Amarchand SinghviInternational School

Subject : Mathematics

Class : VII

Chapter : 4 – Rational Numbers

Topic : Arithmetic Operations

Teacher : Mr. Priyank Bhambhani

E-Learning Programme

Topics Covered

• Introduction

• Basic Facts

• Types of Rational Number

• Standard Form

• Comparison of Rational Numbers

• Addition, Subtraction ,Multiplication of Rational Numbers

• Reciprocal

• Division of Rational Numbers

• Word Problems

Introduction

• The number systems of natural numbers, wholenumbers, fractions and integers are known to us.These all number systems does not include thenegative divisions like -7 ÷ 3. So there was a needto create a new number system which includes allthe number systems mentioned above along withnegative divisions and this number system wascalled as rational numbers.

• A rational number is a number that is named in theform where a and b are integers and b is neverequals to 0.

For example : 36

1,

93

22,

17

11,

3

2

−−

−−

b

a

Types of rational numbers

• There are two types of rational numbers.

• Positive rational numbers

A rational number is said to be positive if itsnumerator and denominator are having same sign(both are positive or both are negative).

For example :

• Negative rational numbers

A rational number is said to be negative if itsnumerator and denominator are having differentsign (either of them is positive and other one isnegative).

For example :

23

1,

17

22,

39

11,

3

2

−

−

−

−

2

3,

70

105,

10

21,

7

5

−−

−−

Basic Facts• Every natural number is a

rational number but everyrational number is not a naturalnumber.

• Zero is a rational number.

• Every integer is a rationalnumber but every rationalnumber is not an integer.

• Every fraction is a rationalnumber but every rationalnumber is not an fraction.

• Every negative integer is anegative rational number.

• Zero is neither positive rationalnumber nor negative rationalnumber.

Standard form• A rational number is said to be in standard form if its

denominator is positive and it is in the lowest terms.For example : Let us find the standard form of

• Now as denominator is not positive. So first makedenominator positive by shifting negative sign fromdenominator to numerator always.

• Now do the cutting until as much as cutting is possible.And after that no more cutting should be possible.

• So the standard of

16

12

16

12 −=

−

4

3

8

6

16

12 −=

−=

−

16

12

−

4

3

16

12 −

−is

Absolute Value• Absolute value of a rational number is the same

rational number itself but with no negative sign.

• The symbol used to denote the absolute value is, twovertical lines ‘| |’ and it is called as ‘mod’.

• For example : Let us find the absolute value of

• For example : Let us find the absolute value of

• For example : Let us find the absolute value of

3

2−16

12

16

12=

−

16

12

−

3

2

3

2=

−

39

21

39

21

39

21=

Addition and Subtraction of Rational Numbers

• Rule 1 – To add or subtract rational numbers with samedenominators we add or subtract the numerators, thedenominator remains the same.

Rule 2 – To add or subtract rational numbers with different denominators we shouldconvert them to equivalent rational numbers and then add or subtract the numeratorskeeping denominator same.

Multiplication of Rational Numbers

• Product of rational numbers = Product of the numeratorsProduct of the denominators

For example :

Reciprocal of a Rational Number• When the product of two rational numbers is 1 then

each of the rational numbers is called the reciprocalof the other. Reciprocal is also called asmultiplicative inverse.

• For example :

• Zero has no reciprocal.

• 1 and -1 are the only rational numbers which aretheir own reciprocals.

• Reciprocal of the reciprocal of a rational number isthe number itself.

3

5

5

3 −=

−ofreciprocal

11

1

15

15

3)5(

)5(3

3

5

5

3==

−

−=

−

−=

−

−because

Division of Rational Numbers

• While dividing two rational numbers we have tomultiply the dividend with the reciprocal of the divisor.

For example :2

7

5

13

−

35

26

75

213

7

2

5

13

2

7

5

13 −=

−=

−=

−= ofreciprocal

Note: This presentation is a part of the E-Learning Program of Amarchand

Singhvi International School and is created only for educational purpose.

Compilation & presentation : Mr. Priyank Bhambhani

Web support & management : Mr. Deepak Chellani

Technical support : Mr. Shivam Gundecha

E-learning Program Co-ordination:

Mr. Prashant Chaturvedi

Produced by

Mr. Mridul Varma (Principal)

Amarchand Singhvi International School

Parekh Parisar, Ward 7A, Gandhidham – Kutch

Gujarat 370201 India