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**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.**Adding Unlike Fractions**Multiples of 2: 2, 4, 6, 8, 10, … Multiples of 3: 3, 6, 9, 12, 15, … is in its simplest form.**Example**Add: Step 1: The LCD of the denominators is 15. Step 2: Step 3: Step 4: The answer is in simplest form.**Example**Add: The LCD of the denominators is 24.**Adding Unlike Fractions**Practice Problem 1 Prime factorization for 6: 2, 3 Prime factorization for 18: 2, 3, 3 2, 3 3 P 192**Adding Unlike Fractions**Practice Problem 2 Prime factorization for 6: 2, 3 Prime factorization for 9: 3, 3 2, 3 3 P 192**Adding Unlike Fractions**Practice Problem 3 Prime factorization for 5: 5 Prime factorization for 9: 3, 3 5 3, 3 P 192**Adding Unlike Fractions**Practice Problem 4 Prime factorization for 4: 2, 2 Prime factorization for 5: 5 Prime factorization for 10: 2, 5 2, 2 5 P 192**Subtracting Unlike Fractions**EXAMPLE Subtract and simplify: SOLUTION Step 1: The LCD of 4 and 7 is 28 Step 2: Step 3: Step 4: is in its simplest form. P 193**Example**Subtract: The LCD of the denominators is 33.**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.**Subtracting Unlike Fractions**Prime factorization for 12: 2, 2, 3 Prime factorization for 24: 2, 2, 2, 3 P 193**Subtracting Unlike Fractions**Practice Problem 6 Prime factorization for 10: 2, 5 Prime factorization for 7: 7 P 193**Subtracting Unlike Fractions**Practice Problem 7 Prime factorization for 8: 2, 2, 2 Prime factorization for 6: 2, 3 2, 2, 2 3 P 194**Solving Problems by Adding or Subtracting Unlike Fractions**EXAMPLE 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) SOLUTION Step 1: The LCD of 10 and 100 is 100 Step 2: Step 3: Step 4: mph is in its simplest form. P 197**Solving Problems by Adding or Subtracting Unlike Fractions**Practice Problem 8 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. SOLUTION 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