Divisibility rules or Divisibility tests

A number is said to be divisible by another number if the remainder is zero. Divisibility rules or divisibility tests are a set of general rules that are often used to determine whether or not a number is completely divisible by another number.  In this article,  some  divisibility tests are given with many examples . Divisibility by  powers of 2 and 5 Let any integer , then  is divisible by     if the integer made up of  the last    digits of  are divisible by  . Suppose we have   to determine whether an integer is divisible by 2, we only …

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Finding rational numbers between two given rational numbers

Rational numbers between two given rational numbers A rational number is a number which can be written in the form of . We can find  infinitely many rational numbers between any two rational numbers. This property of rational numbers is known as the dense property. Methods to  find  rational numbers between any two rational numbers are given below.. Method-1  (Average Technique) Suppose  we are required to find  rational numbers between two rational numbers   and such that . Since the average of two numbers always  lying between the numbers, so is a rational number lying between   and .  We continously …

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Solved examples on rational numbers

Here we are giving some practice  questions based  on  rational numbers. 1. Are the following statements are true or false? Give reason  for your answers. (i)  every whole number is a natural numbers. (ii) every integer is a rational number . (iii)There are infinitely many rational numbers between any two given rational numbers. (iv) 0 is a rational  number. (V)Every rational number is a whole number. ANS. (i) False , beacuse ‘0’ is a whole  number not a natural number. (ii)True,  because every integer can be expressed in the form , so it is a rational number. (iii) True (iv) …

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Various types of numbers: natural numbers, whole numbers, integers and rational numbers

Various types of numbers: natural numbers, whole numbers, integers and rational numbers Various types of numbers : According to the properties and how they are represented in the number line, the numbers are classified into different types.  Natural numbers The natural numbers are those numbers that are used for counting and ordering.  The set of natural numbers is often denoted by the symbol ,        The least natural number is 1 and there are infinitely  many natural numbers.  They are located  at the right side of the number line (after 0) Properties of natural numbers:  (i) closure property: …

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