## Multiplication and Division

Category : 3rd Class

Multiplication and Division

Multiplication

Multiplication means repeated addition. The symbol for the notation of multiplication is ' '.

Multiplication of Three Digit Numbers with One Digit Number

Following are the steps for multiplication of three digit number with one digit number

For example, 236 4

Step 1: Multiplication always start with ones.

Step 2: Multiply ones 6 4 = 24. 2 tens and 4 ones. Write 4 under ones column and carry 2 tens to the tens column.

Step 3: Multiply the tens 4 3 = 12 + 2 (carry over) - 14 tens = 1    hundreds

4 tens. Write 4 under tens column and carry 1 hundred to the hundreds column.

Step 4: Multiply the hundreds 4 2 = 8 + 1 (carry over) = 9 hundreds. Write 9 under- hundreds column. Multiplication of Four Digit Numbers with Two Digit Numbers

Following are the steps for multiplication of four digit numbers with two digit numbers:

For example, 4526 56

Step 1: Arrange the multiplicand and multiplier as shown below.

Step 2: Multiply 4526 by 6 ones of 56 = 4526 6 = 27156.

Step 3: Multiply 4526 by 5 tens of 56 = 4526 50 = 226300.

Step 4: Add 27156 + 226300 to obtain the resulting product = 253456. •           Example

If an amount of  56 is contributed by each of the 8 members of a group, find the total amount collected?

(a)  400                                                           (b)  448

(c)  200                                                            (d) All the above

(e) None of these

Ans.     (b)

Explanation: Total amount = •           Example

A basket contains 21 dozens of eggs. How much eggs 40 such baskets will contain?

(a) 10867                                                           (b) 10080

(c) 14943                                                           (d) All the above

(e) None of these

Ans.     (b)

Explanation: One dozen contains 12 eggs.

Therefore, total eggs = Properties of Multiplication

Commutative or Order Property of Multiplication

Numbers can be multiplied in either order. In other words resulting product does not change on changing the order of the numbers.

Associative or Grouping Property of Multiplication

The product of three numbers remains same even if the group of the numbers is changed.

Multiplicative Property of Zero (Or Null property)

The product of a number and zero is always zero. Therefore, .

Hence, product of every terms and number with zero is always zero.

Multiplicative Property of 1 or Multiplicative Identity Property

The product of a number with 1 is the number itself Therefore, .

Distributive Property of Multiplication on Addition

In the following multiplications: and (8 54) + (8 54) + (8 17) = 432 + 136 = 568. The results of the multiplications are same on distributing 8 to both the numbers 54 and 171

•          Example

Which one of the following is correct about the order property of multiplication?

(a) M N = N M                                                       (b) M A = N B

(c) M B ? N A                                                        (d) Both A and B

(e) None of these

Ans.     (a)

Explanation: As per the order property of multiplication, numbers can be multiplied in either order Therefore, option (a) is correct,

•          Example

Fill in the blank with the number from the options given below: 560 + 40 = 10 __________.

(a) 70                                                                (b) 60

(c) 80                                                                (d) 90

(e) None of these

Ans.     (b)

Explanation: 560 + 40 = 600 = 60 10 = 10 60. Therefore, comparing 10 60 = 10 _______, 60 is the right answer.

Division

Division is the basic arithmetic operation and this is the inverse process of multiplication. The symbol for the notation of division is .

Properties of Division

(i) The division should be continued till the remainder is either W or less than the divisor d.

(ii) A number which is divided by 1 gives the number itself.

(iii) A number which is divided by itself gives 1 as the quotient.

(iv) Zero divided by any number gives 0 as the quotient,

•           Example

Division of A by 1 is A itself. If division of A by 1 is then 1 is:

(a) Divisor                                                          (b) Remainder

(c) Quotient                                                        (d) Dividend

(e) None of these

Ans.     (a)

Explanation: The number dividing a certain number is called divisor

•           Example

Division of A by 0 is:

(a) 0                                                                 (b) Cannot be defined

(c) A                                                                 (d) All the above

(e) None of these

Ans.     (b)

Explanation: Division of any number by 0 is not defined.

Long Division

Following are the steps used in long division.

For example: 4567 7:

Step 1: Arrange the numbers as shown below. Step 2: Consider the minimum dividend from 4567 as 45 because 4 is smaller than divisor 7.

Step 3: Recite the table of 7 till equal to 45 or nearest to 45 and write required number of times of 7 as quotient and their      product 42 below 45. Step 4: Subtract them. Step 5: Write the next number from dividend after the remainder Step 6: Recite the table of 7 till equal to 36 or nearest to 36 and write required number of times of 7 as quotient and their      product given below 36. Step 7: Subtract them. Step 8: Write the next number from dividend after the remainder Step 9: Recite the table of 7 till equal to 17 or nearest to 17 and write required number of times of 7 as quotient and their      product below 17. Step 10: Subtract them. Step 11: Quotient = 652, Remainder = 3 and Divisor = 7.

•           Example

How many group will be formed from the given number of pencils if every group contains 5 pencils? (a) 4                                                                  (b) 5

(c) 7                                                                  (d) 3

(e) None of these

Ans.     (a)

Explanation: Total number of pencils = 20 number of groups of 5 pencils = •            Example

Divide 5636 by 4.

(a) 1407                                                            (b) 1408

(c) 1409                                                             (d) 1406

(e) None of these

Ans.     (c)

Explanation: If be divide the given number by 4, we get 1409 as quotient.

Therefore, (c) is the correct answer.

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