What Is The Biggest Fraction

Comparing Fractions

Learning Objective(south)

· Determine whether 2 fractions are equivalent.

· Apply > or < to compare fractions.

Introduction

You often demand to know when i fraction is greater or less than another fraction. Since a fraction is a office of a whole, to find the greater fraction you demand to find the fraction that contains more of the whole. If the two fractions simplify to fractions with a common denominator, you can then compare numerators. If the denominators are different, you can discover a common denominator first and and then compare the numerators.

Determining Equivalent Fractions

Two fractions are equivalent fractions when they represent the same part of a whole. Since equivalent fractions do not always have the same numerator and denominator, 1 manner to make up one's mind if two fractions are equivalent is to detect a mutual denominator and rewrite each fraction with that denominator. One time the two fractions take the aforementioned denominator, you tin check to come across if the numerators are equal. If they are equal, then the ii fractions are equal besides.

1 style to notice a common denominator is to check to see if one denominator is a factor of the other denominator. If so, the greater denominator can be used as the common denominator.

Case
Problem	Are  and  equivalent fractions?
	Does ?	To solve this problem, find a common denominator for the ii fractions. This will help yous compare the two fractions. Since 6 is a factor of eighteen, you tin write both fractions with 18 equally the denominator.
		Commencement with the fraction . Multiply the denominator, 6, by 3 to get a new denominator of 18. Since you multiply the denominator past 3, you must likewise multiply the numerator by iii.
		The fraction already has a denominator of 18, so you tin leave it as is.
	does not equal	Compare the fractions. Now that both fractions have the same denominator, 18, you tin compare numerators.
Answer	and are not equivalent fractions.

When one denominator is not a factor of the other denominator, you can find a common denominator by multiplying the denominators together.

Case
Problem	Determine whether and  are equivalent fractions.
	6 • 10 = threescore	Utilise 60 as a common denominator.
		Multiply the numerator and denominator of by x to get 60 in the denominator.
		Multiply numerator and denominator of  by 6.
		Now that the denominators are the same, compare the numerators.
Answer	Aye,  and  are equivalent fractions.	Since thirty is the value of the numerator for both fractions, the two fractions are equal.

Find in the above case you can use thirty as the least common denominator since both 6 and x are factors of 30. Whatsoever mutual denominator will work.

In some cases yous can simplify one or both of the fractions, which tin can result in a mutual denominator.

Example
Trouble	Determine whether  and  are equivalent fractions.
		Simplify . Divide the numerator and denominator by the common factor 10.
		is nevertheless not in lowest terms, and so divide the numerator and the denominator again, this time by the mutual gene 2.
		Compare the fractions. The numerators and denominators are the aforementioned.
Answer Yes, and  are equivalent fractions.

Note: In the example above you could have used the mutual factor of xx to simplify directly to .

Determining Equivalent Fractions

To determine whether or not two fractions are equivalent:

Step 1: Rewrite one or both of the fractions so that they have mutual denominators.

Footstep 2: Compare the numerators to see if they have the same value. If and then, then the fractions are equivalent.

Which of the following fraction pairs are equivalent?

A)

B)

C)

D)

Prove/Hide Answer

A)

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

B)

Incorrect. xxx is divisible by 10, and 12 is divisible past 6. Yet, they exercise not share a common multiple: 6 · 2 = 12, and 10 · three = 30. This ways the fractions are not equivalent. The correct answer is .

C)

Correct. Take the fraction  and multiply both the numerator and denominator by 4. Yous are left with the fraction . This means that the ii fractions are equivalent.

D)

Wrong. The numerators of the 2 fractions are the same, simply the denominators are different. This means the fractions are not equivalent. The right answer is .

Comparison Fractions Using < and >

When given two or more fractions, it is often useful to know which fraction is greater than or less than the other. For example, if the discount in 1 shop is  off the original cost and the discount in some other store is  off the original toll, which store is offer a better deal? To answer this question, and others like information technology, yous tin can compare fractions.

To determine which fraction is greater, you need to find a common denominator. Yous can then compare the fractions directly. Since three and four are both factors of 12, you volition split the whole into 12 parts, create equivalent fractions for  and , and then compare.

Now you lot see that  contains 4 parts of 12, and  contains iii parts of 12. So,  is greater than .

As long as the denominators are the same, the fraction with the greater numerator is the greater fraction, every bit it contains more parts of the whole. The fraction with the lesser numerator is the lesser fraction every bit it contains fewer parts of the whole.

Recall that the symbol < ways "less than", and the symbol > means "greater than". These symbols are inequality symbols. So, the true statement 3 < 8 is read as "3 is less than 8" and the statement 5 > 3 is read as "5 is greater than three". I fashion to help you lot call back the stardom betwixt the two symbols is to think that the smaller end of the symbol points to the bottom number.

Every bit with comparing whole numbers, the inequality symbols are used to show when i fraction is "greater than" or "less than" another fraction.

Comparison Fractions

To compare 2 fractions:

Footstep 1: Compare denominators. If they are different, rewrite 1 or both fractions with a common denominator.

Stride 2: Cheque the numerators. If the denominators are the same, then the fraction with the greater numerator is the greater fraction. The fraction with the lesser numerator is the lesser fraction. And, equally noted in a higher place, if the numerators are equal, the fractions are equivalent.

Case
Problem	Use < or > to compare the two fractions  and .
	Is , or is ?	You lot cannot compare the fractions straight because they have different denominators. You demand to detect a mutual denominator for the 2 fractions.
		Since 5 is a gene of 20, you can utilize twenty every bit the common denominator.
		Multiply the numerator and denominator past 4 to create an equivalent fraction with a denominator of 20.
		Compare the two fractions.  is greater than .
Answer		If , then , since .

Which of the following is a true argument?

A)

B)

C)

D)

Prove/Hide Answer

A)

Wrong.  is equivalent to , and since 25 > 24, , which means . The correct answer is .

B)

Incorrect. Both fractions simplify to , and then one isn't greater than or less than the other one. They are equivalent. The correct answer is .

C)

Incorrect. Finding a common denominator, you tin compare  to , and come across that , which means . The correct answer is .

D)

Correct. Simplifying , you get the equivalent fraction . Since you still don't have a common denominator, write as an equivalent fraction with a denominator of eight: . You discover that , so  as well.

Summary

Y'all can compare two fractions with like denominators by comparing their numerators. The fraction with the greater numerator is the greater fraction, equally information technology contains more parts of the whole. The fraction with the lesser numerator is the lesser fraction every bit information technology contains fewer parts of the whole. If ii fractions accept the same denominator, and so equal numerators indicate equivalent fractions.

What Is The Biggest Fraction,

Source: http://content.nroc.org/DevelopmentalMath/COURSE_TEXT_RESOURCE/U02_L1_T5_text_final.html

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