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When adding and subtracting fractions the denominators must be the same. If we wish to combine or take away parts we must be talking about the same sized parts, otherwise it would get confusing.Multiply by a form of one to change the denominators into a common size.Example 8: An electrician has three and seven-sixteenths cm of wire.
Example 6: The Cocozzelli family drove their car for five and five-sixths days to reach their vacation home, and then drove for six and one-sixth days to return home. Analysis: To solve this problem, we will subtract two mixed numbers, with the fractional parts having like denominators.
Solution: Answer: The Cocozzelli family took one-half more days to drive home.
Example 7: A warehouse has 12 and nine-tenths meters of tape in one area of the building, and eight and three-fifths meters of tape in another part. Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having unlike denominators.
Solution: Answer: The warehouse has 21 and one-half meters of tape in all.
Example 4: Dina added five-sixths of a bag of soil to her garden.
Her neighbor Natasha added eleven-eighths bags of soil to her garden. Analysis: To solve this problem, we will subtract two fractions with unlike denominators.If he needs only 10 and five-twelfths feet of wood, then how much wood should he cut?Analysis: To solve this problem, we will subtract a mixed number from a whole number.How many hours did he take to complete his homework altogether?Analysis: To solve this problem, we will add three fractions with unlike denominators. Solution: Answer: It took Nick three and one-fourth hours to complete his homework altogether.Solution: Answer: Example 5: At a pizza party, Diego and his friends ate three and one-fourth cheese pizzas and two and three-fourths pepperoni pizzas. Analysis: To solve this problem, we will add two mixed numbers, with the fractional parts having like denominators.Solution: Answer: Diego and his friends ate six pizzas in all.Solution: Answer: Stefanie swam one-third of a lap farther in the morning.Example 3: It took Nick five-thirds of an hour to complete his math homework on Monday, three-fourths of an hour on Tuesday, and five-sixths of an hour on Wednesday.Solution: Answer: The electrician needs to cut 13 sixteenths cm of wire.Example 9: A carpenter had a piece of wood that was 15 feet in length.