compare the rational number 4/5 and 1/6
Answers
Answer:
We will learn the comparison of rational numbers. We know how to compare two integers and also two fractions. We know that every positive integer is greater than zero and every negative integer is less than zero. Also every positive integer is greater than every negative integer.
Similar to the comparison of integers, we have the following facts about how to compare the rational numbers.
(i) Every positive rational number is greater than 0.
(ii) Every negative rational number is less than 0.
(iii) Every positive rational number is greater than every negative rational number.
(iv) Every rational number represented by a point on the number line is greater than every rational number represented by points on its left.
(v) Every rational number represented by a point on the number line is less than every rational number represented by paints on its right.
How to compare the two rational numbers?
In order to compare any two rational numbers, we can use the following steps:
Step I: Obtain the given rational numbers.
Step II: Write the given rational numbers so that their denominators are positive.
Step III: Find the LCM of the positive denominators of the rational numbers obtained in step II.
Step IV: Express each rational number (obtained in step II) with the LCM (obtained in step III) as common denominator.
Step V: Compare the numerators of rational numbers obtained in step having greater numerator is the greater rational number.
Solved examples on comparison of rational numbers:
1. Which of the two rational numbers 35 and −23 is greater?
Solution:
Clearly 35 is a positive rational number and −23 is a negative rational number. We know that every positive rational number is greater than every negative rational number.
Therefore, 35 > −23.
2. Which of the numbers 3−4 and −56 is greater?
Solution:
First we write each of the given numbers with positive denominator.
One number = 3−4 = 3×(−1)(−4)×(−1) = −34.
The other number = −56.
L.C.M. of 4 and 6 = 12
Therefore, −34 = (−3)×34×3 = −912 and −56 = (−5)×26×2 = −1012
Clearly, −912 > −1012
Hence, 3−4 > −56.
3. Which of the two rational numbers 57 and 35 is greater?
Solution:
Clearly, denominators o f the given rational numbers are positive. The denominators are 7 and 5. The LCM of 7 and 5 is 35. So, we first express each rational number with 35 as common denominator.
Therefore, 57 = 5×77×7 = 2549 and 35 = 3×75×7 = 2135
Now, we compare the numerators of these rational numbers.
Therefore, 25 > 21
⇒ 2549 > 2135 ⇒ 57 > 35.
4. Write of the two rational numbers −49 and 5−12 is greater?
Solution:
First we write each one of the given rational numbers with positive denominator.
Clearly, denominator of −49 is positive. The denominator of 5−12 is negative.
So, we express it with positive denominator as follows:
5−12 = 5×(−1)(−12)×(−1) = −512, [Multiplying the numerator and denominator by -1]
Now, LCM of denominators 9 and 12 is 36.
We write the rational numbers so that they have a common denominator 36 as follows:
−49 = (−4)×49×4 = −1636 and, −512 = (−5)×312×3 = −1536
Therefore, -15 > -16 ⇒ −1536 > −1636 ⇒ −512 > −49 ⇒ 5−12 > −49.