You frequently need to understand when one fraction is better or less than an additional fraction. Because a portion is a component of a whole, to uncover the greater fraction you require to discover the portion that contains more of the whole. If the 2 fractions simplify to fractions through a common denominator, you deserve to then to compare numerators. If the denominators space different, you can discover a common denominator an initial and then to compare the numerators.

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Two fractions are equivalent fractions when they stand for the same component of a whole. Due to the fact that equivalent fractions do not always have the same numerator and denominator, one way to identify if 2 fractions are identical is to uncover a usual denominator and rewrite each fraction with the denominator. When the two fractions have the exact same denominator, you can inspect to watch if the numerators are equal. If they room equal, then the 2 fractions are equal as well.

One means to find a typical denominator is to examine to see if one denominator is a element of the various other denominator. If so, the greater denominator have the right to be supplied as the typical denominator.


Example

Problem

Are

*
 and
*
 equivalent fractions?

Does

*
?

To fix this problem, find a common denominator for the two fractions. This will help you to compare the 2 fractions.

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

*

Start through the portion .

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

The portion  already has actually a denominator the 18, for this reason you can leave it together is.

*
 does no equal

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

Answer

 and  are not indistinguishable fractions.


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


Example

Problem

Determine whether

*
and
*
 are equivalent fractions.

6 • 10 = 60

Use 60 together a usual denominator.

*

Multiply the numerator

and denominator the

*

by 10 to gain 60 in the denominator.

*

Multiply numerator and denominator that  by 6.

*

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

Answer

Yes,

*
 and  are equivalent fractions.

Since 30 is the value of the numerator for both fractions, the two fractions are equal.


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

In some cases you have the right to simplify one or both the the fractions, i m sorry can result in a typical denominator.


Example

Problem

Determine even if it is

*
 and
*
 are indistinguishable fractions.

*

Simplify . Divide

the numerator and denominator by the typical factor 10.

*

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

*

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

Answer Yes, and also  are identical fractions.


Note: In the example over you might have offered the typical factor that 20 to leveling  directly come .

Determining identical Fractions

To determine whether or not 2 fractions space equivalent:

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

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

Which of the following portion pairs room equivalent?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. Return the very same numbers, 5 and 7, are supplied in every fraction, the numerators and denominators are not equal, for this reason the fractions cannot be equivalent. The correct answer is .

B)

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

C)

Correct. Take it the fraction

*
 and main point both the numerator and also denominator through 4. You room left through the fraction
*
. This way that the 2 fractions room equivalent.

D)

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

Comparing Fractions utilizing


When offered two or an ext fractions, that is often beneficial to understand which portion is better than or less than the other. For example, if the discount in one save is

*
 off the original price and also the discount in another store is  off the initial price, which save is giving a better deal? to answer this question, and also others prefer it, you can compare fractions.

*
*

To determine which fraction is greater, you require to discover a common denominator. You deserve to then compare the fractions directly. Because 3 and also 4 space both determinants of 12, you will divide the whole into 12 parts, develop equivalent fractions because that

*
 and
*
, and then compare.

*
*

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

*
.

*

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

Recall that the symbol method “greater than”. This symbols space inequality symbols. So, the true statement 3 3 is read as “5 is greater than 3”. One method to help you remember the difference between the two icons is to think the the smaller finish of the price points come the lesser number.

As with comparing totality numbers, the inequality icons are provided to display when one fraction is “greater than” or “less than” an additional fraction.

Comparing Fractions

To compare two fractions:

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

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


Example

Problem

Use to compare the 2 fractions

*
 and
*
.

Is

*
, or is
*
?

You cannot compare the fractions directly because they have various denominators. You require to find a common denominator for the 2 fractions.

*

Since 5 is a factor of 20, you deserve to use 20 together the typical denominator.

*

Multiply the numerator and also denominator through 4 to produce an equivalent fraction with a denominator of 20.

*

Compare the two 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 tantamount to
*
, and since 25 > 24,
*
, which method
*
. The exactly answer is .

B)

Incorrect. Both fractions leveling to

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

C)

Incorrect. Finding a common denominator, you can compare

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

D)

Correct. Simplifying

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

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Summary


You deserve to compare 2 fractions with like denominators by comparing their numerators. The fraction with the better numerator is the better fraction, together it contains more parts the the whole. The fraction with the lesser molecule is the lesser fraction as it consists of fewer components of the whole. If two fractions have actually the very same denominator, then equal numerators indicate equivalent fractions.