which of the following lies between rational numbers 1/4 and 1/5
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Please Note - The options have not been provided, but the answer can still be deduced.
The number that lies between the rational numbers 1 / 5 and 1 / 4 is 9 / 40.
• First we need to find the L.C.M. of the denominators 5 and 4, which is 20.
• Then, we need to equalise the denominators of both the numbers by multiplying them with a number that results to 20 in the denominator.
(1 × 4) / (5 × 4) = 4 / 20
(1 × 5) / (4 × 5) = 5 / 20
Also, the numerator is multiplied by the same number as the denominator to keep the final value of the number unchanged.
• Now, the new rational numbers are 4 / 20 and 5 / 20.
• Difference between the numerators is 5 - 4 = 1, but, to insert a number between 4 and 5 in the numerator, we need a difference of atleast 2 between the numerators.
• Therefore, we shall now multiply the numerator and denominator of each number by 2.
(4 × 2) / (20 × 2) = 8 / 40
(5 × 2) / (20 × 2) = 10 / 40
• The resultant rational numbers are now, 8 / 40 and 10 / 40.
• The number between 8 and 10 is 9. Therefore, the number between 8 / 40 and 10 / 40 is 9 / 40.
• In other words, the number between 1 / 5 and 1 / 4 is 9 / 40.