Better Students Ask More Questions.
Which is the largest number? 4/5, 5/8, 12/17, 9/11
3 Answers | add yours
High School Teacher
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.
12/17 = 0.70588...
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
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.
Posted by neela on August 18, 2009 at 11:38 PM (Answer #1)
High School Teacher
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
Posted by suzyq1967 on August 18, 2009 at 11:34 PM (Answer #2)
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.
Posted by speamerfam on August 18, 2009 at 11:28 PM (Answer #4)
Join to answer this question
Join a community of thousands of dedicated teachers and students.