Question

How do you order from least to greatest without using a calculator :
\[2, - \dfrac{3}{7},0.75, - \dfrac{3}{2}\]

Answer 1

Hint: In order to solve this question we will put all the denominators equal and then we will compare the numerators the large will be the numerator, greaters the number and if the numerator is small smaller will be the number.

Complete step-by-step answer:
For solving this question we will put the denominator the same and hence for doing this we will have to make all the numbers without decimal so multiplying 0.75 by 100 to make it non changeable we have to divide it by 100.
Now our new numbers will be;
$ 2, - \dfrac{3}{7},\dfrac{{75}}{{100}}, - \dfrac{3}{2} $
Now our all numbers are converted into normal like form without and decimal, since we want to make the denominator equal we will multiply the denominator of:
2 from 700 so in order so that the number not changes we will multiply it by 700;
The new numerator will be 1400.
3 from 100 so in order so that the number not changes we will multiply it by 100;
The new numerator will be -300.
75 from 7 so in order so that the number not changes we will multiply it by 7;
The new numerator will be 525.
Last 3 from 350 so in order so that the number not changes we will multiply it by 350;
The new numerator will be -1050.
Now the new numbers will be;
 $ \dfrac{{1400}}{{700}},\dfrac{{ - 350}}{{700}},\dfrac{{525}}{{700}},\dfrac{{ - 1050}}{{700}} $
Now the denominators of all these are same so the numerators can be compared;
Since the greater negative number is more small so the smallest number will be $ \dfrac{{ - 1050}}{{700}} $ $ $
The second smallest number will $ \dfrac{{ - 350}}{{700}} $
Third smallest number will be $ \dfrac{{525}}{{700}} $
So the correct order of the numbers smaller to the larger will be;
 $ - \dfrac{3}{2}, - \dfrac{3}{7},0.75,2 $
So, the correct answer is “ $ - \dfrac{3}{2}, - \dfrac{3}{7},0.75,2 $”.

Note: This question can also be solved in other ways such that converting all of them in pure decimal form.
And we will have to make sure that you look at the approximations for the numbers with which you are working.