How do I compare fractions with unlike denominators

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lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

To compare fractions with unlike denominators, we have to determine their LCD (least common denominator).

For example: Compare `2/3` and `5/7` .    

The LCD of these two fractions is:

`3*7 = 21`

Next, determine the equivalent fractions of each when their denominator becomes 21.

To do so, multiply the first fraction `2/3` by `7/7` in order to have a denominator 21.

`2/3*7/7=14/21`

Also, multiply the second fraction `5/7` by `3/3` .

`5/7*3/3=15/21`

So the two fractions `2/3` and `5/7` when expressed using the LCD as their denominator, they become

`14/21` and `15/21` .

Now that they have same denominators, to compare them, refer to their numerators.

Since numerator of the first fraction is smaller compared to the numerator of the second fraction, then the first fraction (`14/21`) is less than the second fraction (`15/21`).

Thus, `2/3`  `lt`  `5/7` .

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

You multiply the denominator. Then multiply the numerator. You'll be able to compare the fractions with unlike denominators easily. There's a lot of ways to find out unlike denominators but this is just way one you'll easily find out. 1/10 and 2/20 you turn the 1/10 into 2/20. Make sure whatever you have done on the bottom you do towards to top.

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ik9744 | Student, Grade 9 | (Level 1) Valedictorian

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There is a lot of possible ways to solve any kind of math, it all has to do with the way a person thinks, and how they react to the way the math problem is laid out. Now that is said here is my answer:

To compare fractions with unlike denominators could be a whole lot of mess if you do it wrong, eventually leading your answer down the trash bin. I'll give some examples to you that people commonly mess up with.

Ex. 3/6 and comparing 1/2. Well people don't really mess up with this, but it's good to show this because you have two fractions that are equivalent. 3/6 = 1/2 but how would you compare it without knowing it is equivalent. A easy method is taking both the denominators and multiplying it by each other. 2 times 6 would be 12. Now people get mistaken by they think the answer would be 3/12 ans 1/12. Which is WRONG. If the denominator was multiplied by 2 you would multiply it by 2. Safe thing goes on the bottom goes towards to top. 3/6 = 3•2/6•2 = 6/12 = 1/2. Another way to do this is and easier because you wouldn't have to simplify it is turning the bigger denominator into the smaller denominator. Note this trick doesn't apply all the time, mostly 20% of the time. Yet this trick is very good to use, especially if you only have limited amount of time. 3/6 could go into 2, and 3 could go into 1 by multiplying it by 3. This doesn't happen often but when it does you'll get an easy answer.

Ex. 5/8 and comparing it to 1/23. This is what I usually fail on doing back in elementary school. This is what I usually do, I don't know if others do this but here we go. 8 almost makes it into 23... so 8 x 3 = 8/24 compared to 1/23

8/24 compared to 1/23 this is how I do it. 7/23 compared to 1/23. Which is absolutely wrong!

The real answer to this question is eight times twenty four is  192. Both denominator is 192.

/192       /192

Now multiply 1 by 8 and 5 by 23

115/192 and 8/192

By the way both can't be simplified.

Short Answer:

To be honest to easiest way to answer this is by multiplying the denominator by each other. 1/2 and 5/6 = 10/12 & 6/12

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

Posted on

When you compare fractions, you have to have a common denominator. When your fractions don't have the same denominator, you have to find the least common denominator or LCD. For example, if you have the fractions 1/4 and 1/3, you will have to find a number that both 4 and 3 go into or are divisible by. The easiest way to do that, with small numbers like this, is to multiply the two denominators together. This will give you and LCD of 12, however you can't forget to multiply the numerators (by 3 and 4) as well.

(1/4)*(3/3)

(1/3)*(4/4)

This gives you the the equivalent fractions of 3/12 and 4/12 which you can now compare.

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xlauren531x | eNotes Newbie

Posted on

To compare fractions with unlike denominators, you need to find a common denominator. If you find the least common denominator (LCD) it will be simpler and you wont have to simplify as much. With that said, you don't need to use the LCD to compare fractions. If you look at the denominators you can multiply tone two denominators together to get a common denominator  For instance if you are comparing 1/3 and 5/6 you could multiply 6 and 3 to get a common denominator of 18. That's not the LCD. If you look at 1/3 and 5/6 you see that 3 is a factor of 6 and can just use 6 as a common denominator which is also your LCD. You then would create an equivalent fraction to 1/3 with a denominator of 6 And you don't change 5/6 because it is already in the common denominator. 

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Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

If you have trouble finding the least common denominator just multiply one fraction by the denominator of the other. For instance...

`5/8 and 2/5`

`5/8 xx5/5 = 25/40`

`2/5 xx 8/8 = 16/40`

``Its just a convenient way to multiply by 1. 

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