Rational numbers, sometimes abbreviated as RN are those numbers which can be expressed in the form of p/q, where q ? 0. Since 1 also can be considered for ‘q’, all whole numbers are included in this category. . Since it is only an option to include whole numbers, we will refer in the numbers in fraction form as rational numbers.
It is a natural tendency that when you see two (or more) quantities, you start comparing. Even if you those are given for any other purpose, you do compare them mentally by intuition. Similarly the RNs are also are required to be compared. With the given RNs you can identify and arrange them in order by comparing rational numbers.
Now let us see how to compare rational numbers. To compare two rational numbers, the first step is to compare the denominators and numerators. If the denominators are same, then the RN with a greater value in the numerator is greater. For example, between ¼ and ¾ , ¾ is greater among the two. On the other hand, if the numerators are same, then the RN with a lower value in the denominator is greater. For example, between 1/8 and 1/16 ,1/8 is greater among the two.
From what we explained so far, comparing the numbers with same denominator or with same numerators is very easy and mostly done mentally. However in cases of numbers with different numerators and denominators, the comparison may not be that apparent. The process of comparing RN is a bit laborious. What needs to be done first is to rewrite the equivalents of the given numbers with same denominators and now compare the numerators. But how do you find a ‘common denominator’ (which is also called as least common denominator, LCD)?
The LCD of two given RN is the lowest common multiple (LCM) of their denominators. Now take the given fractions and write their equivalents with this LCM as the denominator. Now the transformed numerators are compared for actual comparison of the given fractions. Let us explain this with an example. I have recently faced lot of problem while learning Finding the least Common Denominator, But thank to online resources of math which helped me to learn myself easily on net.
Suppose we need to compare (3)/(4) and (5)/(6). It is not apparent which is greater of the two. The LCM of the denominators 4 and 6 is 12. The equivalent fraction of (3)/(4) with denominator 12 is (9/12). The equivalent fraction of (5)/(6) with denominator 12 is (10/12). Now by comparing the numerators we find is (10/12).is greater of the two. Accordingly we conclude that (5)/(6) is greater among (3)/(4) and (5)/(6).
It is a natural tendency that when you see two (or more) quantities, you start comparing. Even if you those are given for any other purpose, you do compare them mentally by intuition. Similarly the RNs are also are required to be compared. With the given RNs you can identify and arrange them in order by comparing rational numbers.
Now let us see how to compare rational numbers. To compare two rational numbers, the first step is to compare the denominators and numerators. If the denominators are same, then the RN with a greater value in the numerator is greater. For example, between ¼ and ¾ , ¾ is greater among the two. On the other hand, if the numerators are same, then the RN with a lower value in the denominator is greater. For example, between 1/8 and 1/16 ,1/8 is greater among the two.
From what we explained so far, comparing the numbers with same denominator or with same numerators is very easy and mostly done mentally. However in cases of numbers with different numerators and denominators, the comparison may not be that apparent. The process of comparing RN is a bit laborious. What needs to be done first is to rewrite the equivalents of the given numbers with same denominators and now compare the numerators. But how do you find a ‘common denominator’ (which is also called as least common denominator, LCD)?
The LCD of two given RN is the lowest common multiple (LCM) of their denominators. Now take the given fractions and write their equivalents with this LCM as the denominator. Now the transformed numerators are compared for actual comparison of the given fractions. Let us explain this with an example. I have recently faced lot of problem while learning Finding the least Common Denominator, But thank to online resources of math which helped me to learn myself easily on net.
Suppose we need to compare (3)/(4) and (5)/(6). It is not apparent which is greater of the two. The LCM of the denominators 4 and 6 is 12. The equivalent fraction of (3)/(4) with denominator 12 is (9/12). The equivalent fraction of (5)/(6) with denominator 12 is (10/12). Now by comparing the numerators we find is (10/12).is greater of the two. Accordingly we conclude that (5)/(6) is greater among (3)/(4) and (5)/(6).
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