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Rational Expressions Rational numbers can form expressions when we join rational numbers with various mathematical operators namely addition, subtraction, multiplication and division. Rational Numbers are the numbers which are written in form of p/q, where p and q are integers, and q≠ 0. In this, p is the numerator and q is the denominator. Always remember all natural, whole numbers, integers including zero(0) are all the members of the family of rational numbers because they all have 1 as the denominator, which is not 0. Two rational numbers can be added like the addition procedure of simple fractions and follow the laws of addition of integers. Let us take an example in order to understand the concept, Add 2 + 4/7 + (-3/2), Know More About Limits in calculus


Here, we find that the denominators are 1, 7 and 2. So we take the L.C.M. of the three numbers that is 14. Further, we try to make all the denominators = L.C.M. i.e. 14. For this we multiply numerator and denominator of 2 by 14, numerator and denominator of 4/7 by 2 and numerator and denominator of (-3/2) by 7 We get: (2*14)/14 + (4*2)/(7*2) + (-3*7) /(2*7) = (28/14) + (8/14) + (-21)/14 =(28 +8 -21)/14 = 15/14 Ans. We can also do Subtraction with the rational numbers. If we take a pair of rational numbers and try how subtraction works: Subtract (-2/4) from (-4/6) = (-4/6) – (-2/4) L.C.M. of 6 and 4 is 12, So now we make the denominator =12. For this we multiply and divide (-4/6) by 2, and multiply and divide (-2/4) by 3. We get: (-4 * 2)/ (6*2) – (-2*3) /(4*3) =-8/12 – (-6) / (12) =(-8 +6 )/12 = -2/12 Now further we convert it into standard form. For this first we find H.C.F. of 2 and 12 is 2. So we divide numerator and denominator of -2/12 by 2 We get -1/6.

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Rational Expressions