order fractions from least to greatest?

Question

order these fractions from least to greatest explain the stragety you usede 3/11, 1/8, 2/9

Answer 1

easiest way when you have 3 is to change to decimals
3/11=.2727272727...
1/8=.125
2/9=.2222...
compare decimal places
.125 smallest, .222...next, .272727 biggest
1/8,2/9,3/11
another way...rewrite with common denominator
just multiply 11*8*9=792
3/11=216/792
1/8=99/792
2/9=176/792
so smallest 1/8 then 2/9 then 3/11

Answer 2

First, you must convert these fractions to a special type of equivalent fractions (i.e. 1/2 = 2/4 or 3/6 ...). The type of fractions we are going for are called fractions of a common base.

For example, if you wanted to see which of 2/5 and 1/2 was bigger, you make 2/5 = 4/10 and 1/2 = 5/10. The 1/10 here you can think of as being one unit "piece" or "thing". So then the answer boils down to--which is more: 4 things, or 5 things? Obviously, it's 5 things. The 5 things = 5/10 = 1/2, so 1/2 is the greater of the two.

Those were simpler numbers, now we'll apply it the numbers you gave. There is a strategy for finding the SMALLEST common base (i.e. bottom part of the fraction) called finding the least common multiple. A simpler strategy can find a common base, though not necessarily the smallest one: simply multiply together the bases of all the numbers. Here that's 11 * 8 * 9 = 792 (for your information, this also happens to be the smallest one).

Next, you multiply each of the numbers so it's now expressed in that common base. For example, to get the bottom 11 of 3/11 to become 792, you times it by 8 * 9 = 72. We also times 3 by 72 so it's still essentially the same fraction (that is, we times the original fraction by 72/72 = 1, and multiplying any number by one leaves it unchanged). Thus, we have 3/11 = 216/792, 1/8 = 99/792, and 2/9 = 176/792.

This problem, like the earlier problem boils down to ranking which are biggest out of: 216, 99, and 176. It's trivially 99, then 176, and then 216. And going back, those numbers correspond to 1/8, 2/9, and 3/11. Hope that answers it for you!

Answer 3

The only way you can order fractions by looking at them is if they all have the same denominator. Then the smaller the numerator, the smaller the fraction. So convert these 3 fractions to have the same denominator.

The current denominators are 11, 8, and 9. The simplest common denominator (which might not be the lowest, but that's OK), is 11*8*9. So multiply the top and bottom of the first fraction by 8*9, the second by 11*9, and the third by 11*8:

3*8*9 / 8*9*11
1*9*11 / 8*9*11
2*8*11 / 8*9*11

Now multiply the numbers through:

216 / 792
99 / 792
176 / 792

We know 99 < 176 < 216. So to rearrange these from lowest to highest, write down the second one, followed by the third one, and then the first one. This means the final answer is 1/8, 2/9, 3/11.

An alternative way is to write the fractions as decimals, then compare the corresponding decimals. But you might have had this as an assigment to help teach how to convert fractions, so the expected method might be the first one.

Answer 4

If you want to visually see the order, then you must achieve a common denominator for each fraction.

3/11, 1/8, 2/9 at first glance do not seem to have an easier denominator than 11*8*9=792

3/11 = ? / 792 (Using the rules of equivalent fractions, you would say, what happened to the 11 to get 792 -well, it was multiplied by 8*9. So what was done to the denominator must be done to the numerator. 3*8*9=216

3/11 = 216/792

1/8 = ?/792
What was done to the 8 - it was multiplied by 11*9

so, 1*9*11 = 99

1/8 = 99/792

And

2/9 = ?/792

What did I do to the 9? It was multiplied by 8*11, so 2*8*11=176

2/9 = 176/792

So if we looked at all the new equivalent fractions, they would be

3/11 = 216/792
1/8 = 99/792
2/9 = 176/792

Compare the three fractions and the order is 99/792, 176/792 , and 216/792.

Therefore the fraction order is 1/8, 2/9, 3/11

Hope that helped.

Answer 5

3/11 = .2727
1/8 = .125
2/9 = .222

using a calculator you can find those out

therefore, in order the fractions are: 1/8, 2/9, 3/11

Answer 6

well firstly you need to find a common denominator for all these fractions.for this Q the common denominator is 12. So, 3/12 , 1/6 = 2/12 as you need to times the numerator by 2 ... whatever yu times the denominator by you need to times the numerator by in order to arrange the fractions. 2/3 = 8/12 so in order, least first it is, 1/6 , 3/12 , 2/3

Answer 7

Find the common denominator (i.e. 792).
3/11 = 216/792
1/8 = 99/722
2/9 = 176/722

Hence, the answer is 1/8, 2/9, 3/11.

Answer 8

tip:- same denominator, compare numerator

3/11, 1/8
= 24/88, 11/88
therefore, 3/11 is bigger than 1/8

1/8, 2/9
= 9/81, 16/81
therefore, 2/9 is bigger than 1/8

3/11, 2/9
=27/99, 22/99
therefore, 3/11 is bigger than 2/9

Ans:
1/8, 2/9, 3/11

Answer 9

1/8= .125
2/9= .222222..
3/11= .272727...

1/8 < 2/9 < 3/11

Answer 10

1/8, 2/9, 3/11

Strategy:
1+1 = 2
8+1 = 0
1/1 is greater than 1/8
Therefore, 2/9 is bigger than 1/8

2+1 = 3
9+2 = 11
1/2 is greater than 2/9
Therefoer, 3/11 is bigger than 2/9.