You regularly need to understand when one portion is higher or much less than one more fraction. Since a fraction is a component of a whole, to find the greater fraction you require to uncover the fraction that contains much more of the whole. If the two fractions leveling to fractions with a common denominator, you have the right to then compare numerators. If the denominators room different, you can find a typical denominator first and then to compare the numerators.

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Two fractions room equivalent fractions as soon as they stand for the same part of a whole. Due to the fact that equivalent fractions execute not constantly have the very same numerator and also denominator, one means to recognize if 2 fractions are equivalent is to uncover a common denominator and also rewrite each portion with the denominator. When the 2 fractions have actually the very same denominator, friend can check to see if the numerators space equal. If they space equal, climate the 2 fractions are equal as well.

One method to uncover a common denominator is to examine to watch if one denominator is a variable of the various other denominator. If so, the better denominator can be offered as the common denominator.


Example

Problem

Are

*
 and
*
 equivalent fractions?

Does

*
?

To resolve this problem, uncover a common denominator for the two fractions. This will help you compare the two fractions.

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

*

Start with the fraction .

Multiply the denominator, 6, through 3 to acquire a brand-new denominator that 18. Because you main point the denominator by 3, friend must likewise multiply the molecule by 3.

The fraction  already has a denominator that 18, so you deserve to leave it together is.

*
 does not equal

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

Answer

 and  are not indistinguishable fractions.


When one denominator is no a aspect of the other denominator, you can find a usual denominator by multiplying the denominators together.


Example

Problem

Determine even if it is

*
and
*
 are equivalent fractions.

6 • 10 = 60

Use 60 as a common denominator.

*

Multiply the molecule

and denominator of

*

by 10 to get 60 in the denominator.

*

Multiply numerator and denominator the  by 6.

*

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

Answer

Yes,

*
 and  are equivalent fractions.

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


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

In some situations you have the right to simplify one or both of the fractions, which can an outcome in a common denominator.


Example

Problem

Determine whether

*
 and
*
 are equivalent fractions.

*

Simplify . Divide

the numerator and also denominator by the common factor 10.

*

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

*

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

Answer Yes, and also  are tantamount fractions.


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

Determining indistinguishable Fractions

To determine whether or not two fractions are equivalent:

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

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

Which of the following portion pairs space equivalent?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect. Back the very same numbers, 5 and 7, are provided in every fraction, the numerators and also denominators space not equal, therefore the fractions cannot be equivalent. The correct answer is .

B)

Incorrect. 30 is divisible by 10, and 12 is divisible by 6. However, they perform not re-superstructure a common multiple: 6 · 2 = 12, and 10 · 3 = 30. This means the fractions are not equivalent. The exactly answer is .

C)

Correct. Take it the portion

*
 and main point both the numerator and denominator through 4. You space left with the fraction
*
. This method that the two fractions are equivalent.

D)

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

Comparing Fractions utilizing


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

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

*
*

To recognize which portion is greater, you need to uncover a common denominator. You can then to compare the fractions directly. Because 3 and also 4 room both determinants of 12, you will certainly divide the whole into 12 parts, produce equivalent fractions because that

*
 and
*
, and then compare.

*
*

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

*
.

*

As long as the denominators space the same, the fraction with the better numerator is the better fraction, as it contains much more parts of the whole. The portion with the lesser numerator is the lesser portion as it contains fewer parts of the whole.

Recall that the prize way “greater than”. These symbols are inequality symbols. So, the true explain 3 3 is review as “5 is higher than 3”. One method to assist you psychic the difference between the two icons is to think the the smaller end of the price points come the lesser number.

As through comparing entirety numbers, the inequality signs are supplied to display when one portion is “greater than” or “less than” one more fraction.

Comparing Fractions

To compare two 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 fraction with the higher numerator is the higher fraction. The fraction with the lesser molecule is the lesser fraction. And, as detailed above, if the numerators space equal, the fractions are equivalent.


Example

Problem

Use 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 for the two fractions.

*

Since 5 is a aspect of 20, you can use 20 together the typical denominator.

*

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

*

Compare the two fractions.

*
 is higher than
*
.

Answer

*

If

*
, then
*
, because
*
.


Which of the complying with 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

*
, for this reason one isn’t better than or less than the other one. They room equivalent. The correct answer is .

C)

Incorrect. Detect a typical denominator, you deserve to compare

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

D)

Correct. Simplifying

*
, you acquire the equivalent fraction . Due to the fact that you tho don’t have a usual denominator, create as one equivalent portion with a denominator the 8:
*
. You find that
*
, for this reason
*
 as well.

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Summary


You have the right to compare 2 fractions with choose denominators through comparing their numerators. The fraction with the greater numerator is the better fraction, as it contains more parts of the whole. The portion with the lesser numerator is the lesser portion as it contains fewer parts of the whole. If 2 fractions have the very same denominator, then same numerators suggest equivalent fractions.