Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.3 Adding and Subtracting Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Unlike Fractions Adding or Subtracting Unlike Fractions Step 1: Find the LCM of the denominators of the fractions. This number is the least common denominator (LCD). Step 2: Write each fraction as an equivalent fraction whose denominator is the LCD. Step 3: Add or subtract the like fractions. Step 4: Write the sum or difference in simplest form.

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Unlike Fractions StepExample Step 1: Find the LCM of the denominators of the fractions. This number is the least common denominator (LCD). Step 2: Write each fraction as an equivalent fraction whose denominator is the LCD. Step 3: Add or subtract the like fractions. Step 4: Write the sum or difference in simplest form. Multiples of 2: 2, 4, 6, 8, 10, … Multiples of 3: 3, 6, 9, 12, 15, … is in its simplest form.

Martin-Gay, Basic Mathematics, 4e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Add: Step 1: The LCD of the denominators is 15. Step 2: Step 3: Step 4: The answer is in simplest form.

Martin-Gay, Basic Mathematics, 4e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Add: The LCD of the denominators is 24.

Martin-Gay, Basic Mathematics, 4e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 2: Step 3: Prime factorization for 6: 2, 3 Prime factorization for 18: 2, 3, 3 P 192 Practice Problem 1 2, 33 Adding Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 2: Step 3: Prime factorization for 6: 2, 3 Prime factorization for 9: 3, 3 P 192 Practice Problem 2 2, 33 Adding Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 2: Step 3: Prime factorization for 5: 5 Prime factorization for 9: 3, 3 P 192 Practice Problem 3 53, 3 Adding Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 2: Step 3: Prime factorization for 4: 2, 2 Prime factorization for 5: 5 Prime factorization for 10: 2, 5 P 192 Practice Problem 4 2, 25 Adding Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Subtracting Unlike FractionsEXAMPLE SOLUTION Subtract and simplify: Step 1: The LCD of 4 and 7 is 28 Step 2: Step 3: Step 4: is in its simplest form. P 193

Martin-Gay, Basic Mathematics, 4e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Subtract: The LCD of the denominators is 33.

Martin-Gay, Basic Mathematics, 4e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example A freight truck has 1/4 ton of computers, 1/3 ton of televisions, and 3/8 ton of small appliances. Find the total weight of its load. To find the total weight, add the weights of the individual items.

Martin-Gay, Basic Mathematics, 4e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 3: Prime factorization for 12: 2, 2, 3 Prime factorization for 24: 2, 2, 2, 3 P 193 Subtracting Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 14 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 2: Step 3: Prime factorization for 10: 2, 5 Prime factorization for 7: 7 P 193 Practice Problem 6 Subtracting Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. StepExample Step 1: Write the prime factorization of each number. Step 2: Step 3: Prime factorization for 8: 2, 2, 2 Prime factorization for 6: 2, 3 P 194 Practice Problem 7 2, 2, 23 Subtracting Unlike Fractions

Martin-Gay, Basic Mathematics, 4e 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Adding or Subtracting Unlike FractionsEXAMPLE SOLUTION The slowest mammal is the three-toed sloth from South America. The sloth has an average ground speed of mph. In the trees, it can accelerate to mph. How much faster can a sloth travel in the trees? (Source: The Guiness Book of World Records) Step 1: The LCD of 10 and 100 is 100 Step 2: Step 3: Step 4: mph is in its simplest form. P 197

Martin-Gay, Basic Mathematics, 4e 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Adding or Subtracting Unlike Fractions Practice Problem 8 SOLUTION To repair her sidewalk, a homeowner must pour small amounts of cement in three different locations. She needs of a cubic yard, of a cubic yard, and of a cubic yard for these locations. Find the total amount of cement the homeowner needs. Step 1: The LCD of 5, 10 and 15 is 30 Step 2: Step 3: Step 4: cubic yard is in its simplest form. P 194

Martin-Gay, Basic Mathematics, 4e 18 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. DONE