Comparison of Rational Numbers
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Among the positive rational numbers with the same denominator, the number with the greatest numerator is the largest. It is easy to compare the rational numbers with same denominators. e.g. $\frac{\text{28}}{\text{30}}$ > $\frac{\text{26}}{\text{30}}$ > $\frac{\text{21}}{\text{30}}$. A negative rational number is to the left of zero whereas a positive rational number is to the right of zero on a number line. So, a positive rational number is always greater than a negative rational number. To compare two negative rational numbers with the same denominator, their numerators are compared ignoring the minus sign. The number with the greatest numerator is the smallest. e.g. – < – ; – $\frac{\text{6}}{\text{7}}$ < –  To compare rational numbers with different denominators, they are converted into equivalent rational numbers with the same denominator, which is equal to the LCM of their denominators. There are unlimited number of rational numbers between two rational numbers. To find a rational number between the given rational numbers, they are converted to rational numbers with same denominators.

#### Summary

Among the positive rational numbers with the same denominator, the number with the greatest numerator is the largest. It is easy to compare the rational numbers with same denominators. e.g. $\frac{\text{28}}{\text{30}}$ > $\frac{\text{26}}{\text{30}}$ > $\frac{\text{21}}{\text{30}}$. A negative rational number is to the left of zero whereas a positive rational number is to the right of zero on a number line. So, a positive rational number is always greater than a negative rational number. To compare two negative rational numbers with the same denominator, their numerators are compared ignoring the minus sign. The number with the greatest numerator is the smallest. e.g. – < – ; – $\frac{\text{6}}{\text{7}}$ < –  To compare rational numbers with different denominators, they are converted into equivalent rational numbers with the same denominator, which is equal to the LCM of their denominators. There are unlimited number of rational numbers between two rational numbers. To find a rational number between the given rational numbers, they are converted to rational numbers with same denominators.

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