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Let us learn in detail how to arrange Rational Numbers in Ascending Order. Have a look at the general method to arrange the Rational Numbers in Increasing Order. To help you get a better idea of the concept we even listed the solved examples provided step by step.
Procedure to arrange from Smallest to Largest Rational Numbers
Go through the below-listed guidelines in order to arrange Rational Numbers from smallest to largest. They are along the lines
Step 1: Express the given rational number in terms of a positive denominator.
Step 2: Determine the Least Common Multiple of the positive denominators obtained.
Step 3: Express each rational number with the LCM acquired as the common denominator.
Step 4: The number which has the smaller numerator is the smaller rational number.
Solved Examples for Rational Numbers in Ascending Order
1. Write the following rational numbers in Ascending Order -3/5, -1/5, -2/5
Solution:
Since all the numbers have a common denominator the one with a smaller numerator is the smaller rational number. However, when it comes to negative numbers the higher one is the smaller one.
Therefore arranging the given rational numbers we get -3/5, -2/5, -1/5
2. Arrange the rational numbers 1/2, -2/9, -4/3 in Ascending Order?
Solution:
Find the LCM of the denominators 2, 9, 3
LCM of 2, 9, 3 is 18
Express the given rational numbers with the LCM in terms of common denominator.
1/ 2= 1*9/2*9 = 9/18
-2/9 = -2*2/9*2 = -4/18
-4/3 = -4*6/3*6 = -24/18
Check the numerators of all the rational numbers expressed with a common denominator.
Since -24 is less than the other two we can arrange the given rational numbers in Ascending Order.
-4/3, -2/9, 1/2 is the Ascending Order of Given Rational Numbers.
3. Arrange the Rational Numbers 5/8, 4/-6, 3/5 in Ascending Order?
Solution:
Firstly, express the rational numbers with positive denominators by multiplying with -1
4/-6 = 4*(-1)/-6*(-1) = -4/6
So, find the LCM of the denominators 8, 6, 5
LCM of 8, 6, 5 is 120
5/8 = 5*15/8*15 = 75/120
-4/6 = -4*20/6*20 = -80/120
3/5 = 3*24/5*24 = 72/120
Check the numerator of the rational numbers having common denominators.
since -80 is the smallest that itself is the smallest rational number.
Therefore, 4/-6, 3/5, 5/8 are in Ascending Order.
