Rational Numbers – Solved Examples Example 1: Write the numerator of the following rational numbers. (i) (2/7) (ii) (-4/5) (iii) (-11/3) (iv) (-10/-17) (v) (13/-14) (vi) (9/8) (vii) (8/9) (viii) (29/4) (ix) (12/5) (x) (22/7) Solution: (i) Numerator of (2/7) is 2 (ii) Numerator of (-4/5) is -4 (iii) Numerator of (-11/3) is -11 (iv) […]

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Multiplying Exponents with Square Roots In this tutorial, we will learn the multiplication of exponents, where bases have a square root. When multiplying square roots that contain exponents, we can rewrite the term with a rational exponent. The square root of a positive number (√a) can be expressed as a rational exponent and (√a) = […]

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Real Numbers – Definition and Examples In this tutorial, we will learn all about real numbers. What are Real Numbers? Real numbers are the set of rational and irrational numbers in number system. Real Number Definition Real numbers are union of rational and irrational numbers. Real numbers can be represented on number line and all […]

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           Multiplicative inverse When we divide 1 by the number, we get “Reciprocal” of the number. The reciprocal = 1/number         Example- The reciprocal of 5 is 1/5 When we multiply a number by its “Multiplicative Inverse” we get 1. Simply the product of a numbers and its reciprocal is 1, then each number is known as Reciprocal […]

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Irrational Numbers – Definition & Examples  Irrational Numbers  Definition:  An “Irrational Number” is a Real Number that cannot be expressed as a simple fraction for any Integers. Simply Irrational means not Rational.    2.5 =  5/2  is a ratio or fraction, but       𝝅 = 3.1415926…is not a ratio or fraction. Decimal expansions of irrational Numbers does […]

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Representation of numbers on Number Line Natural numbers Natural numbers : A set of counting numbers, is known as natural numbers. N = (1, 2, 3, 4, 5,…..) This is a number line for Natural Numbers. Whole numbers Whole numbers : When we add the number zero (0) to the natural numbers, we get whole numbers. W = […]

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 Important sets in Mathematics  1.  N = Set of all “Natural” numbers. 2.  W = Set of all “Whole” numbers. 3.  Q = Set of all “Rational” numbers. 4.   Z = Set of all “Integers”. 5.  R = Set of all “Real” numbers. 6.  Z +  = Set of “Positive” Integers. 7. Q + = Set of “Positive Rational” numbers. 8.  R +  = Set of “Real” numbers.

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Rational and Irrational numbers Usually most students feel difficult to understand the difference between rational and irrational numbers with the help of their definitions. First we know about the terms that are useful to understand the concept of rational and irrational numbers. 1. Perfect square:  If we multiply an integer with itself or same integer, we […]

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