Difference between revisions of "Find the Least Common Denominator"
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| − | In order to add or subtract fractions with different denominators (the bottom number of the fraction), you must first find the least common denominator shared between them. This refers to the lowest multiple shared by each original denominator in the equation, or the smallest whole number that can be divided by each denominator.<ref>http://www.helpwithfractions.com/math-homework-helper/least-common-denominator/</ref> You may also see the phrase [[Find the Least Common Multiple of Two Numbers|least common multiple]]. This generally refers to whole numbers, but the methods to find it are the same for both. Determining the least common denominator allows you convert the denominators to the same number so you can then add and subtract them. | + | In order to add or subtract fractions with different denominators (the bottom number of the fraction), you must first find the least common denominator shared between them. This refers to the lowest multiple shared by each original denominator in the equation, or the smallest whole number that can be divided by each denominator.<ref name="rf1">http://www.helpwithfractions.com/math-homework-helper/least-common-denominator/</ref> You may also see the phrase [[Find the Least Common Multiple of Two Numbers|least common multiple]]. This generally refers to whole numbers, but the methods to find it are the same for both. Determining the least common denominator allows you convert the denominators to the same number so you can then add and subtract them. |
[[Category:Fractions]] | [[Category:Fractions]] | ||
==Steps== | ==Steps== | ||
| − | === Listing Multiples<ref>http://www.epcc.edu/tutorialservices/valleverde/Documents/Common_Denominators.pdf</ref>=== | + | === Listing Multiples<ref name="rf2">http://www.epcc.edu/tutorialservices/valleverde/Documents/Common_Denominators.pdf</ref>=== |
#List the multiples of each denominator. Make a list of several multiples for each denominator in the equation. Each list should consist of the denominator numeral multiplied by 1, 2, 3, 4, and so on. | #List the multiples of each denominator. Make a list of several multiples for each denominator in the equation. Each list should consist of the denominator numeral multiplied by 1, 2, 3, 4, and so on. | ||
#*Example: 1/2 + 1/3 + 1/5 | #*Example: 1/2 + 1/3 + 1/5 | ||
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#*Example: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30 | #*Example: 15/30 + 10/30 + 6/30 = 31/30 = 1 1/30 | ||
| − | === Using the Greatest Common Factor<ref>http://www.aaamath.com/fra66jx2.htm</ref>=== | + | === Using the Greatest Common Factor<ref name="rf3">http://www.aaamath.com/fra66jx2.htm</ref>=== |
| − | #List all of the factors of each denominator. The factors of a number are all of the whole numbers that are evenly divisible into that one number.<ref>https://www.mathsisfun.com/greatest-common-factor.html</ref> The number 6 has four factors: 6, 3, 2, and 1. Every number has a factor of 1 because every number can be multiplied by one. | + | #List all of the factors of each denominator. The factors of a number are all of the whole numbers that are evenly divisible into that one number.<ref name="rf4">https://www.mathsisfun.com/greatest-common-factor.html</ref> The number 6 has four factors: 6, 3, 2, and 1. Every number has a factor of 1 because every number can be multiplied by one. |
#* For example: 3/8 + 5/12. | #* For example: 3/8 + 5/12. | ||
#* Factors of 8: 1, 2, 4, and 8 | #* Factors of 8: 1, 2, 4, and 8 | ||
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#*Example: 9/24 + 10/24 = 19/24 | #*Example: 9/24 + 10/24 = 19/24 | ||
| − | === Factoring Each Denominator into Primes<ref | + | === Factoring Each Denominator into Primes<ref name="rf1" />=== |
| − | #Break each denominator into prime numbers. Factor each denominator digit into a series of prime numbers that multiply together to make that number. Prime numbers are numbers that cannot be divided by any other number. <ref>https://www.mathsisfun.com/prime_numbers.html</ref> | + | #Break each denominator into prime numbers. Factor each denominator digit into a series of prime numbers that multiply together to make that number. Prime numbers are numbers that cannot be divided by any other number. <ref name="rf5">https://www.mathsisfun.com/prime_numbers.html</ref> |
#*Example: 1/4 + 1/5 + 1/12 | #*Example: 1/4 + 1/5 + 1/12 | ||
#*''Prime factorization of 4:'' 2 * 2 | #*''Prime factorization of 4:'' 2 * 2 | ||
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#*Example: 15/60 + 12/60 + 5/60 = 32/60 = 8/15 | #*Example: 15/60 + 12/60 + 5/60 = 32/60 = 8/15 | ||
| − | === Working with Integers and Mixed Numbers<ref>http://www.calculatorsoup.com/calculators/math/lcd.php#.Ua0eFkDryj4</ref>=== | + | === Working with Integers and Mixed Numbers<ref name="rf6">http://www.calculatorsoup.com/calculators/math/lcd.php#.Ua0eFkDryj4</ref>=== |
#Convert each integer and mixed number into an improper fraction. Convert mixed numbers into improper fractions by multiplying the integer by the denominator and adding the numerator to the product. Convert integers into improper fractions by placing the integer over a denominator of “1.” | #Convert each integer and mixed number into an improper fraction. Convert mixed numbers into improper fractions by multiplying the integer by the denominator and adding the numerator to the product. Convert integers into improper fractions by placing the integer over a denominator of “1.” | ||
#*Example: 8 + 2 1/4 + 2/3 | #*Example: 8 + 2 1/4 + 2/3 | ||
