ncert solutions for class 7 maths
class 7 maths
Foundation of any subject is important specifically when you are taking about maths . maths is important subject for your academic journey and class 7 maths build your interest as well we as solid foundations in the subject in this class you start learning the algebra and its applications . so always take class 7 maths studies seriously . you must be wondering what is the best approach to study class 7 maths ? how to score good marks in class 7 maths ? so to answering to your questions lets discuss the right approach of studying class 7 maths .
Right approach to study class 7 maths
About class 7 Books: Selection of right books will help you to have better understanding of the concepts so always make NCERT maths book for class 7 your primary book , follow the sequence of chapters given in NCERT book don’t skip any chapters . after doing NCRET take a reference book or follow entrancei notes which are prepared such a way that it will build your solid foundation in class 7 maths
About class 7 maths class: Always attend the class in school or in tuitions never skip any class , if you have any work or family function or you are sick plan the missing topic during the holidays and be reedy your topics before the next class. In class listen what teacher wants to explain and make all important points notes in your note book . ask your questions don’t hesitate while asking silly questions in class 7 maths .
Brief descriptions about Important Chapters covered in class 7 maths
1. Class 7 maths chapter- NUMBERS
Natural Numbers: The counting numbers are called Natural Numbers.
Thus, N = {1, 2, 3, 4, 5,....} is the set of all natural numbers.
Whole Numbers: Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, …
Thus, W = {0, 1, 2, 3, 4, 5.....} is the set of all Whole Numbers.
Integers: Integers are like whole numbers, but they also include negative numbers ... but still no fractions allowed!
So, integers can be negative {-1, -2,-3, -4, -5, … }or positive {1, 2, 3, 4, 5, … }, or zer{0}
We can put that all together like this:
I or Z = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
Rational Numbers: A rational number is a number that can be written as a ratio (p/q form). That means it can be written as a fraction, in which both the numerator (p) and the denominator (q) are integers and q not zero.
The number 8 is a rational number because it can be written as the fraction 8/1.
Likewise, 3/4 is a rational number because it can be written as a fraction.
Even a big, clunky fraction like 7,324,908/56,003,492 is rational, simply because it can be written as a fraction.
Equivalent rational numbers: Numbers that have the same value but are represented differently.
2. Class 7 maths chapter- DIVISIBILITY TESTS, SQUARES, CUBES,SQUARE AND CUBE ROOTS
OVISIBILITY
DIVISIBILITY TEST:
Test of Divisibility by 2 : A number is divisible by 2, if its units digit is any of the digits 0, 2, 4, 6 and 8.
Example: Each of the numbers 24, 36, 78, 192, 310, 214166 is divisible by 2.
Prime Factors: A factor of a given number is called a prime factor if this factor is a prime number.
Example: The factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42. Out of these 2, 3 and 7 are prime numbers. Therefore, 2, 3 and 7 are the prime factors of 42.
Common Factors: A number which divides each one of the given numbers exactly, is called a common factor of each of the given numbers.
Example: 4 divide each one of 212 and 356 exactly. Therefore, 4 is a common factor of 212 and 356.
H.C.F. (HIGHEST COMMON FACTOR) OR G.C.D. (GREATEST COMMON DIVISOR) :
H.C.F. or G.C.D. of two or more numbers is the greatest number that divides each one of them exactly.
3. Class 7 maths chapter- ALGEBRAIC EXPRESSIONS AND IDENTITIES
In the previous class, we have learnt about algebraic expressions and their addition and subtraction. In this chapter we shall study multiplication and division of algebraic expressions in the form of monomials and binomials etc.
Constants: A symbol having a fixed numerical value is called a constant.
Variables or Literals: A symbol which takes on various numerical values is known as a variable or a literal.
We know that the perimeter of a square of side a is given by the formula, P = 4a.
Here 4 is a constant, while a and P are variables.
We may give any value to a and get the corresponding value of P.
Algebraic Expressions : A combination of constants and variables, connected by +, - , and is known as an algebraic expression.
Types of algebraic expressions:
1. Monomial : An algebraic expression containing only one term, is called a monomial.
2. Binomial : An algebraic expression containing 2 terms is called a binomial.
3. Trinomial: An algebraic expression containing 3 terms is called a trinomial.
4. Multinomial: An algebraic expression containing more than 3 terms, is called a
multinomial.
Factors of A Term: When numbers and literals are multiple to form a product, then each quantity multiplied is called a factor of the product. A constant factor is called a numerical factor while a variable factor is called a literal factor.
Constant Term: A term of the expression having no literal factor is called the constant term.
Coefficients: Any factor of a term is called the coefficient of the product of other factors.
4. Class 7 maths chapter- EXPONENTS
INTRODUCTION:
we know that can be written as that is read as two raised to the power three. Similarly, 10 times = , read as three raised to the power ten. In general, if x is any number and m is a positive integer, then we have
m times.
The number x is called the base and m is called the exponent or the index of the exponential expression.
5. Class 7 maths chapter- FACTORISATION
Factorisation:
When an algebraic expression can be written as the product of two or more expressions, then each of these expressions is called a factor of the given expression.
G.C.F. or H.C.F of Monomials: The greatest common factor of given monomials is the common factor having greatest coefficient and highest power of the variables.
G.C.F. or H.C.F of Monomials = (G.C.F. or H.C.F of numerical coefficients)
(G.C.F. or H.C.F of literal coefficients)
6. Class 7 maths chapter- SETS
Objects: Everything in this universe, whether living or non living, is called an object. Well-defined collection of objects : A collection of objects is said to be well-defined if itis possible to tell beyond doubt about every object of the universe, whether it is there inour collection or not.
Set : A well-defined collection of objects is called a set.
The objects in a set are called its members or elements.
We usually denote sets by capital letters A, B, C etc.
If x is an element of a set A, we say that x belongs to A and we write, .
If x does not belong to A, we write.
There are two methods of describing a set :
(i) Roster Method or Tabulation Method.
(ii) Description Method or Set-builder Form.
7. Class 7 maths chapter- QUADRATIC EQUATIONS
Quadratic Equations: A polynomial of degree 2 when equated to zero, gives an equations, called a quadratic equations.
Solving Quadratic Equation:
By solving a quadratic equation, we mean finding its roots.
Zero Product Rule:
If a and b are any two numbers or expressions, then ab = 0 a = 0 or b =0.
8. Class 7 maths chapter- LINEAR EQUATION IN TWO VARIABLES
In this chapter we shall we shall learn how to solve linear equations in two variables. For this we shall learn graphical representation of a point in a plane. We shall represent a point with the help of two numbers known as coordinates of that point. The concept of coordinates was given by the French Mathematician Rene Desartes, which integrates Algebra and geometry.
9. Class 7 maths chapter- SPEED, DISTANCE AND TIME
Speed: The rate of change of distance is known as speed.
When an athlete runs a race, the change in the time taken is directly proportional to the change in the distance covered. A change in speed is directly proportional to the change in distance covered. More the speed more is the distance covered in the same time.
Units of Speed: Speed is measured in i) meters/ second or m/s
ii) Kilometers/ hour or km/hr
10. Class 7 maths chapter- Simple Interest:
When money is borrowed, interest is charged for the use of that money for a certain period of time. When the money is paid back, the principal (amount of money that was borrowed) and the interest is paid back. The amount of interest depends on the interest rate, the amount of money borrowed (principal) and the length of time that the money is borrowed.
Simple interest is generally charged for borrowing money for short periods of time. Compound interest is similar but the total amount due at the end of each period is calculated and further interest is charged against both the original principal but also the interest that was earned during that period.
Interest = Principle x rate of interest x time
CO
ORDINATE SYSTEM
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