Sub. :- Mathematics Operations on numbers: Multiplication& division Std. :- 5 th Chapter no. 3.

Sub. :- Mathematics

Operations on numbers: Multiplication& division

Std. :- 5th

Chapter no. 3

To multiply numbers having upto five digits by a three –digit number.

Multiplication

Ex. (1) 879 x 248

8 7 9x 2 4 87 0 3 2 On multiplying by 8 units

+ 3 5 1 6 0 On multiplying by 4 tens+ 1 7 5 8 0 0 On multiplying by 2 hundreds

1 12 1 7 9 9 2

In the multiplication 879x248 = 2,17,992; 879 is the multiplicand, 248 is the multiplier

and 2,17,992 is the product.

8 7 9On multiplying by 8 units x 8 U

7 0 3 2 U

8 7 9On multiplying by 4 tens x 4 T

3 5 1 6 TThat is , 3 5 1 6 0

8 7 9On multiplying by 2 hundreds x 2 H

1 7 5 8 HThat is , 1 7 5 8 0 0

7 0 3 2+ 3 5 1 6 0+ 1 7 5 8 0 0

1 12 1 7 9 9 2

In the multiplication 879x248 = 2,17,992; 879 is the multiplicand, 248 is the multiplier

and 2,17,992 is the product.

Ex. (2) 5327 X 360

5 3 2 7x 3 6 0

0 0 0 0 On multiplying by 0 units+ 3 1 9 6 2 0 On multiplying by 6 tens+ 1 5 9 8 1 0 0 On multiplying by 3 hundreds

1 9 1 7 7 2 0

Ex. (3) 23,457 X 408

2 3 4 5 7x 4 0 81 8 7 6 5 6

+ 0 0 0 0 0 0+ 9 3 8 2 8 0 0

9 5 7 0 4 5 6

Ex. (4) 70,006 X 388

7 0 0 0 6  x     3 8 8

5 6 0 0 4 8+ 5 6 0 0 4 8 0+ 2 1 0 0 1 8 0 0

2 7 1 6 2 3 2 8

Learn to remember the carried over number without noting it down.

To divide five digit numbers by a two digit number.

Division

We know that to divide is to make a given number of equal parts of a certain number. To revise the method of division, study the example

Ex. (1) 170

TTh Th H T U7 8 6 8 4

- 07 8

0 4TTh Th H T U7 8 6 8 4

- 07 8

- 6 81 0 6

0 4 6 2 8TTh Th H T U7 8 6 8 4

- 07 8

- 6 81 0 6

- 1 0 20 0 4 8

- 3 41 4 4

- 1 3 60 0 8

17

17

17

78,684 ÷ 7TTh cannot be divided into 17 equal parts. So, the quotient is zero . Write ‘0’ on top of 7. 17x0=0. Subtract ‘0’ from 7. Now 7 TTh and 8 thousand together make 78 thousand.

Let us say the 17 times table.17x1=17, 17x2=34 , 17x3=51 , 17x4=68 , 17x5=85, 17x6=102, 17x7=119 85>78 and 68<78. Hence the quotient will be 4.

When 68 is subtracted from 78, the remainder is 10. Now , these 10 thousand make 100H. 100H and 6H together is 106H. Let us divide it by 17. 17x6=102, 17x=119. 119>106, 102<106 Therefore quotient is 6. the remainder is 4

Now these 4H make 40tens. 40 tens and 8 tens together is 48 tens. 17x2=34, So quotient is 2. the remainder is 14

The remainder is 14T. These 14T make 140U. 140U and 4 unit together is 144U. 17x8=136, Hence 8 id the quotient and the remainder is also 8.

Quotient = 4,628 Remainder = 8

Ex. (2) 350 2 1 0 4

35 7 3 6 4 2- 0

7 3- 7 0

3 6- 3 5

1 4- 0

1 4 2- 1 4 0

0 0 2

73,642 ÷ To do this division let us prepare the 35 times table. The example has been solved using 35 times table prepared alongside. Study it carefully.

35 x 1 = 3535 x 2 = 7035 x 3 = 10535 x 4 = 14035 x 5 = 17535 x 6 = 21035 x 7 = 24535 x 8 = 28035 x 9 = 315

Quotient = 2,104Remainder = 2

Ex. (2) 460 1 2 4 2

46 5 7 1 5 4- 0

5 7- 4 6

1 1 1- 9 2

0 1 9 5- 1 8 4

1 1 4- 0 9 2

0 2 2

57,154 ÷ Let us write the 46 times table

Quotient = 2,104Remainder = 2

46 x 1 = 4646 x 2 = 9246 x 3 = 13846 x 4 = 18446 x 5 = 23046 x 6 = 27646 x 7 = 32246 x 8 = 36846 x 9 = 414

Observe each of the following groups of numbers written in a series.

Series of numbers

(1) 1, 4, 7, 10, 13, 16, …..(2) 3, 6, 12, 24, 48, 96, ….(3) 2, 5, 10, 17, 26, 37, …..