3rd Class Mathematics Multiplication Multiplication and Its Properties

        Introduction

Multiplication means repeated addition. The symbol for the notation of multiplication is x. Sometime a dot mark (.) is used for the notation of multiplication. If there is no sign between two or more numbers then the product sign is considered. Two variables x and y when written as there is a product sign between x and y. In this chapter we will learn about the multiplication or product of numbers.

        Multiplication and its Properties

The multiplication of 3 and 4 is the addition of 4 times 3 = 3 + 3 + 3 + 3 = 12 or it is the addition of 3 times of 4 = 4 + 4 + 4 = 12. The resulting numbers of both the addition are same. In the short form, the multiplication of 3 and 4 is written as 3 x 4 or 4 x 3. In 4 x 3, 4 and 3 are multiplicand and multiplier respectively and their multiplication 12 is called product. Therefore, in a multiplication the number which is multiplied is known as multiplicand, the number by which it is multiplied is known as multiplier and the answer or the result of multiplication is known as product. The multiplication of a number with zero is always zero. e.g. 4252 x 0 = 0 and the product of a number by 1 is the number itself, e.g. 6240 x 1 = 6240.

            Multiplication of a Number by 10, 100 and 1000

The product of 7456 by 10 is obtained by placing one zero after the multiplicand or 7456 = 7456 x 10 = 74560. The product of a number by 100 is obtained by simply placing 2 zeroes after the number. Therefore, the product of the number 8765 by 100 = 8765 x 100 = 876500. The product of a number by 1000 is obtained by simply placing 3 zeroes after the number. Therefore, the product of the number 56438 by 1000 = 56438 x 1000 = 56438000. So, in order to multiply the number by 1,000, 2,000, 5,000, etc. The given number of thousands (i.e. by 1, 2, 5, etc.) should be multiplied to the number and then put three zeroes at the end from left, i.e.and put 3 zeroes = 35000.

A train travels a distance of 90 kilometres in 1 hour. The distance covered by the train in 10 hours is:

 (a) 900km

 (b) 1000km

 (c) 1090km

 (d) All of these

 (e) None of these

Answer (a)

 Explanation 90 x 10 = 900 km (Multiplying 90 and I and putting the number of zeroes that multiplier containing).

            Multiplication of Three Digit Numbers with One Digit Number

The following steps are used for the multiplication of three digit numbers (236) with one digit number (4):

Step 1: Multiplication always starts with ones.

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

Step 3: Multiply the tens 4 x 3 = 12 + 2 (carry over) = 14 tens = 1 hundred + 4 tens. Write 4 under tens column and carry 1 hundred to the hundreds column.

Step 4: Multiply the hundreds 4x2=8+1 (carry over) = 9 hundreds. Write 9 under hundreds column.

2     3      6

            4

9     4      4      

The price of an article is Rs 576. What is total price of 16 such articles?

 (a) Rs 9200

 (b) Rs 9216

 (c) Rs 9250

 (d) Rs 9876

 (e) None of these

Answer (b)

Explanation

             Multiplication of Four Digit Numbers with Two Digit Numbers

The following steps are used for the multiplication of 4526 and 56:

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

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

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

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

A big container contains 7865 small containers. Each small container has 19 pieces of folded cots. The total number of folded cots in the big container is?

(a) 108675

(b) 140035

(c) 149435

(d) All of these

(e) None of these

Answer (c)

Explanation