Which is the largest number? 4/5, 5/8, 12/17, 9/11

Here are 4 fractions given to identify the largest. We can determine the value of each fraction by converting them into decimal numbers or by finding  comparable equivalent fractions with one common denominator. The first one is easy, but I do not understand  level of difficulty of the question raiser.Since it is only 4 fractions we can determine which is greater by comparing 2 of them at a time also.

(i) Comparing method: a/b > or = or <  c/d  according as ad > or = or < bc.

4/5 and 5/8 : 4*8=32 and 5*5 =25. 32>25. Therefore,4/5>5/8 ....(A)

12/17 and 9/11: 12*11 =132 and 17*9=153.132<153. Therefore, 9/11 is larger. or  12/17 < 9/11 ---------(B)

From (A) and (B) , it remains to identify the larger of 4/5 and 9/11:

4/5 an9/11:  4*11=44 and 5*9 =45.  44<45. So, 9/11 is  the lager.  (C).

Considering the facts at (A), (B) and (C), we conclude the fraction 9/11 is the lagest.

(ii) By finding decimal equivalents.

We convert each fraction to their decimal equivalents.

4/5=0.8000.

5/8=0.6250

12/17 = 0.70588...

9/11=0.818181.

One example of  how 12/17 is converted into decimal:

12/17 : 17 cannot go in 12 . So put 0 as quotient and 12 as reminder.

Remainder 12*10/17 = 120/17 =quotient  7 and remainder 1

reminder1*10/17= 10/17  = Qutient 0 and  remainder 10

remainder 10*10/17 =100/17=quotient 5 and reminder 15.

remainder 15*10/17 = 150 /17= 8 qnd remainder 14

remainder14*10/17 = 140/17 =8 and remainder 4

Put all the qutients together in order, putting a decimal point after the 1st zero as below and you get the decimal value:

Therefore ,12/17= 0.70588 nearly still some remainder value we neglected.

Therefore, by looking at the decimal values of all fractions you can notice that  9/11 is the largest of the given 4 fractions.

(iii)By finding a common denominator, which is equivalent to LCM of denominators:

We can easily compare the fractions by their size of the numerator, when all  fractions are expressed in equivalent fraction with a common denominator. The common denominator is any common multiple or least common multiple of the denominators of thr fractions.

The Least Common Multiple (LCM) of denominators:

5,8,17,11 has the LCM=5*8*17*11=7480.

Therefore the equivalent fractions of the given fractions are as follows:

4/5  = 4*1496/(5*1496) = 5984/7480

5/8=5*935/(8*935)=4675/7480

12/17=12*440/(17*440)=5280/7480

9/11=9*680/(11*680)=6120/7480 largest numerator with common denominator 7480. Threfore, 9/11 is the lagest of the given fractions.

I suggest the first method for beginners with fractions. But it is easy when the number of fractions to be compared are considerably more.

Hope this helps.