Multiplication of Whole Numbers | Whole Numbers|Multiplication|Numbers

Multiplication of whole numbers is the sort way to do repeated addition.

Multiply 2345081 and 4 by expansion method.

Solution:

(2000000 + 300000 + 40000 + 5000 + 80 + 1) × 4

= (2000000 × 4) + (300000 × 4) + (40000 × 4) + (5000 × 4) + (80
× 4) + (1 × 4)

= 8000000 + 1200000 + 160000 + 20000 + 320 + 4

= 9380324

The number by which any number is multiplied is known as the
multiplicand. The result of the multiplication is known as the product

Let us recall multiplication of a number by two or three digit number. Now we will learn multiplication of large numbers.

Note: Multiplication can also be referred as product.

Multiplication of 4-Digit by 3-Digit Numbers:

1. Multiply 6285 by 289.

When we multiply 6285 by 289 we know, 6285 is the multiplicand and 289 is the multiplier. First with the multiplicand i.e. 6285 we will multiply by 9 and we get 56565. Then we will multiply 6285 by 8 and we get 50280 and atlast when we will multiply 6285 by 2 and we get 125700.

Therefore, after adding we get 1816365.

2. Multiply 1432 by 235.

Solution:

                     1 4 3 2

                  ×   2 3 5

                    7 1 6 0        ← 1432 × 5       Step I: Multiplication with ones

                 4 2 9 6 0        ← 1432 × 30     Step I: Multiplication with tens

          +  2 8 6 4 0 0        ← 1432 × 200   Step I: Multiplication with hundreds.

              3 3 6 5 2 0    

Therefore, 1432 × 235 = 3,36,520.

3. Multiply 73162453 by 2435.

In multiply 73162453 by 2435 we
know, 73162453 is the multiplicand and 2435 is the multiplier.

First
with the multiplicand i.e. 73162453 we will multiply by 5 and we get
365812265. Then we will multiply 73162453 by 3 and we get 2194873590,
again when we will multiply 73162453 by 4 and we get 29264981200 and
atlast when we will multiply 73162453 by 2 and we get 146324906000.

Therefore, after adding we get 178150573055.

Examples on multiplication
of large numbers:

We multiply large numbers as usual.

Let us consider some more examples.

4. Multiply 10201 by 132

Solution:

We first arrange the numbers one below the other in columns.

Hence 10201 × 132 = 1346532

5. Multiply 98357 by 2904

Solution:

We first arrange the numbers one below the other in columns.

Hence 98357 × 2904 = 285628728

Multiplication of 6-digit by 1-digit number (Indian Numbering System)

6. Multiply 2,56,883 by 8.

Solution:

             2  5  6  8  8  3

                            ×  8 

         2  0  5  5  0  6  4 

Therefore, 2,56,883 × 8 = 20,55,064.

Multiplication of 6-digit by 1-digit number (International Numbering System)

7. Multiply 340,386 by 9.

Solution:

             3  4  0  3  8  6

                            ×  9 

         3  0  6  3  4  7  4 

Therefore, 340,386 × 9 = 3,063,474.

Multiplication of 7-digit by 2-digit number (Indian Numbering System)

8. Multiply 41,32,431 by 11.

Solution:

             4  1  3  2  4  3  1

                            ×  1  1 

         4  5  4  5  6  7  4   1 

Therefore, 41,32,431 × 11 = 4,54,56,741

Multiplication of 7-Digit by 1-Digit Number (International Numbering System)

9. Multiply 2,218,421 by 7.

Solution:

             2  2  1  8  4  2  1

                               ×  7 

        1  5  5  2  8  9  4   7 

Therefore, 2,218,421 × 7 = 15,528,947.

Multiplication of 8-Digit by 2-Digit Number (Indian Numbering System)

10. Multiply 4,32,21,531 by 24.

Solution:

             4  3  2  2  1  5  3  1

                                ×  2  4 

         1  7  2  8  8  6  1   2  4 

         8  6  4  4  3  0  6   2     

     1  0  3  7  3  1  6   7  4  4  

Therefore, 4,32,21,531 × 24 = 1,03,73,16,744.

Multiplication of 8-Digit by 2-Digit Number (International Numbering System)

11. Multiply 30,438,721 by 42.

Solution:

               3  0  4  3  8  7  2  1

                                  ×  4  2 

               6  0  8  7  7  4  4   2 

       1  2  1  7  5  4  8   8  4      

       1  2  7  8  4  2   6  2  8  2  

Therefore, 30,438,721 × 42 = 1,278,426,282.

Multiplication of 6-Digit by 3-Digit Number (Indian Numbering System)

12. Multiply 2,92,138 by 321.

Solution:

             2  9  2  1  3  8

                    ×  8  2  1

             2  9  2  1  3  8 

         5  8  4  2  7  6 

     8  7  6  4  1  4          

     9  3  7  7  6  2  9  8  

Therefore, 2,92,138 × 321 = 9,37,76,298.

Multiplication of 6-Digit by 3-Digit Number (International Numbering System)

13. Multiply 475,226 by 212.

Solution:

               4  7  5  2  2  6

                      ×  2  1  2

               9  5  0  4  5  2 

           4  7  5  2  2  6 

       9  5  0  4  5  2          

   1  0  0  7  4  7  9  1  2   

Therefore, 475,226 × 212 = 100,747,912.

Word Problems on Multiplication of Whole Numbers:

1. A company manufactures 5580 cartoons of chocolates in a month. A cartoon contains 1200 chocolates. How many chocolates will the company manufacture in 12 months?.

Solution:

Number of cartoons manufacture in a month = 5580

Number of chocolates a cartoon contains = 1200

So, chocolates manufacture in one month = 5580 × 1200

                                                             = 6696000 chocolates

Chocolates manufacture in twelve months = 6696000 × 12

                                                             = 8,03,52,000 chocolates

Worksheet on Multiplication of Whole Numbers:

Questions and Answers on Multiplication of Whole Numbers:

I. Multiply the given numbers by expansion method.

(i) 669023 × 7

(ii) 6652309 × 6

Answers:

(i) 4683161

(ii) 39913854

II. Multiply the given numbers by column method.

(i) 27613 × 26

(ii) 66924 × 35

(iii) 615028 × 43

(iv) 781145 × 57

(v) 748250 × 69

(vi) 8417129 × 81

Answers:

(i) 717938

(ii) 2342340

(iii) 26446204

(iv) 44525265

(v) 51629250

(vi) 681787449

III. Multiply the following:

(i) 39176 × 264

(ii) 86542 × 5406

(iii) 789331 × 318

(iv) 96203 × 6815

(v) 845017 × 497

(vi) 55159 × 2000

Answers:

(i) 10342464

(ii) 467846052

(iii) 251007258

(iv) 655623445

(v) 419973449

(vi) 110318000

● Operations On Whole Numbers

5th Grade Math problems

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