You regularly need to recognize when one portion is greater or less than an additional fraction. Because a portion is a component of a whole, to find the greater portion you require to discover the fraction that contains much more of the whole. If the 2 fractions simplify to fractions with a common denominator, you can then compare numerators. If the denominators space different, you can uncover a usual denominator very first and then to compare the numerators.

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Two fractions room equivalent fractions once they represent the same component of a whole. Since equivalent fractions perform not constantly have the exact same numerator and denominator, one means to recognize if 2 fractions are identical is to uncover a usual denominator and rewrite each portion with that denominator. When the two fractions have actually the very same denominator, you can examine to check out if the numerators are equal. If they space equal, then the 2 fractions are equal as well.

One means to uncover a typical denominator is to inspect to view if one denominator is a aspect of the other denominator. If so, the better denominator have the right to be offered as the common denominator.


Example

Problem

Are

*
 and
*
 equivalent fractions?

Does

*
?

To settle this problem, uncover a typical denominator for the two fractions. This will assist you compare the two fractions.

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

*

Start with the portion .

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

The fraction  already has a denominator the 18, for this reason you deserve to leave it together is.

*
 does not equal

Compare the fractions. Currently that both fractions have actually the exact same denominator, 18, you deserve to compare numerators.

Answer

 and  are not tantamount fractions.


When one denominator is not a factor of the other denominator, girlfriend can find a usual denominator by multiplying the platform together.


Example

Problem

Determine even if it is

*
and
*
 are indistinguishable fractions.

6 • 10 = 60

Use 60 together a usual denominator.

*

Multiply the molecule

and denominator that

*

by 10 to obtain 60 in the denominator.

*

Multiply numerator and also denominator of  by 6.

*

Now that the denominators are the same, compare the numerators.

Answer

Yes,

*
 and  are identical fractions.

Since 30 is the worth of the numerator for both fractions, the two fractions space equal.


Notice in the above example you can use 30 as the least typical denominator due to the fact that both 6 and also 10 are components of 30. Any kind of common denominator will work.

In some instances you can simplify one or both that the fractions, i m sorry can result in a typical denominator.


Example

Problem

Determine even if it is

*
 and
*
 are identical fractions.

*

Simplify . Divide

the numerator and also denominator through 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 room the same.

Answer Yes, and  are tantamount fractions.


Note: In the example over you can have supplied the typical factor the 20 to simplify  directly come .

Determining tantamount Fractions

To identify whether or not two fractions room equivalent:

Step 1: Rewrite one or both of the fountain so that they have common denominators.

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

Which the the following fraction pairs are equivalent?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. Although the same numbers, 5 and also 7, are supplied in each fraction, the numerators and denominators are 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 perform not re-superstructure a typical multiple: 6 · 2 = 12, and 10 · 3 = 30. This method the fractions room not equivalent. The exactly answer is .

C)

Correct. Take it the fraction

*
 and multiply both the numerator and denominator by 4. You are left with the fraction
*
. This means that the two fractions room equivalent.

D)

Incorrect. The molecule of the two fractions room the same, however the denominators are different. This method the fractions room not equivalent. The correct answer is .

Comparing Fractions using


When provided two or much more fractions, it is often valuable to know which portion is better than or less than the other. Because that example, if the discount in one save is

*
 off the initial price and the discount in an additional store is  off the initial price, which store is providing a far better deal? to answer this question, and also others choose it, you can compare fractions.

*
*

To recognize which fraction is greater, you require to uncover a usual denominator. You have the right to then compare the fountain directly. Since 3 and also 4 space both components of 12, you will certainly divide the entirety into 12 parts, develop equivalent fractions because that

*
 and
*
, and also then compare.

*
*

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

*
.

*

As long as the denominators space the same, the fraction with the better numerator is the greater fraction, together it contains an ext parts of the whole. The portion with the lesser molecule is the lesser fraction as it includes fewer components of the whole.

Recall that the symbol method “greater than”. These symbols space inequality symbols. So, the true declare 3 3 is review as “5 is better than 3”. One means to help you psychic the distinction between the two signs is to think the the smaller end of the prize points come the lesser number.

As v comparing whole numbers, the inequality icons are supplied 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 are different, rewrite one or both fractions through a typical denominator.

Step 2: examine the numerators. If the denominators room the same, climate the portion with the better numerator is the better fraction. The portion with the lesser numerator is the lesser fraction. And, as listed above, if the numerators space equal, the fractions room equivalent.


Example

Problem

Use to to compare the two fractions

*
 and
*
.

Is

*
, or is
*
?

You cannot compare the fountain directly due to the fact that they have various denominators. You require to find a usual denominator because that the 2 fractions.

*

Since 5 is a factor of 20, you can use 20 together the usual denominator.

*

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

*

Compare the 2 fractions.

*
 is higher than
*
.

Answer

*

If

*
, climate
*
, since
*
.


Which the the following is a true statement?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect.

*
 is identical to
*
, and also since 25 > 24,
*
, which way
*
. The exactly answer is .

B)

Incorrect. Both fractions simplify to

*
, therefore one isn’t greater than or less than the other one. They are equivalent. The correct answer is .

C)

Incorrect. Finding a usual denominator, you deserve to compare

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

D)

Correct. Simple

*
, you get the equivalent portion . Because you still don’t have a usual denominator, compose as an equivalent portion with a denominator that 8:
*
. You find that
*
, therefore
*
 as well.

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Summary


You can compare two fractions with prefer denominators by comparing their numerators. The portion with the higher numerator is the higher fraction, together it contains more parts of the whole. The fraction with the lesser molecule is the lesser portion as it includes fewer components of the whole. If two fractions have actually the exact same denominator, then equal numerators show equivalent fractions.