Rational numbers on a number line Rational numbers on a number line We know that rational numbers are expressed in form of p/q where ‘p’ and ‘q’ are integers and q <> 0. Rational numbers can be all positive numbers and the negative numbers including zero. They all can be expressed on a number line. If we need to draw the rational numbers on a number line, we must remember that positive numbers exist in the right side of the number line and the negative numbers appear on the negative side of the number line. All rational numbers can be expressed on number line. We must remember that if the rational number is in the form of proper positive rational number, it always lies between ‘0’ and ‘1’. On other hand if the rational number is in the form of improper rational number, it is first converted into mixed fraction and then a point is located on the number line. If we find a negative rational number, then all the above rules apply but in the left side of zero. Additive inverse of the given number is at equal distance from ‘0’ appearing in the opposite direction. Zero is the additive inverse of itself and it is neither positive nor negative. Every Rational number has its Additive inverse, which exist on the equal distance in the opposite direction.
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It means inverse of a positive rational number is a negative rational number and the additive inverse of a negative rational number is a positive rational number. For every rational number p/q, their exist its additive inverse –p/q, such that p/q + (-p/q) = 0. We say zero is the additive identity. If any rational number is added to its additive inverse, the result is always zero. Here are some examples of additive inverse: Additive inverse of 3/5 is -3/5. So we can also write 3/5 + (-3/5) = 0 Also Additive inverse of -5/9 is - (-5/9) = 5/9 . SO -5/9 + 5/9 = 0. So we observe Additive inverse of -5/9 is 5/9 Similarly we can say additive inverse of 4 is -4 and additive inverse of -3 is 3. Let us try it with solving it: If we have p/q = 3/7, then its additive inverse is -3/7. Now to check that the additive inverse of 3/7 is -3/7, then it must satisfy p/q + ( -p/q ) = 0 So, 3/7 + (- 3/7 ), = ( 3 – 3 ) / 7, = 0/7, = 0. Which is the additive identity. We observe that the sum of the above two numbers is ‘0’. We also know that ‘0’ is the additive identity, it means that the two numbers are additive inverse of each other. Which means 3/7 is the additive inverse of -3/7 and -3/7 is the additive inverse of 3/7.
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So, after comparing whole numbers the output in ascending order will be 4,557, 4,584 and 4,589 Comparing whole numbers with the numbers in the form of p/q i.e. rational numbers we convert the fraction numbers into decimal numbers and then we compare the numbers. Remember that on number line values move from lowest to highest and the direction of the symbol (< or >) always opens towards the greater number. Which is the additive identity. We observe that the sum of the above two numbers is ‘0’. We also know that ‘0’ is the additive identity, it means that the two numbers are additive inverse of each other. Which means 3/7 is the additive inverse of -3/7 and -3/7 is the additive inverse of 3/7
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