Rational Numbers

A rational number is defined as a number that can be expressed in the form p/q where p and q are integers and q ≠ 0.

Rational numbers include natural numbers, whole numbers, integers, fractions, decimals (terminating, and non-terminating and repeating) and negative fractional quantities.

Two rational numbers are equivalent if one can be obtained from the other by multiplying/dividing the numerator and denominator by the same non-zero integer.

A rational number which has both the numerator and the denominator as positive or negative integers is called a positive rational number. A rational number which has either numerator or denominator as negative integer is called a negative rational number.

The number 0 is neither a positive nor a negative rational number. Rational numbers can be represented on a number line.

A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and denominator have no common factor other than 1.

Unlimited or infinite number of rational numbers can be found between any two rational numbers.

Rational numbers can be compared using number line or like comparison of fractions.

Addition of rational numbers with same denominator is done by adding their numerators and keeping the denominator same. While adding two rational numbers with different denominators, take the L.C.M. of the denominators of rational numbers and make them equivalent with L.C.M as denominator and then add the obtained rational numbers. The additive inverse or opposite of a number ‘a’ is the number that, when added to ‘a’, yields ‘zero’. The additive inverse of ‘a’ is denoted as ‘–a’. Subtraction of two rational numbers is done by adding the additive inverse of the rational number that is being subtracted, to the other rational number.

Product of two rational numbers is calculated as product of numerators divided by the product of denominators.

Reciprocal of a number is obtained by interchanging the numerator and denominators of a given number. Product of a number with its reciprocal is always 1.

While dividing two rational numbers, multiply the reciprocal of the rational number, which is acting as a divisor, by the other rational number.

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  • Q1

    Value of   is equal to

    Marks:1
    Answer:

     (-4/3).

    Explanation:
     = (3/14) x (-56/9)    [by a/b = a x (1/b)]
                          = (-4/3)

     

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  • Q2

    The length and the breadth of a rectangle are 5/4 m and 7/3 m respectively. The perimeter of the rectangle is

    Marks:1
    Answer:

    43/6 m.

    Explanation:
    Given that, length = 5/4 m and breadth = 7/3 m
    We know that perimeter of the rectangle = 2(length + breadth) 
    perimeter = 2(5/4+7/3
                   = 2(15+28)/12 
                   = 2 43/12 
                   = 43/6 m

     

     

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  • Q3

    is equal to

    Marks:1
    Answer:

    -97/160.

    Explanation:

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  • Q4

    The Value of   is equal to

    Marks:1
    Answer:

    - 15/4.

    Explanation:

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  • Q5

    If  2/3 , y/6 and x/15 are equivalent, then the value of x and y are

    Marks:1
    Answer:

    10 and 4.

    Explanation:

    Since 2/3 , y/6 and x/15 are equivalent
    then 2/3 = y/6 = x/15
    from first and third ratios
    2/3 = x/15
        x= 2 15/3 = 10

    Now from first and second ratios

    2/3 = y/6
       y = 6 2/3 = 4
    Thus, x= 10 and y = 4. 

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