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Contents Lesson 6-1Rounding Fractions and Mixed Numbers Lesson 6-2Estimating Sums and Differences Lesson 6-3Adding and Subtracting Fractions with Like Denominators Lesson 6-4Adding and Subtracting Fractions with Unlike Denominators Lesson 6-5Adding and Subtracting Mixed Numbers Lesson 6-6Subtracting Mixed Numbers with Renaming

Lesson 1 Contents Example 1Round to the Nearest Half Example 2Round to the Nearest Half Example 3Use Rounding to Solve a Problem

Example 1-1a Round to the nearest half. The numerator of is almost as large as the denominator. Answer: So, rounds to 7.

Example 1-1b Round to the nearest half. Answer: 4

Example 1-2a Find the length of the segment to the nearest half inch. To the nearest half inch, rounds to 1. Answer: 1 inch

Example 1-2b Find the length of the segment to the nearest half. Answer: inches

Example 1-3a Answer: The family should purchase the -foot wide bookshelf. DECORATING There is a -foot gap between the entertainment center and a wall in a family’s living room. Should the family purchase a 5-foot wide bookshelf or a -foot wide bookshelf? is less than five. So, a 5-foot wide bookshelf would be too large.

Example 1-3b COOKING Phyllis has a recipe that calls for cups of spaghetti sauce. Should she purchase a 4-cup jar of spaghetti sauce or a cup jar of spaghetti sauce for the recipe? Answer: 4-cup jar

End of Lesson 1

Lesson 2 Contents Example 1Fractions Sums and Differences Example 2Fractions Sums and Differences Example 3Mixed Number Sum Example 4Mixed Number Difference Example 5Round Up to Solve a Problem

Example 2-1a rounds to 1. is about Answer:Estimate rounds to.

Example 2-1b Sample answer: Estimate

Example 2-2a rounds to 0. rounds to 1. Answer: is about or 1. Estimate

Example 2-2b Sample answer: 1 Estimate

Example 2-3a rounds to 5. rounds to 9.Answer: So, is about Estimate

Example 2-3b Sample answer: 10 Estimate

Example 2-4a Estimate Answer: Estimate

Example 2-4b Sample answer: 6 Estimate

Example 2-5a CATERING A caterer needs to put a -foot submarine sandwich and a -foot long dessert tray end-to-end on a buffet table. About how long does the buffet table need to be? The caterer wants to make sure the table is long enough. So, he rounds up. Estimate Answer: So, the table needs to be about 14 feet long.

Example 2-5b Answer: 13 in. KNITTING On Monday, Stephanie starts knitting a scarf. She knits a length of inches. On Tuesday, Stephanie continues her knitting with an additional length of inches. About how much of the scarf has Stephanie completed in those two days?

End of Lesson 2

Lesson 3 Contents Example 1Add Like Fractions Example 2Subtract Like Fractions Example 3Use Fractions to Solve a Problem

Example 3-1a Find the sum of Estimate

Example 3-1b Simplify. Write the improper fraction as a mixed number. Compared to the estimate, the answer is reasonable. Answer: Add the numerators.

Example 3-1c Find the sum of Answer:

Example 3-2a Subtract the numerators. Simplify. Answer: Write in simplest form. Find

Example 3-2b Answer: Find

Example 3-3a SWIMMING During swimming practice at the lap pool, Darcy swam of a mile and Rene swam of a mile. How much farther did Darcy swim than Rene? Answer: Darcy swam mile more than Rene. Subtract the numerators. Simplify.

Example 3-3b SEWING One pattern for a skirt required yards of fabric for the lining and a second pattern required yards of fabric for the lining. How much more fabric was required for the first pattern? Answer:

End of Lesson 3

Lesson 4 Contents Example 1Add Unlike Fractions Example 2Subtract Unlike Fractions Example 3Use Fractions to Solve a Problem Example 4Evaluate an Expression with Fractions

Example 4-1a The LCD of is 20. Write the problem. Add the fractions. Answer: Find

Example 4-1b Answer: Find

Example 4-2a The LCD of and is 30. Write the problem. Subtract the fractions. Answer: Find

Example 4-2b Answer: Find

Example 4-3a PET ADOPTION Use the table to find the fraction of adopted dogs in one town that are either golden retrievers or mixed breed. Fraction Mixed breed Jack Russell terrier Golden retriever German shepherd Breed Adopted Dogs Poodle

Example 4-3b The LCD of is 25. Write the problem. Subtract the fractions. Answer: So, of the adopted dogs are either golden retrievers or mixed breed..

Example 4-3c ICE CREAM Use the table to find the fraction of the orders that are for either vanilla or chocolate ice cream. Vanilla Strawberry Cookie dough Chocolate chip Chocolate FractionFlavor Ice Cream Orders Answer:

Example 4-4a Answer: Replace p with and q with Rename using the LCD, 6. Simplify. Subtract and write in simplest form. ALGEBRA Evaluate and

Example 4-4b Answer: ALGEBRA Evaluate and

End of Lesson 4

Lesson 5 Contents Example 1Subtract Mixed Numbers Example 2Add Mixed Numbers Example 3Use Mixed Numbers to Solve a Problem Example 4Evaluate an Expression

Example 5-1a Estimate Subtract the fractions. Subtract the whole numbers. Compare to the estimate. Answer: Find

Example 5-1b Answer: Find

Example 5-2a Estimate Answer: The LCM of 5 and 4 is 20. Rename the fractions. Add the fractions. Add the whole numbers. Find

Example 5-2b Answer: Find

Example 5-3a MULTIPLE-CHOICE TEST ITEM Refer to the diagram. How far will Steve travel if he rides his bike from home to the bank and then to the grocery store? A miles B miles C miles D miles

Example 5-3b Read the Test Item You need to find the distance Steve rides his bike. Solve the Test Item First use the LCD to rename the fractions. Then add. Steve will ride his bike miles. Answer: A

Example 5-3c Answer: B Refer to the diagram. How far will Claire travel if she rides a bus from school to the library and then home? MULTIPLE-CHOICE TEST ITEM D miles A miles B miles C miles

Example 5-4a Replace a with and b with Rename and using the LCD, 24. Simplify. Answer: ALGEBRA Evaluate if and

Example 5-4b Answer:

End of Lesson 5

Lesson 6 Contents Example 1Rename to Subtract Example 2Rename to Subtract Example 3Rename to Subtract Example 4Use Renaming to Solve a Problem

Example 6-1a 5 Answer: Find

Example 6-1b Answer: Find

Example 6-2a Answer: Find

Example 6-2b Answer: Find

Example 6-3a Step 1 Step 2 The LCM of 6 and 3 is 6. Rename as Find

Example 6-3b Answer:

Example 6-3c Answer: Find

Example 6-4a LAND A farmer gave acres of land to the local historical society for a historical park. Previously, the farmer owned acres of land. How much farmland does she have left? Estimate

Example 6-4b Rename as Answer: So, the farmer has acres of farmland left.

Example 6-4c CROPS A farmer planted acres of corn at the beginning of the summer. Now that it is fall, he has already harvested acres. How many acres of corn still need to be harvested? Answer:

End of Lesson 6

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