MATH PROBLEM FRACTION

Question

the product of the numerator and denominator of a certain fraction is 588. What is the fraction if it is equivalent to 3/4? 

Answer 1

1)  x/y = 3/4     the fraction is equivalent to 3/4

2)  xy = 588      the product of numerator*denominator is 588

 

from 1:

x = 3y/4

 

substituting into 2:

(3y/4)y = 588

3y²/4 = 588

3y² = 2352

y² = 2352/3

y² = 784

y = ±√784

y = ±28

 

For y=28:

x = 3(28)/4 = 21

 

For y = -28

x = 3(-28)/4 = -21

 

Your numbers are 21, 28 and -21, -28

 

As fractions:  21/28   or  -21/-28

Answer 2

Let the fraction be a/b.

 

a/b = 3/4

 

ab = 588

 

Solve for a and b:

 

a = 588/b

 

588/b² = 3/4

 

b = √(4*588 / 3) = ±28

 

a = ±588/28 = ±21

 

a/b = 21/28 or -21/(-28) = 21/28