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

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jeanine76 | eNotes Newbie

Posted August 18, 2009 at 11:18 PM via web

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

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neela | High School Teacher | Valedictorian

Posted August 18, 2009 at 11:38 PM (Answer #1)

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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.

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suzyq1967 | High School Teacher | eNotes Newbie

Posted August 18, 2009 at 11:34 PM (Answer #2)

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just divide the top (numerator) by the bottom (denominator) to get a decimal. think of each resulting decimal in terms of dollars and cents. The one that represents more money is the biggest.

in this case 9/11 is biggest because 9 divided by 11 is more than .81 and the next biggest is 4/5 since 4 divided by 5 is .8 which is the same as .80

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Lorraine Caplan | College Teacher | (Level 2) Senior Educator

Posted August 18, 2009 at 11:28 PM (Answer #4)

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The  best way for you to answer this question is to change each of these fractions to decimal form.  Some people do not understand that every fraction can be made into a decimal because every fraction is a division problem.  Let's take 4/5 as an example.  If you divide 5 into 4, you will get 0.8 as an answer.  If you use this method to change every fraction to a decimal, you will be able to see which is the largest. 

It is important to understand the relationship between fractions and decimals because sometimes it is easier to think in decimal form and sometimes it is easier to think in fraction form, depending on our task. We all need to be able to move back and forth between them.  Take money, for example.  It is easier for us to calculate decimals when we are dealing with money. If we had to add or subtract in fractions, it would probably take longer.  But when we are cooking or baking, we use fractions because it would take us longer to figure out ingredients using decimals.  If you want to double a recipe that uses 1/3 cup of milk, you will be much happier calculating that 1/3 + 1/3 = 2/3 than you would calculating 0.33 + 0.33. 

Work on understanding this relationship, and you will be much more comfortable in the world of math and the world in which we need math. 

Good luck! 

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atyourservice | Student, Grade 10 | Valedictorian

Posted April 17, 2014 at 8:02 PM (Answer #6)

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4/5, 5/8, 12/17, 9/11

4/5 = .8

5/8 = .625

12/17 = .705882353

9/11 = .818181818

9/11 is the largest number

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zumba96 | Student, Grade 11 | Valedictorian

Posted May 16, 2014 at 12:33 AM (Answer #7)

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4/5, 5/8, 12/17, 9/11

4/5 = .8

5/8=.625

12/17=.706

9/11=.8181..

Clearly 9/11 is the largest number

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jess1999 | Student, Grade 9 | Valedictorian

Posted June 19, 2014 at 5:02 AM (Answer #8)

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4/5 , 5/8 , 12/17 , 9/11 to find which of these fraction is larger, you can change these fractions into decimals.

4 / 5 = .8

5 / 8 = .625

12 / 17 = .706

9 / 11 = 8181

After changing these fractions into decimals you can see that 9/11 is larger than the rest of the other fractions.

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ik9744 | TA , Grade 9 | Valedictorian

Posted June 26, 2014 at 6:05 AM (Answer #9)

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Change the fractions into decimals.

4/5 = .8

5/8 = .625

12/17 = .706

9/11 = .8181

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