4th Class Mathematics Multiplication and Division Operation on Numbers Multiplication Division

                                    Operation on Numbers Multiplication and Division

Introduction

In this chapter we will study two important arithmetic operations "multiplication and division". Multiplication is repeated addition of a specific quantity, whereas division is a distribution of a quantity into some equal parts. Let us study them.

Multiplication

When a quantity is added to itself for a number of times, we use operation of multiplication to find the resulting quantity.

• Example

Find correct option for

\[7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg\]\[+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg.\]

(a) \[7\times 7.5\,kg\]                   (b) \[9\times 7.5\,kg\]

(c) \[11\times 7.5\,kg\]                 (d) \[13\times 7.5\,kg\]

(e) None of these

Answer (a)

Explanation:

\[7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+7.5\text{ }kg+\]

\[7.5\text{ }kg+7.5\text{ }kg=~\]\[7\times 7.5\text{ }kg\]

• Example

There are 7546 books and each of the books contains 245 pages. Find the total of pages.

Solution:

Total number of pages = \[7546\times 245\]

= 1848770

Terms Related to Multiplication

(i) Multiplicand: In the multiplication, the number which is multiplied is known as multiplicand.

(ii) Multiplier: The number by which the multiplicand is multiplied is known as

(iii) Product: The answer or the result of multiplication is known as product.

Look at the example given below:

Multiplication of Two Natural Number

Place the multiplicands and multipliers of multiplicands with the first number multiplication by second number of the line in column, leaving the first place the products, the result is your answer

Look at the example below:

Example

Find the product of 24 and 15

\[24\times 15=360\]

 Solution:

Word Problems Based on Multiplication

• Example

An aeroplane is flying with the speed 1072 km/h. How much distance will it cover in 720 minutes?

Solution:

 Distance covered by the aeroplane      

Note:

The product of two natural numbers is always a natural number.

Division

Division is the distribution of a quantity into some equal parts in such a way that each part contains equal amount.

• Example

Distribute 433035 kg wheat into 45 equal parts. Find the amount of wheat each part contains.

Solution:

Amount of wheat contained in each part \[=\frac{433035}{45}kg=9623\,kg\]

• Example

If 264 apples are distributed among 24 peoples, find the number of apples that everyone will get.

Solution:

Number of apples each people will get \[=\frac{264}{24}=11\]

Terms Related to Division

Dividend: The quantity that is to be divided is called dividend.

Divisor: Number of parts in which the quantity to be divided is called Divisor.

Quotient: The amount that each group gets is termed as Quotient.

Remainder: The extra amount which is left after equally distribution is called remainder.

Relation between the terms of division.

\[Dividend=Divisor\times Quotient+\operatorname{Re}mainder\]

• Example

Divide and verify the relation.

Solution: 

\[Dividend=Divisor\times Quotient+\operatorname{Re}mainder\]

Dividend = 213157, Divisor =25, Quotient = 8526, Remainder =7                

Thus\[213157=25\times 8526+7\]

Or\[213157=213150+7\]

Or\[213157=213157.\]

Word Problem Based on Division

• Example

A train covers 7308 km in 58 hours. Find the distance covered by the train in 4 hours.

Solution:

Distance covered by the train in 1 hour \[=\frac{7308}{58}km\]

Distance covered by the train in 4 hours\[=126km\times 4=504km\]