Chapter 5 – 8 Add and Subtract Unlike Fractions UNIT 2 Chapter 5 – 8 Add and Subtract Unlike Fractions

Adding Unlike Fractions Rule: To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify. Example: 1 3 + 2 5 {Least Common denominator is 15} = 1 •5 3 •5 + 2 •3 5 •3 {Rename each fraction using the LCD} = 5 15 + 6 15 {Add numerator} = 11 15

Adding Unlike Fractions Example: Find 1 4 + 2 3 = 1 • 3 4 •3 + 2 • 4 3 • 4 {LCD is 12} = 3 12 + 8 12 = 11 12

Adding Mixed Number Find 1 2 9 + (-2 1 3 ) = 1 2 9 + (-2 1 3 ) = 11 9 + ( −7 3 ) {Write the mixed number as improper fractions} = 11 9 + ( −7 • 3 3 • 3 ) {LCD is 9 – rename −7 3 fractions using LCD} = 11 9 + ( −21 9 ) {Simplify} = −10 9 {Add the numerators} = - 1 1 9 {Simplify}

Subtracting Unlike Fractions Rule: To subtract fractions with unlike denominators, rename the fractions with a common denominator. Then subtract and simplify. Example: Find 5 21 - 6 7 = 5 21 - 6 •3 7 •3 {LCD is 21- rename 6 7 using LCD} = 5 21 - 18 21 {Subtract numerators} = −13 21

Subtract Mixed Numbers Find 6 1 2 - 4 1 5 = 6 1 2 - 4 1 5 = 13 2 - 21 5 {Write mixed numbers as improper fractions} = 13 •5 2 •5 - 21 •2 5 •2 {Rename the fraction with the LCD of 10} = 65 10 - 42 10 {Subtract the numerators} = 23 10 or 2 3 10 {Simplify}

Let’s Try Some Examples! Find the sum or difference. Write in simplest form. 1) 1 10 + 1 3 2) −1 6 + 7 18 3) 6 4 5 + (-1 3 4 ) 4) 1 4 - 2 3 5) −7 10 − 2 15

Let’s Check Our Answers! Find the sum or difference. Write in simplest form. 1) 1 10 + 1 3 2) −1 6 + 7 18 3) 6 4 5 + (-1 3 4 ) = 13 30 = 2 9 =5 1 20 4) 1 4 - 2 3 5) −7 10 − 2 15 = −5 12 = 5 6