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Rational Numbers on a Number Line

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Rational Number on a number line:

Let us represent the number `-3/2` on the number line.

  • The points to the right of 0 are denoted by + sign and are positive integers. The points to the left of 0 are denoted by – sign and are negative integers.
  • Being a negative rational number, it would be marked to the left of 0.
  • You know that while marking integers on the number line, successive integers are marked at equal intervals. Also, from 0, the pair 1 and – 1 is equidistant. So are the pairs 2 and -2, 3 and -3.
  • In the same way, the rational numbers `3/2 "and" -3/2` would be at equal distance from 0.
  • We know how to mark `-3/2` on the number line. It is marked on the left of 0 and lies halfway between 1 and 2.
  • Let us now mark `3/2` on the number line. It lies on the Right of 0 and is at the same distance as `-3/2` from 0.
  • In decreasing order, we have, `(-1)/2, (-2)/2 (= -1), (-3)/2, (-4)/2 (= 2)`.
  • This shows `(-3)/2` lies between – 1 and -2.

Example

Show the following numbers on a number line.

`7/3, 2, (-2)/3`

Steps:

  1. Let us draw a number line.
  2. We can show the number 2 on a number line.
  3. `7/3 = 7 xx 1/3`, therefore each unit on the right side of zero is to be divided in three equal parts. The seventh point from zero shows `7/3; or 7/3 = 2 + 1/3,` hence the point at `1/3"rd distance of unit after 2 shows" 7/3`.
  4. To show `(-2)/3` on the number line, first, we show `2/3` on it. The number to the left of 0 at the same distance will show the number `(-2)/3`.
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