Question

Find a rational number lying at one fourth of the way between 3/4 and 2/3 from the greater side

(with steps)​

Answer 1

13 / 20

Explanation:

This question does not require an understanding of number theory.

NUMBER THEORY

A rational number is any real number that can be represented as a fraction or an integer. This group of numbers excludes imperfect squares or constants like pi.

THE MATH PART

We can use a bit of logic and algebra to do this.

(2/3) > (3/5)

This means we need to find a number relative to (2/3).

1. Calculate the distance between (2/3) and (3/5) by finding the least common multiple denominators. Two brackets placed together mean multiplication.
   d = (2/3) - (3/5);
   d = ( ( 5 ( 2 ) ) - ( 3 )( 3 ) ) / ( ( 3 )( 5 ) );
   d = ( 10 - 9 ) / ( 15 );
   d = 1 / 15;
2. Find 1 - (1 / 4) of the distance because we are taking it from the greater side.
   x = ( 3 / 5 ) + ( 1 - ( 1 / 4 ) )( 1 / 15 );
   x = ( 3 / 5 ) + ( 3 / 4 )( 1/ 15 );
   x = ( 3 / 5 ) + ( 3 / 60 );
   x = ( 3 / 5 ) + ( 1 / 20 );
   x = 13 / 20;

The rational number is ( 13 / 20 ).

I could have probably made step 2 easier by subtracting ( 1 / 4 ) of ( 1 / 15 ) from ( 2 / 3 ).