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Rational Numbers

Rational Numbers
science Square
Science Square

  • Any number that can be expressed in the form a/b, where a and b are integers and b≠0 is called a rational number.


For example:4/7,2/3,-6
are all rational numbers.

Addition of rational numbers

To add two rational numbers, first express each rational number with a positive denominator.

Maths class 8 Rational numbers

  • Associative Property: If a/b, c/d, and e/f are three rational numbers, then [(a/b + c/d) + e/f] = [a/b + (c/d + e/f)]

Maths class 8 Rational numbers

Maths class 8 Rational numbers

Subtraction of rational numbers

Subtracting one rational number from another rational number is same as adding the additive inverse(negative) of the rational number that is being subtracted to the other rational number

Maths class 8 Rational numbers

EXAMPLE 1: Sum of two rational number is 1/6. If one of them is -1/2, then find the other rational number.

SOLUTION: The other rational number is = 1/6 – (-1/2) =1/6 + ½ = 2/3 [ANS]

EXAMPLE 2: What number should be added to -1/4 to get -4/5?

SOLUTION: The number is = -4/5 – (-1/4) = -4/5 + ¼ = -11/20 [ANS]

Multiplication of rational number

  • To multiply two rational numbers proceed as under:
    Multiply the numerators together and the denominators together, place the products of numerators above the products of the denominator.


Maths class 8 Rational numbers

  • The number 1 is called the multiplicative identity of rational numbers.

Maths class 8 Rational numbers


  • Multiplication is distributive over addition and subtraction.

Maths class 8 Rational numbers

  • To divide one rational number by another(non-zero) rational number proceed as under:
    Multiply the dividend by the reciprocal of the another

Maths class 8 Rational numbers


  • Division of rational numbers is not associative.

Maths class 8 Rational numbers

Representation of a rational number on a number line

To represent rational number on a number line proceed as under:

Maths class 8 Rational numbers


Maths class 8 Rational numbers


Rational numbers between two rational numbers

To insert n rational numbers between two rational numbers, do the following:

  • When given rational numbers have the same denominator multiply the denominator and numerator by (n+1).
  • When given rational numbers have different denominators: find the LCM of the denominators; change the given rational number into equivalent rational numbers with LCM as their denominator; If necessary multiply the denominator and numerator of each by (n+1).

Maths class 8 Rational numbers

Practice these questions

Maths class 8 Rational numbers

Q4) Vivan donated of his salary to the orphanage, 1/4th of his salary on food, 1/3 of his salary on rent and electricity, and 1/15th of his salary on telephone bills. This month he donated Rs. 6000 in a charity. He is left with Rs. 4000. Find his monthly salary.

Q5) Area of a square is 1 sq. metre more than ½ of the area of a rectangle. If the area of the square is 91 sq. metre. Then find the dimensions of the rectangle. Given breadth is ¾ times of length.

Maths class 8 Rational numbers

Recap

  • A number that can be addressed in the form a/b where a and b are integers and b≠0, then the number is a rational
  • All integers and fractions are real numbers
  • All decimals except non-terminal and non-recurring are rational numbers
  • Addition is closed, commutative, associative.
  • Subtraction is closed. But neither commutative nor associative.
  • Multiplication is closed, commutative, associative and distributive

Division is not closed, not commutative, not associative.

Quiz for Rational Numbers

Q.1

A number of the form (a/b) is said to a rational number if

a) a and b are integers
b) a and b are integers and a is not equal to 0
c) a and b are integers and b is not equal to 0
d) a and b are integers and a and b are not equal to 0

Q.2

(1/2) + (2/3) = (7/6). This expression proves which property of addition of rational numbers?

a) Associative
b) Commutative
c) Closure
d) none of the above

Q.3

Which of the following is false?

a) Rational numbers are closed under addition
b) Rational numbers are closed under subtraction
c) Rational numbers are closed under multiplication
d) Rational numbers are closed under division

Q.4

The additive inverse of -4/37 is

a) 4/37
b) 37/4
c) -37/4
d) -4/37

Q.5

The multiplicative inverse of -4/37 is

a) 4/37
b) 37/4
c) -37/4
d) -4/37

Q.6

Value of (2/3) - (-4/6) is

a) 0
b) 4/3
c) -4/3
d) 1/3

Q.7

Which of the following expression proves commutativity property of rational numbers?

a) (2/3 - 3/4) = (3/4 - 2/3)
b) [(24/5) / (3/7)] = [(3/7) / (24/5)]
c) 8/3 * 2/ 9 = 2/9 * 8/3
d) 1/3 - 1/3 = 0

Q.8

-1/(-1/x) is same as

a) 1/x
b) -x
c) x
d) -1/x

Q.9

The reciprocal of -1 is

a) 1
b) -1
c) 0
d) Undefined

Q.10

The reciprocal of 0 is

a) 1
b) -1
c) 0
d) Undefined

Your Score: 0/10

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