Comparing Fractions
TotalFinder 1.12.3. Jul 11, 2007 1.420. GBM Home combines all data protection needs in one simple solution for all users. WorshipCenter Pro Oct 19. TotalFinder 1.11.7 Cracked for macOS. Mac Apps Lingki-July 14, 2020 0. TotalFinder application delivers exceptional performance, user-friendly interface, compact,.
Learning Objective(s)
·Determine whether two fractions are equivalent.
·Use > or < to compare fractions.
You often need to know when one fraction is greater or less than another fraction. Since a fraction is a part of a whole, to find the greater fraction you need 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 find a common denominator first 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, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator. Once the two fractions have the same denominator, you can check to see if the numerators are equal. If they are equal, then the two fractions are equal as well.
One way to find 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.
Example | |
Problem | Are and equivalent fractions? |
Does ? | To solve this problem, find a common denominator for the two fractions. This will help you compare the two fractions. Since 6 is a factor of 18, you can write both fractions with 18 as the denominator. |
Start with the fraction . Multiply the denominator, 6, by 3 to get a new denominator of 18. Since you multiply the denominator by 3, you must also multiply the numerator by 3. | |
The fraction already has a denominator of 18, so you can leave it as is. | |
does not equal | Compare the fractions. Now that both fractions have the same denominator, 18, you can compare numerators. |
Answer | andare 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.
Example | ||
Problem | Determine whether and are equivalent fractions. | |
6 • 10 = 60 | Use 60 as a common denominator. | |
Multiply the numerator and denominator of by 10 to get 60 in the denominator. | ||
Multiply numerator and denominator of by 6. | ||
Exactscan pro 17 4 18 – powerful fast document scanning. Now that the denominators are 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 above example you can use 30 as the least common denominator since both 6 and 10 are factors of 30. Any common denominator will work.
In some cases you can simplify one or both of the fractions, which can result in a common denominator.
Iina 1 0 6 grams. Example | |
Problem | Determine whether and are equivalent fractions. |
Simplify . Divide the numerator and denominator by the common factor 10. | |
is still not in lowest terms, so divide the numerator and the denominator again, this time by the common factor 2. | |
Compare the fractions. The numerators and denominators are the same. | |
Answer Yes, and are equivalent fractions. |
Note: In the example above you could have used the common factor of 20 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 common denominators. Step 2: Compare the numerators to see if they have the same value. If so, then the fractions are equivalent. |
Which of the following fraction pairs are equivalent? A) B) C) D) |
Totalfinder 1 11 5 Equals Mm
Comparing 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 one store is off the original price and the discount in another store is off the original price, which store is offering a better deal? To answer this question, and others like it, you can compare fractions.
To determine which fraction is greater, you need to find a common denominator. You can then compare the fractions directly. Since 3 and 4 are both factors of 12, you will divide the whole into 12 parts, create equivalent fractions for and , and then compare.
Now you see that contains 4 parts of 12, and contains 3 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, as it contains more parts of the whole. The fraction with the lesser numerator is the lesser fraction as it contains fewer parts of the whole.
Recall that the symbol < means '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 3'. One way to help you remember the distinction between the two symbols is to think that the smaller end of the symbol points to the lesser number.
Totalfinder 1 11 5 Equals What Fraction
As with comparing whole numbers, the inequality symbols are used to show when one fraction is 'greater than' or 'less than' another fraction.
Comparing Fractions To compare two fractions: Step 1: Compare denominators. If they are different, rewrite one or both fractions with a common denominator. Step 2: Check 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, as noted above, if the numerators are equal, the fractions are equivalent. |
Example | |
Problem | Use < or > to compare the two fractions and . |
Is , or is ? | You cannot compare the fractions directly because they have different denominators. You need to find a common denominator for the two fractions. |
Since 5 is a factor of 20, you can use 20 as the common denominator. | |
Multiply the numerator and denominator by 4 to create an equivalent fraction with a denominator of 20. | |
Compare the two fractions. is greater than . | |
Answer | If , then , since . |
Totalfinder 1 11 5 Equals Grams
Which of the following is a true statement? A) B) C) D) |
Summary
You can compare two fractions with like denominators by comparing their numerators. The fraction with the greater numerator is the greater fraction, as it contains more parts of the whole. Microsoft onenote 15 41 – free digital notebook pdf. The fraction with the lesser numerator is the lesser fraction as it contains fewer parts of the whole. If two fractions have the same denominator, then equal numerators indicate equivalent fractions.
