INTRODUCTION You began your study of numbers by counting objects around you. The numbers used for this purpose were called counting numbers or natural numbers. They are 1, 2, 3, 4, ... By including
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NEED FOR RATIONAL NUMBERS Earlier, we have seen how integers could be used to denote opposite situations involving numbers. For example, if the distance of 3 km to the right of a place was denoted
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WHAT ARE RATIONAL NUMBERS? The word ‘rational’ arises from the term ‘ratio’. You know that a ratio like 3:2 can also be written as \(\frac{3}{2}\) . Here, 3 and 2 are natura
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POSITIVE AND NEGATIVE RATIONAL NUMBERS Consider the rational number \(\frac{2}{3}\) . Both the numerator and denominator of this number are positive integers. Such a rational number is called a pos
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RATIONAL NUMBERS ON A NUMBER LINE The points to the right of 0 are denoted by + sign and are positive integers. The points to the left of 0 are denoted by – sign and are negative integers
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RATIONAL NUMBERS IN STANDARD FORM Observe the rational numbers \(\frac{3}{5},\frac{-5}{8},\frac{2}{7},\frac{-7}{11}\). The denominators of these rational nu
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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COMPARISON OF RATIONAL NUMBERS We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. Let us now see how we can compare two rational numbers.
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RATIONAL NUMBERS BETWEEN TWO RATIONAL NUMBERS Reshma wanted to count the whole numbers between 3 and 10. From her earlier classes, she knew there would be exactly 6 whole numbers between 3 and 10.
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OPERATIONS ON RATIONAL NUMBERS You know how to add, subtract, multiply and divide integers as well as fractions. Let us now study these basic operations on rational numbers. Addition: Let us
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