You regularly need to recognize when one fraction is higher or much less than one more fraction. Since a portion is a part of a whole, to discover the greater portion you need to uncover the fraction that contains much more of the whole. If the two fractions leveling to fractions through a common denominator, you deserve to then compare numerators. If the denominators room different, friend can uncover a common denominator first and then to compare the numerators.

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Two fractions space equivalent fractions once they stand for the same part of a whole. Because equivalent fractions do not constantly have the same numerator and denominator, one way to recognize if 2 fractions are equivalent is to uncover a typical denominator and rewrite each portion with the denominator. Once the 2 fractions have actually the exact same denominator, girlfriend can check to watch if the numerators are equal. If they space equal, climate the 2 fractions are equal together well.

One means to discover a common denominator is to examine to watch if one denominator is a aspect of the other denominator. If so, the higher denominator can be offered as the usual denominator.


Example

Problem

Are

*
 and
*
 equivalent fractions?

Does

*
?

To fix this problem, uncover a typical denominator for the 2 fractions. This will help you compare the 2 fractions.

Since 6 is a factor of 18, you have the right to write both fractions v 18 as the denominator.

*

Start with the portion .

Multiply the denominator, 6, by 3 to gain a brand-new denominator of 18. Because you main point the denominator by 3, girlfriend must likewise multiply the molecule by 3.

The fraction  already has actually a denominator that 18, for this reason you have the right to leave it together is.

*
 does not equal

Compare the fractions. Currently that both fractions have actually the very same denominator, 18, you can compare numerators.

Answer

 and  are not indistinguishable fractions.


When one denominator is not a variable of the other denominator, friend can discover a usual denominator by multiply the platform together.


Example

Problem

Determine whether

*
and
*
 are tantamount fractions.

6 • 10 = 60

Use 60 together a typical denominator.

*

Multiply the molecule

and denominator of

*

by 10 to get 60 in the denominator.

*

Multiply numerator and denominator of  by 6.

*

Now the the denominators space the same, compare the numerators.

Answer

Yes,

*
 and  are indistinguishable fractions.

Since 30 is the worth of the molecule for both fractions, the two fractions are equal.


Notice in the over example you deserve to use 30 together the least typical denominator due to the fact that both 6 and also 10 are determinants of 30. Any type of common denominator will work.

In some instances you can simplify one or both that the fractions, i beg your pardon can result in a usual denominator.


Example

Problem

Determine even if it is

*
 and
*
 are identical fractions.

*

Simplify . Divide

the numerator and also denominator by the usual factor 10.

*

*
 is still not in lowest terms, so division the numerator and the denominator again, this time by the common factor 2.

*

Compare the fractions. The numerators and denominators are the same.

Answer Yes, and also  are equivalent fractions.


Note: In the example above you could have provided the common factor the 20 to simplify  directly come .

Determining equivalent Fractions

To determine whether or not 2 fractions space equivalent:

Step 1: Rewrite one or both that the fractions so the they have usual denominators.

Step 2: compare the molecule to view if they have actually the same value. If so, then the fractions are equivalent.

Which of the following fraction pairs are equivalent?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. Return the same numbers, 5 and also 7, are supplied in every fraction, the numerators and also denominators room not equal, so the fractions can not be equivalent. The exactly answer is .

B)

Incorrect. 30 is divisible by 10, and also 12 is divisible by 6. However, they carry out not re-publishing a usual multiple: 6 · 2 = 12, and also 10 · 3 = 30. This means the fractions are not equivalent. The correct answer is .

C)

Correct. Take the portion

*
 and multiply both the numerator and denominator by 4. You space left v the fraction
*
. This way that the two fractions space equivalent.

D)

Incorrect. The molecule of the 2 fractions are the same, yet the denominators space different. This means the fractions space not equivalent. The exactly answer is .

Comparing Fractions using


When given two or much more fractions, it is often useful to recognize which fraction is higher than or less than the other. For example, if the discount in one store is

*
 off the original price and also the discount in an additional store is  off the initial price, which keep is giving a far better deal? come answer this question, and others like it, you have the right to compare fractions.

*
*

To identify which portion is greater, you need to discover a typical denominator. You can then compare the fractions directly. Due to the fact that 3 and 4 room both determinants of 12, you will divide the entirety into 12 parts, develop equivalent fractions for

*
 and
*
, and then compare.

*
*

Now you check out that  contains 4 components of 12, and  contains 3 components of 12. So,  is higher than

*
.

*

As lengthy as the denominators room the same, the fraction with the greater numerator is the higher fraction, together it contains more parts of the whole. The portion with the lesser numerator is the lesser portion as it includes fewer components of the whole.

Recall the the price way “greater than”. This symbols room inequality symbols. So, the true declare 3 3 is read as “5 is greater than 3”. One means to aid you remember the difference between the two symbols is come think the the smaller finish of the prize points come the lesser number.

As v comparing whole numbers, the inequality icons are offered to show when one fraction is “greater than” or “less than” an additional fraction.

Comparing Fractions

To compare 2 fractions:

Step 1: to compare denominators. If they room different, rewrite one or both fractions v a common denominator.

Step 2: check the numerators. If the denominators space the same, then the portion with the greater numerator is the higher fraction. The fraction with the lesser molecule is the lesser fraction. And, as listed above, if the numerators are equal, the fractions room equivalent.


Example

Problem

Use to compare the two fractions

*
 and
*
.

Is

*
, or is
*
?

You cannot to compare the fountain directly due to the fact that they have different denominators. You need to discover a typical denominator for the 2 fractions.

*

Since 5 is a element of 20, you have the right to use 20 as the common denominator.

*

Multiply the numerator and also denominator by 4 to develop an equivalent portion with a denominator that 20.

*

Compare the 2 fractions.

*
 is higher than
*
.

Answer

*

If

*
, climate
*
, because
*
.


Which of the complying with is a true statement?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect.

*
 is equivalent to
*
, and also since 25 > 24,
*
, which means
*
. The exactly answer is .

B)

Incorrect. Both fractions simplify to

*
, so one isn’t better than or much less than the other one. They room equivalent. The exactly answer is .

C)

Incorrect. Detect a common denominator, you can compare

*
 to
*
, and see that
*
, which method
*
. The correct answer is .

D)

Correct. Simple

*
, you acquire the equivalent fraction . Because you tho don’t have actually a common denominator, write as one equivalent portion with a denominator of 8:
*
. You uncover that
*
, so
*
 as well.

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Summary


You have the right to compare two fractions with like denominators by comparing your numerators. The fraction with the greater numerator is the greater fraction, together it contains much more parts of the whole. The fraction with the lesser molecule is the lesser portion as it includes fewer parts of the whole. If 2 fractions have the same denominator, then same numerators suggest equivalent fractions.