Subtracting FractionsSubtracting Fractions

Kory WilsonGrand Canyon University

Team RedTEC 539

Dr. Holly Strickland

Least Common Denominator (LCD same as LCM): Least Common Denominator (LCD same as LCM): The The smallest multiple that two denominators have that smallest multiple that two denominators have that are the same. LCD is used to find equivalent are the same. LCD is used to find equivalent fractions when subtracting fractions with unlike fractions when subtracting fractions with unlike denominators.denominators.

Example: Example:

11

22 multiples of 2 are: 2, 4, multiples of 2 are: 2, 4, 66, 8, 10. . . , 8, 10. . . (2 x 3 =6)(2 x 3 =6)

LCD = LCD = 66

11

33 multiples of 3 are: 3, multiples of 3 are: 3, 66, 9, 12, 15 . . . , 9, 12, 15 . . . (3 x 2 = (3 x 2 = 6)6)

Terms to KnowTerms to Know

Equivalent Fractions: Equivalent Fractions: Equivalent fractions are two Equivalent fractions are two fractions with the same value. Just as in money, one fractions with the same value. Just as in money, one can represent the value of fifty cents with two can represent the value of fifty cents with two quarters or five dimes. Although there is more than quarters or five dimes. Although there is more than one way to represent of fifty cents, it’s worth is still one way to represent of fifty cents, it’s worth is still the same. There may be multiple ways to represent the same. There may be multiple ways to represent one value in fractions too. one value in fractions too.

The rule with equivalent fractions is, The rule with equivalent fractions is, “What you do to the “What you do to the numerator, you must do to the denominator to keep it numerator, you must do to the denominator to keep it equal”.equal”.

Example:Example:

1 1 x 2x 2 22

2 2 x 2 x 2 44

Terms to KnowTerms to Know

OR

Greatest Common Factor (GCF): Greatest Common Factor (GCF): The largest factor The largest factor that can be evenly divided into two other numbers. that can be evenly divided into two other numbers. Commonly used to reduce fractions into simplest Commonly used to reduce fractions into simplest form.form.

Example: Example: Find the GCF of the following fraction.Find the GCF of the following fraction.

4 4 Factors of 4 are: 1, 2, Factors of 4 are: 1, 2, 44

12 Factors of 12 are: 1, 2, 3,12 Factors of 12 are: 1, 2, 3,44,6,12,6,12

GCF of 4 and 12 is GCF of 4 and 12 is 44..

Simplify fraction by dividing numerator and Simplify fraction by dividing numerator and denominator by the GCF denominator by the GCF 44..

44 44 11

1212 44 33

Terms to KnowTerms to Know

Step 1: Step 1: When the denominators are the same, only When the denominators are the same, only subtract the numerators. Denominator in the subtract the numerators. Denominator in the answer is the same as in the equation. Do not answer is the same as in the equation. Do not subtract denominators.subtract denominators.

55 33 2 2

88 88 8 8

Step 2: Step 2: Simplify to simplest form using Simplify to simplest form using GCFGCF..

2 factors of 2 are: 1, 2 factors of 2 are: 1, 22

8 factors of 8 are: 1, 8 factors of 8 are: 1, 22, 4, 8, 4, 8 GCFGCF is is 22

22 22 11

88 22 44

How to Subtract Simple FractionsHow to Subtract Simple Fractions

Answer in simplest form.

Step 1: Step 1: Rename both fractions to an equivalent fraction Rename both fractions to an equivalent fraction with the same denominators by using the LCD. with the same denominators by using the LCD. (See (See LCD definition)LCD definition)

22 22

66 88

( ( 22 x 4) x 4) 8 8 ((22 x 3) x 3) 6 6

((66 x 4) x 4) 2424 ((88 x 3) x 3) 2424

Step 2: Step 2: Subtract numerators and simplify using GCF.Subtract numerators and simplify using GCF.

88 6 6 2 2 22 1 1

2424 2424 24 24 22 12 12

How to Subtract Fractions with How to Subtract Fractions with Unlike DenominatorsUnlike Denominators

Multiples 6: 6, 12, 18, 24 . . .8: 8, 16, 24, 32 . . .

LCD: 24

Factors:2: 1, 2

24: 1, 2, 3, 4, 6, 8, 12, 24GCF: 2

Eather, J. (2010). Eather, J. (2010). A Maths dictionary for kidsA Maths dictionary for kids. . Retrieved: July 4, 2010 from Retrieved: July 4, 2010 from http://amathsdictionaryforkids.com/dictionahttp://amathsdictionaryforkids.com/dictionary.htmlry.html

Math is funMath is fun. (2010). Retrieved: July 4, 2010 . (2010). Retrieved: July 4, 2010 from http://www.mathsisfun.com/from http://www.mathsisfun.com/

ReferencesReferences