Question

Which is greater, 3/4 or 11/16? how can you be sure?

Answer 1

The correct answer is: 3/4 is greater than 11/16.

Step-by-step explanation:
Method 1 (Simplistic way):
3/4 can be represented as 12/16.

Now if we compare 12/16 with 11/16, we can see that 11 is less than 12 (cancelling 16). Hence 3/4 is greater than 11/16.

Method 2 (Long method):
The simplest method is to familiarize yourself with the division operation. For example:

If we have the following rational number: 8/4, the division tells us how many 4s are needed to make 8. In this case, there are 2 fours needed to make 8.


Likewise:
3/4: There are 0.75 fours needed to make 3 as 0.75*4 = 3.
11/16: There are 0.6875 sixteens needed to make 11 as 0.6875*16 = 11.

It means that 0.75 > 0.6875; therefore, 3/4 > 11/16.

Answer 2

when comparing fractions we need to bring the fractions to the same denominator
to compare and see which is bigger or smaller.
the denominators of the 3/4 and 11/16 are 4 and 16 respectively.
we can mulitply both numerator and denominator of 3/4 by 4 so that the denominator is now 16,
then the fraction
`(3*4)/(4*4) = (12)/(16)`
now we can compare the 2 fractions 12/16 and 11/16,
when denominator is same then bigger numerator is the bigger fraction. therefore 3/4 is the greater fraction