You often need to understand when one portion is greater or less than another fraction. Because a fraction is a part of a whole, to find the greater portion you need to uncover the fraction that contains more of the whole. If the 2 fractions leveling to fractions through a common denominator, you have the right to then to compare numerators. If the denominators space different, girlfriend can find a usual denominator an initial and then compare the numerators.

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Two fractions are equivalent fractions as soon as they stand for the same component of a whole. Since equivalent fractions execute not constantly have the same numerator and also denominator, one means to identify if two fractions are identical is to find a typical denominator and rewrite each fraction with the denominator. When the 2 fractions have actually the very same denominator, girlfriend can inspect to watch if the numerators room equal. If they are equal, then the 2 fractions space equal as well.

One way to uncover a usual denominator is to examine to watch if one denominator is a factor of the various other denominator. If so, the greater denominator deserve to be provided as the typical denominator.


Example

Problem

Are

*
 and
*
 equivalent fractions?

Does

*
?

To deal with this problem, find a typical denominator because that the two fractions. This will aid you to compare the 2 fractions.

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

*

Start through the portion .

Multiply the denominator, 6, by 3 to obtain a new denominator of 18. Due to the fact that you main point the denominator by 3, you must additionally multiply the molecule by 3.

The fraction  already has actually a denominator the 18, so 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 factor of the various other denominator, girlfriend can find a common denominator by multiply the platform together.


Example

Problem

Determine whether

*
and
*
 are identical fractions.

6 • 10 = 60

Use 60 as a typical denominator.

*

Multiply the numerator

and denominator that

*

by 10 to gain 60 in the denominator.

*

Multiply numerator and denominator the  by 6.

*

Now the the denominators room the same, to compare the numerators.

Answer

Yes,

*
 and  are indistinguishable fractions.

Since 30 is the worth of the molecule for both fractions, the 2 fractions room equal.

Notice in the above example you can use 30 as the least common denominator since both 6 and also 10 are components of 30. Any type of common denominator will certainly work.

In some instances you deserve to simplify one or both the the fractions, which can an outcome in a common denominator.


Example

Problem

Determine whether

*
 and
*
 are equivalent fractions.

*

Simplify . Divide

the numerator and denominator by the common factor 10.

*

*
 is still not in shortest terms, so divide the numerator and the denominator again, this time through the common factor 2.

*

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

Answer Yes, and  are tantamount fractions.

Note: In the example above you might have provided the usual factor that 20 to leveling  directly come .

Determining indistinguishable Fractions

To identify whether or not two fractions are equivalent:

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

Step 2: compare the numerators to watch if they have actually the very same value. If so, climate the fractions space equivalent.

Which that the following fraction pairs are equivalent?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. Although the same numbers, 5 and also 7, are used in each fraction, the numerators and also denominators room not equal, so the fractions cannot be equivalent. The correct answer is .

B)

Incorrect. 30 is divisible by 10, and also 12 is divisible by 6. However, they perform not share a usual multiple: 6 · 2 = 12, and also 10 · 3 = 30. This means the fractions space not equivalent. The correct answer is .

C)

Correct. Take it the fraction

*
 and multiply both the numerator and denominator by 4. You space left through the portion
*
. This method that the two fractions space equivalent.

D)

Incorrect. The numerators of the two fractions are the same, but the denominators are different. This means the fractions space not equivalent. The exactly answer is .

Comparing Fractions utilizing


When offered two or much more fractions, it is often helpful to know which fraction is greater than or less than the other. Because that example, if the discount in one keep is

*
 off the initial price and also the discount in another store is  off the initial price, which store is supplying a far better deal? come answer this question, and others like it, you can compare fractions.

*
*

To determine which portion is greater, you need to uncover a common denominator. You can then compare the fountain directly. Since 3 and also 4 are both determinants of 12, you will certainly divide the entirety into 12 parts, create equivalent fractions for

*
 and
*
, and then compare.

*
*

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

*
.

*

As long as the denominators are the same, the portion with the higher numerator is the greater fraction, as it contains more parts that the whole. The fraction with the lesser molecule is the lesser portion as it includes fewer parts of the whole.

Recall that the prize means “greater than”. These symbols are inequality symbols. So, the true statement 3 3 is review as “5 is better than 3”. One means to assist you psychic the difference between the two signs is come think that the smaller finish of the prize points to the lesser number.

As through comparing entirety numbers, the inequality icons are provided to show when one fraction is “greater than” or “less than” one more fraction.

Comparing Fractions

To compare 2 fractions:

Step 1: to compare denominators. If they are different, rewrite one or both fractions with a usual denominator.

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


Example

Problem

Use to compare the two fractions

*
 and
*
.

Is

*
, or is
*
?

You cannot to compare the fountain directly since they have different denominators. You need to uncover a usual denominator because that the 2 fractions.

*

Since 5 is a aspect of 20, you deserve to use 20 as the common denominator.

*

Multiply the numerator and denominator by 4 to develop an equivalent fraction with a denominator of 20.

*

Compare the two fractions.

*
 is better than
*
.

Answer

*

If

*
, climate
*
, because
*
.

Which of the following is a true statement?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect.

*
 is tantamount to
*
, and also since 25 > 24,
*
, which way
*
. The correct answer is .

B)

Incorrect. Both fractions simplify to

*
, so one isn’t greater than or much less than the other one. They space equivalent. The correct answer is .

C)

Incorrect. Recognize a usual denominator, you deserve to compare

*
 to
*
, and also see that
*
, which way
*
. The exactly answer is .

D)

Correct. Simple

*
, you gain the equivalent fraction . Since you still don’t have a usual denominator, write as an equivalent portion with a denominator the 8:
*
. You discover that
*
, therefore
*
 as well.

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Summary


You can compare two fractions with favor denominators through comparing your numerators. The portion with the better numerator is the higher fraction, together it contains more parts that the whole. The portion with the lesser molecule is the lesser fraction as it has fewer components of the whole. If two fractions have the same denominator, then same numerators show equivalent fractions.