WBBSE Notes For Class 6 Maths Algebra Chapter 1 Concept Of Algebraic Variables Or Quantities Or Symbols

Algebra Chapter 1 Concept Of Algebraic Variables Or Quantities Or Symbols

Algebra Chapter 1 What Is Constant

Constant:

1. In mathematics, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 these ten symbols are called digits.
2. Arranging these digits in different ways we get an infinite number of numbers.
3. The magnitudes of these numbers are Definite.
4. In mathematics wherever they are used, the magnitude of these numbers never changes.
5. For example, the magnitude of the digit 2, anywhere in mathematics it is used, its value is the same in the whole world, never its value is changed.
6. So the number 2 is a constant.
7. These types of numbers are called constants.
8. So all the mathematical symbols each of whose magnitudes are always the same and definite and never value changed, are called constants.
9. For example, 1, 2, 3, 4, etc. are constants.
10. Using any mathematical symbol before or after or above or below a constant, we can change the direction of any other measure of the mathematical symbol but its magnitude or absolute value will always remain the same.
11. For example, +2, – 2, 2⁺, 2^–, —>2, etc. represent the different measures of 2 but its magnitude will be the same as 2.
12. This definite magnitude of the number is called its absolute value and the absolute value of any number is always positive.
13. For example | + 2 | = 2 ; | – 2 | = 2.
14. The definition of the absolute value of any number x is | x | which is
    | x | = x if x > 0
    = – x if x < 0
    = 0 if x = 0

WBBSE Class 6 Algebraic Variables Notes

Algebra Chapter 1 What Is Variable

Variable:

1. The variable is a quantity whose value is not fixed or definite and which accepts different values in different mathematical problems.
2. For example: In the mathematical problem 2x = 4, 2 and 4 are constants but x is a variable.
3. Here x = 2.
4. Again in the mathematical problem x + 1 = 0, x = – 1.
5. In any mathematical problem, x can take any value, for this reason, x is called a variable.
6. In general, we use the English alphabets a, b, c, x, y, z, etc. to express the variables.
7. In the mathematical problem 2n + 2 = 0, n is a variable quantity.
8. The variables obey the rules of mathematical operations like constants or real numbers.
9. For example—
   1. Associative law of addition:
   2. If x, y, z be any 3 variables, then x + (y + z) = (x + y) + z
   3. Commutative law of addition:
   4. If x, and y be any two variables, then x + y = y + x.
   5. Associative law of multiplication:
   6. If x, y, and z be any 3 variables, then x. (y.z) = (x.y).z.
   7. Commutative law of multiplication:
   8. If x, y be any two variables, then x x y = y x x.
   9. Distributive law:
   10. If x, y, z be any 3 variables, then x.(y + z) – x.y + x.z.

Understanding Algebraic Symbols for Kids

Algebra Chapter 1 Use Of Variables

Use Of Variables:

1. In an algebraical problem, for any unknown quantity or number, we use a variable.
2. For example “The present age of the father is twice that of the son”—In this type of mathematical problem, we take the present age of the son or father as a variable.
3. Let the present age of the son be x
4. We use a variable to express a general quantity which is denoted for different values of a quantity.
5. For example—to express the quantities 2¹, 2², 2³, etc. a general quantity, we write 2ⁿ, n = 1, 2, 3,…………….., where n is taken as a variable.
6. The branch of mathematics in which we can solve the problems of mathematics using English alphabetic symbols is called Algebra.
7. A big branch of mathematics Algebra is formed based on different use of variables.
8. Algebra is a more generalized form of the problems of Arithmetic.
9. For example, in Arithmetic,
   (2 + 3)² = 2² + 2.2.3 + 3²
   (3 + 4)² = 3² + 2.3.4. + 4⁴
   i.e., the square of the sum of two numbers = The square of the first number + 2 x the first number x the second number + the square of the second number.
10. This formula in arithmetic can be written through the variables as (a + b)² = a² + 2ab + b²
11. This is the algebraic formula which is a more simplified form.
12. There is a fantastic use of variables in modem mathematics.
13. For these reasons he or she who will learn the use of variables correctly and accurately would be able to show his or her credit in solving the mathematical problem.

Important Definitions Related to Algebra

Algebra Chapter 1 Algebraic Sign And Symbol

Algebraic Sign And Symbol:

1. ‘+’: Addition sign: For example, x + y, where x and y are two variables.
2. ‘-‘: Subtraction sign: For example, x – y.
3. ‘x’: Multiplication sign: For example, x x y.
4. ‘÷’: Division sign : For example, x -f y or ~.
5. ‘=’: Equal sign : For example, x = y i.e., the values of .x and y are same.
6. ‘>’: Greater sign: For example, x > y means that the value of x is greater than the value of y (or simply x is greater than y).
7. ‘<’: Less (smaller sign) : For example, x < y means that the value of * is less than the value of y (or simply x is less than y).
8. ‘≥’: Greater than or equal sign: For example, a: > y means that the value of x is greater than the value of y or x is equal to y.
9. ‘≤’: Less than or equal sign: For example, x < y means that the value of x is less than the value of y or x is equal to y.
10. ‘>≠’: Not greater than a sign: For example, x > y means that the value of x is not greater than the value of y.
11. ‘<≠’: Not less than a sign: For example, x <≠ y means that the value of x is not less than the value of y.
12. ‘≠’: Not equal to sign: for example, x * y means that the value of x is not equal to the value of y.
13. ‘∼’: Difference sign: For example, x ~ y means that the smaller number between x and y is to be subtracted from the greater number.
    x ~ y means that
    1. x – y if x > y
    2. y – x if y > x.
14. ‘≡’: Equivalent to sign: For example, x = y means that x is equivalent to y.