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TRANSCRIPT
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