 = 25 | 25 is five times as many as 5 |

5 × 6 = 30 | 30 is six times as many as 5 and 5 times as many as six |

5 × 7 = 35 | 35 is seven times as many as and 5 times as many as seven |

5 × 8 = 40 | 40 is eight times as many as 5 and 5 times as many as eight |

5 × 9 = 45 | 45 is nine times as many as 5 and 5 times as many as nine |

5 × 10 = 50 | 40 is ten times as many as 5 and 5 times as many as ten |

5 x 11 = 55 | 55 is eleven times as many as 5 and 5 times as many as eleven |

5 x 12 = 60 | 60 is twelve times as many as 5 and 5 times as many as twelve |

5 x 13 = 65 | 65 is thirteen times as many as 5 and 5 times as many as thirteen |

5 x 14 = 70 | 70 is fourteen times as many as 5 and 5 times as many as fourteen |

5 x 15 = 75 | 75 is fifteen times as many as 5 and 5 times as many as fifteen |

5 x 16 = 80 | 80 is sixteen times as many as 5 and 5 times as many as sixteen |

5 x 17 = 85 | 85 is seventeen times as many as 5 and 5 times as many seventeen |

5 x 18 = 90 | 90 is eighteen times as many as 5 and 5 times as many as eighteen |

5 x 19 = 95 | 95 is nineteen times as many as 5 and 5 times as many as nineteen |

5 x 20 = 100 | 100 is twenty times as many as 5 and 5 times as many as twenty |

**Multiplication as Comparison for Table of 6**

Multiplication Table | Multiplication as Comparison |

6 × 1 = 6 | 6 is one time as many as 6 and 6 times as many as one |

6 × 2 = 12 | 12 is two times as many as 6 and 6 times as many as two |

6 × 3 = 18 | 18 is three times as many as 6 and 6 times as many as three |

6 × 4 = 24 | 24 is four times as many as 6 and 6 times as many as four |

6 × 5 = 30 | 60 is five times as many as 6 and 6 times as many as five |

6 × 6 = 36 | 36 is six times as many as 6 |

6 × 7 = 42 | 42 is seven times as many as and 6 times as many as seven |

6 × 8 = 48 | 48 is eight times as many as 6 and 6 times as many as eight |

6 × 9 = 54 | 54 is nine times as many as 6 and 6 times as many as nine |

6 × 10 = 60 | 60 is ten times as many as 6 and 6 times as many as ten |

6 ×11 = 66 | 66 is eleven times as many as 6 and 6 times as many as eleven |

6 × 12 = 72 | 72 is twelve times as many as 6 and 6 times as many as twelve |

6× 13 = 78 | 78 is thirteen times as many as 6 and 6 times as many as thirteen |

6 × 14 = 84 | 84 is fourteen times as many as 6 and 6 times as many as fourteen |

6 × 15 = 90 | 90 is fifteen times as many as 6 and 6 times as many as fifteen |

6 × 16 = 96 | 96 is sixteen times as many as 6 and 6 times as many as sixteen |

6 × 17 = 102 | 102 is seventeen times as many as 6 and 6 times as many seventeen |

6× 18 = 108 | 108 is eighteen times as many as 6 and 6 times as many as eighteen |

6 × 19 = 114 | 114 is nineteen times as many as 6 and 6 times as many as nineteen |

6 × 20 = 120 | 120 is twenty times as many as 6 and 6 times as many as twenty |

**Multiplication as Comparison for Table of 7**

Multiplication Table | Multiplication as Comparison |

7 × 1 = 7 | 7 is one time as many as 7 and 7 times as many as one |

7 × 2 = 14 | 14 is two times as many as 7 and 7 times as many as two |

7 × 3 = 21 | 21 is three times as many as 7 and 7 times as many as three |

7 × 4 = 28 | 28 is four times as many as 7 and 7 times as many as four |

7 × 5 = 35 | 35 is five times as many as 7 and 7 times as many as five |

7 × 6 = 42 | 42 is six times as many as 7 and 7 times as many as six |

7 × 7 = 49 | 49 is seven times as many as 7 |

7 × 8 = 56 | 56 is eight times as many as 7 and 7 times as many as eight |

7 × 9 = 63 | 63 is nine times as many as 7 and 7 times as many as nine |

7 × 10 = 70 | 70 is ten times as many as 7 and 7 times as many as ten |

7 X 11 = 77 | 77 is eleven times as many as 7 and 7 times as many as eleven |

7 X 12 = 84 | 84 is twelve times as many as 7 and 7 times as many as twelve |

7 X 13 = 91 | 91 is thirteen times as many as 7 and 7 times as many as thirteen |

7 X 14 = 98 | 98 is fourteen times as many as 7 and 7 times as many as fourteen |

7 X 15 = 105 | 105 is fifteen times as many as 7 and 7 times as many as fifteen |

7 X 16 = 112 | 112 is sixteen times as many as 7 and 7 times as many as sixteen |

7 X 17 = 119 | 119 is seventeen times as many as 7 and 7 times as many seventeen |

7 X 18 = 126 | 126 is eighteen times as many as 7 and 7 times as many as eighteen |

7 X 19 = 133 | 133 is nineteen times as many as 7 and 7 times as many as nineteen |

7 X 20 = 140 | 140 is twenty times as many as 7 and 7 times as many as twenty |

**Advantages of learning multiplication by comparison**

Following are the advantages of learning multiplication by comparison –

- Understanding multiplication by comparing quantities allows the students to understand the concepts as they raise the level of difficulties in multiplication.
- It is easier to relate how numbers are multiplied with each other when projected as comparative quantities.

**Key Facts and Summary**

- The process of finding out the product between two or more numbers is called multiplication. The result thus obtained is called the product.
- The symbol (x) is generally used to represent multiplication. Other common symbols that are used for multiplication are the asterisk (*) and dot (.)
- Multiplication, by comparison, means that you compare two quantities in such a manner that when one quantity is multiplied by a specific number the other quantity is produced.
- Understanding multiplication by comparing quantities allows the students to understand the concepts as they raise the level of difficulties in multiplication.
- It is easier to relate how numbers are multiplied with each other when projected as comparative quantities.

## Recommended Worksheets

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