You regularly need to recognize when one fraction is better or less than one more fraction. Due to the fact that a fraction is a component of a whole, to find the greater fraction you require to discover the portion that contains more of the whole. If the 2 fractions simplify to fractions v a common denominator, you deserve to then compare numerators. If the denominators room different, friend can discover a typical denominator very first and then compare the numerators.

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Two fractions space equivalent fractions once they stand for the same component of a whole. Because equivalent fractions perform not always have the same numerator and also denominator, one way to recognize if two fractions are equivalent is to find a typical denominator and also rewrite each portion with the denominator. As soon as the 2 fractions have actually the very same denominator, girlfriend can examine to check out if the numerators space equal. If they are equal, climate the two fractions room equal together well.

One means to uncover a common denominator is to check to check out if one denominator is a factor of the various other denominator. If so, the better denominator deserve to be provided as the usual denominator.


Example

Problem

Are

*
 and
*
 equivalent fractions?

Does

*
?

To resolve this problem, discover a usual denominator for the two fractions. This will assist you to compare the 2 fractions.

Since 6 is a element of 18, you can write both fractions v 18 together the denominator.

*

Start through the fraction .

Multiply the denominator, 6, by 3 to gain a new denominator that 18. Due to the fact that you main point the denominator by 3, friend must likewise multiply the numerator by 3.

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

*
 does no equal

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

Answer

 and  are not indistinguishable fractions.


When one denominator is no a variable of the other denominator, friend can discover a usual denominator by multiplying the platform together.


Example

Problem

Determine even if it is

*
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 of  by 6.

*

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

Answer

Yes,

*
 and  are identical fractions.

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


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

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


Example

Problem

Determine even if it is

*
 and
*
 are equivalent fractions.

*

Simplify . Divide

the numerator and denominator through the usual factor 10.

*

*
 is still no in lowest terms, so division the numerator and 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 equivalent fractions.


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

Determining equivalent Fractions

To determine whether or not 2 fractions space equivalent:

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

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

Which that the following portion pairs are equivalent?

A)

B)

C)

D)


Show/Hide Answer

A)

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

B)

Incorrect. 30 is divisible by 10, and 12 is divisible by 6. However, they carry out not re-superstructure a common multiple: 6 · 2 = 12, and 10 · 3 = 30. This method the fractions space not equivalent. The correct answer is .

C)

Correct. Take the portion

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

D)

Incorrect. The molecule of the two fractions room the same, yet the denominators space different. This method the fractions room not equivalent. The exactly answer is .

Comparing Fractions making use of


When given two or an ext fractions, that is often useful to know which fraction is better than or much less than the other. Because that example, if the discount in one store is

*
 off the original price and also the discount in another store is  off the original price, which store is offering a far better deal? come answer this question, and others prefer it, you have the right to compare fractions.

*
*

To determine which portion is greater, you need to discover a usual denominator. You have the right to then to compare the fountain directly. Because 3 and 4 space both factors of 12, you will divide the whole into 12 parts, develop equivalent fractions because that

*
 and
*
, and then compare.

*
*

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

*
.

*

As lengthy as the denominators space the same, the portion with the better numerator is the higher fraction, as it contains more parts of the whole. The fraction with the lesser molecule is the lesser fraction as it consists of fewer components of the whole.

Recall the the symbol means “greater than”. These symbols are inequality symbols. So, the true statement 3 3 is review as “5 is better than 3”. One method to aid you mental the distinction between the two signs is come think the the smaller finish of the price points to the lesser number.

As with comparing entirety numbers, the inequality icons are offered to show when one fraction is “greater than” or “less than” another fraction.

Comparing Fractions

To compare two fractions:

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

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


Example

Problem

Use to compare the two fractions

*
 and
*
.

Is

*
, or is
*
?

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

*

Since 5 is a aspect of 20, you have the right 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 greater than
*
.

Answer

*

If

*
, then
*
, due to the fact that
*
.


Which that the adhering to is a true statement?

A)

B)

C)

D)


Show/Hide Answer

A)

Incorrect.

*
 is identical to
*
, and since 25 > 24,
*
, which means
*
. The correct answer is .

B)

Incorrect. Both fractions simplify to

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

C)

Incorrect. Finding a common denominator, you have the right to compare

*
 to
*
, and also see the
*
, which method
*
. The exactly answer is .

D)

Correct. Simple

*
, you obtain the equivalent fraction . Since you tho don’t have a typical denominator, create as an equivalent portion with a denominator of 8:
*
. You find that
*
, so
*
 as well.

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Summary


You have the right to compare two fractions with like denominators by comparing their numerators. The portion with the greater numerator is the higher fraction, as it contains an ext parts that the whole. The fraction with the lesser molecule is the lesser portion as it consists of fewer parts of the whole. If two fractions have actually the same denominator, then equal numerators suggest equivalent fractions.