
Chapter 1  Integers
 Addition of like integers
 Addition of unlike integers
 Properties of Addition of Integers
 Additive Inverse
 Difference of two positive Integers
 Finding second integer, when one value and sum is given
 Finding integer value when the difference and other integer
 Difference of two negative Integers
 Difference of a Positive Integer from a Negative Integer
 Difference of a Negative Integer from a Positive Integer
 Multiplication of like integers
 Multiplication of Unlike integers
 Properties of Multiplication of Integers
 Multiplicative Inverse
 Product of repeating nonzero negative integers
 Division of Like Integers
 Division of unlike integers

Chapter 2  Lines and Angles

Chapter 3  Rational numbers
 Whether given number is a Rational Numbers
 Numerator and Denominator of Rational Number
 Standard form of Rational Number
 Equivalent Rational Numbers
 Equivalent Rational Number with given Numerator
 Equivalent Rational Number with given Denominator
 Finding Numerator of Equivalent Rational Numbers
 Additive Inverse
 Sum of Rational Numbers whose Denominators are equal
 Sum of Rational Number with unequal Denominators
 Subtraction of Rational Number When Denominators are Equal
 Subtraction of Rational Number with Different Denominators
 Finding number that should be added or subtracted
 Multiplication of Rational Numbers
 Reciprocal or Multiplicative Inverse of Rational Number
 Division of Rational Numbers

Chapter 4  Fractions
 Proper Fraction
 Improper Fraction
 Like or Unlike Fractions
 Comparison of Fractions
 Conversion of Improper Fraction into a Mixed Fraction
 Conversion of Mixed Fraction into an Improper Fraction
 Convert Unlike Fraction into Like Fraction
 Division of Fraction by Whole number
 Division of Fractions
 Division of Mixed Fraction by Improper or Proper fraction
 Division of Whole number by Fraction
 Equivalent fraction
 Fraction of a Year
 Fraction of an Hour
 Fraction of Kilometres
 Fraction of Metres
 Fraction of Metres
 Fraction of Rupees
 Multiplication of Fractions
 Problem based on Multiplication of Fraction
 Product of Mixed and Improper or Proper Fraction
 Product of Three Fractions
 Product of Two Fractions
 Simplest form of fraction
 Subtraction of Like Fractions
 Subtraction of Unlike Fractions
 Sum of Like Fraction
 Sum of Mixed Fraction with different Denominator
 Sum of Mixed Fraction with same Denominator
 Sum of more than two Like Fractions
 Sum of Unlike Fractions

Chapter 5  Decimals
 Like Decimals
 Finding Unlike Decimals
 Place values
 Converting mixed fraction into Decimal
 Converting Decimals into a fractions
 Decimal in Descending Order
 Express Given kilometres and metres into kilometres
 Express Given kilograms and grams into kilograms
 Express Given Rupees and Paisa into Rupees
 Decimal word problem of Addition
 Decimal word problem of Subtraction
 Multiplication of Decimal by 10, 100, 1000
 Multiplication of Decimal by whole number
 Multiplication of Two Decimal
 Multiplication of Three Decimals
 Problem based on Multiplication of Decimal
 Division of Decimal by 10, 100, 100

Chapter 6  Properties of Triangles
 Finding Angles of a Triangle, when Ratio of Angle is Given
 Angle sum property of a triangle
 Angle Sum property on Isosceles Triangle
 Find whether given Triangle is Acute, Obtuse, Right Triangle
 Equilateral Triangle, Isosceles Triangle & Scalene Triangle
 Finding if a Triangle of given length exists
 Finding Sides of Right Triangle

Chapter 7  Percentage
 Converting a Fraction into Percentage
 Converting a Percentage into a Fraction
 Converting Decimal into Percentage
 Expressing a given Percentage as a Ratio
 To convert Percentage into decimal fraction
 Finding Percent of a Given Whole number
 To convert a given ratio into Percentage
 Find sum of money when a Percentage of such sum is given
 Finding actual quantity ( in metres ) from Percentage value
 Finding actual quantity ( in Litres ) from Percentage value
 Finding actual quantity ( in Kg ) from Percentage value
 Finding actual quantity ( in Rupees ) from Percentage value
 Find what percentage of a given quantity is another term (m)
 Find what percentage of a given quantity is another term(kg)
 Find what percentage of given quantity is another term(lit)
 Finding a number when its decreased percentage is given
 Finding a number when its increased percentage is given

Chapter 8  Simple interest
 Find Simple Interest ( SI ) when time is given in years
 Find Simple Interest ( SI ) when time is given in months
 Find Simple Interest ( SI ) when time is given in days
 Find the Amount when time is given in years
 Find the Amount when time is given in months
 Find Amount when time is given in days
 Find rate of interest when principal, amount & time is given
 Find the Rate of interest when Principal, SI & Time is given
 Find Time when Principal, Amount & Rate of interest is given
 Find Time when Principal, SI & Rate of interest is Given
 Problem on Simple Interest (SI)

Chapter 9  Profit and loss
 Find the Gain when Cost Price and Selling Price is Given
 Find the Loss when Cost Price and Selling Price is Given
 Find the Gain % when Cost Price and Selling Price is Given
 Finding Loss % when Cost Price and Selling Price is given
 Find Gain and Gain %
 Find Loss and Loss%
 Find Cost Price when Selling Price & Loss Percent is given
 Find Cost Price when Selling Price & Gain Percent is given
 Find Selling Price when Cost Price & Loss Percent is given
 Find Selling Price when Cost Price & Gain Percent is given

Chapter 10  Unitary method

Chapter 11  Ratio and proportion
 Convert Ratio into its simplest form
 Ratio of two quantities, by converting them into same units
 Equivalent ratios
 Find the numbers when their ratio and sum are given
 Divide sum of money between two persons when ratio are given
 Divide sum of money among three persons when ratio are given
 Comparison of ratios
 Find the missing term in a pair of Equivalent ratios
 Find the missing terms in given pair of Ratios
 Are the given ratio in proportion
 Are the given number are in proportion
 Find the value of y when four numbers are in proportion – 1
 Find the value of y when four numbers are in proportion – 2
 Find the value of y when four numbers are in proportion – 3
 Finding ratio of given data
 Finding Ratio A : B : C
 Finding Ratio A : B : C if Ratio A : B and B : C given
 Converting Ratio into another Ratio
 Solve equation for given ratio
 Finding ratio of present ages
 Finding ratio of ages of persons after some years.
 Finding ratio of ages of persons some year ago.
 Third proportional value
 Mean proportional value
 Continued proportion

Chapter 12  Exponents
 Expressing Negative fraction as a Rational Number
 Expressing Negative fraction in an Exponential Form
 Expressing Rational Number in an Exponential Form – Power 3
 Expressing Rational Number in an Exponential Form – Power 4
 Expressing Rational Number in an Exponential Form – Power 5
 Finding Cube of a Negative Fraction
 Finding Cube of a positive Fraction
 Finding exponent of order 5 of a Negative Fraction
 Finding exponent of order 5 of a Positive Fraction
 Finding square of a Negative Fraction
 Finding square of a positive Fraction
 Reciprocal of Rational Number in an Exponential Form Power2
 Reciprocal of Rational Number in an Exponential Form Power3
 Reciprocal of Rational Number in an Exponential Form Power 4
 Reciprocal of Rational Number in an Exponential Form Power 5
 Simplification as a Rational Number with different exponents
 Simplification as a Rational Number
 Simplification of Negative fraction as a Rational Number
 Expressing Fraction as a Rational Number
 Expressing Positive fraction in an Exponential Form

Chapter 13  Probability

Chapter 14  Mensuration
 Area of an Equilateral Triangle
 Area of Parallelogram
 Area of rectangle
 Area of Right Triangle
 Area of Right Triangle
 Area of square
 Diameter of a circle when circumference is given
 Finding Area of Circle if its Diameter is Given
 Finding Area of Circle If its Radius is Given
 Finding Area of Circle When its Circumference is Given
 Finding Area of Rectangle When Breadth & Diagonal is Given
 Finding Area of Rectangle When Length & Diagonal is Given
 Finding Area of Rhombus If Length of Diagonals is Given
 Finding Area of Square When Length of its Diagonal is given
 Finding Area of Triangle When Its Height and Base are Given
 Finding Circumference of the circle when diameter is given
 Finding Circumference of the circle when radius is given
 Finding Height of Triangle, when its Base and Area is Given
 Finding Length of Diagonal of Square When its Area is Given
 Finding length of Rhombus’ Diagonal
 Finding perimeter of Rectangle
 Finding Ratio of Area When Ratio of their Radii is Given
 Finding Ratio of Circumference – Ratio of Radii given
 Finding the Base of a Triangle when Area & Height is Given
 Problem based on circumference of a circle
 Radius of a circle
Subtraction of Rational Number When Denominators are Equal
Rational numbers – Subtraction of Rational Number When Denominators are Equal
Question : –
Subtract:
–
Explanation : –
Difference of Rational Numbers when Denominators are equal =
=
=
So, the difference of and is
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