Is 1/5 larger than 1/4? Prove it.

Question

How do I do this using an equation?

 

Answer 1

If you have to use an equation, as your question specifies, create the common-denominator fractions as Michael said, then try to subtract:

 

4/20 - 5/20 = -1/20, and therefore, since the answer is negative, you've proven that 5/20 (or the original 1/4) is actually the bigger number, not the 4/20 (or 1/5).

 

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Answer 2

Lets rewrite 1/5 and 1/4 using the lowest common denominators (LCD).  The LCD of 5 and 4 is 20.

 

(1/5) = (x/20)          and       (1/4) = (y/20)

 

 

Cross multiply to find x and y.

 

5x = 20               and         4y = 20

  x = 4                 and          y = 5

 

1/5 = 4/20           and         1/4 = 5/20

 

Since the denominators are the same, we just compare the numerators.

 

4 < 5

 

Therefore, 1/5 is not larger than 1/4.

 

 

Answer 3

....................        '20 dots

 

....                        '1/5 of the dots

 

.....                       '1/4 of the dots

 

It would be very difficult to prove 1/5 is greater than 1/4, but stranger things have happened.