Question

Arrange `-5/9, 7/12, -2/3 and 11/18` in ascending order of their magnitudes.
Also, find the difference between the largest and smallest of these rational numbers. Express this difference as a decimal fraction correct to one decimal place.

Answer 1

Consider the given number : `-5/9, 7/12, -2/3 and 11/18`

The L.C.M. of 9, 12, 3 and 18 is 36.
Thus, the given numbers are:

`-5/9, 7/12, -2/3 and 11/18`

`= - [ 5 xx 4 ]/[ 9 xx 4 ], [ 7 xx 3 ]/[ 12 xx 3 ], -[ 2 xx 12 ]/[ 3 xx 12 ] and [ 11 xx 2 ]/[ 18 xx 2 ]`

= `-20/36, 21/36, -24/36 and 22/36`

Thus, the numbers in ascending order are shown below:

`-24/36 <  -20/36 < 21/36 < 22/36`

Thus, the given numbers in ascending order are shown below:

`-2/3 <  -5/9 <  7/12 < 11/18`

We must find the difference between the largest and smallest of the above numbers.

Thus, difference = `11/18 - ( -2/3) `

 = `11/18 + 2/3`

 = `11/18 + [ 2 xx 6 ]/[ 3 xx 6 ]`

= `11/18 + 12/18`

= `[ 11 + 12 ]/18`

= `23/18`

We need to express this fraction as a decimal,
Correct to one decimal place.
Thus, we have `23/18 = 1.2bar7` ≈ 1.3.