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Ch 4 Sec 5: Slide #1 Columbus State Community College Chapter 4 Section 5 Problem Solving: Mixed Numbers and Estimating

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Ch 4 Sec 5: Slide #2 Problem Solving: Mixed Numbers and Estimating 1.Identify mixed numbers and graph them on a number line. 2.Rewrite mixed numbers as improper fractions, or the reverse. 3.Estimate the answer and multiply or divide mixed numbers. 4.Estimate the answer and add or subtract mixed numbers. 5.Solve application problems containing mixed numbers.

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Ch 4 Sec 5: Slide #3 Illustrating a Mixed Number with a Diagram EXAMPLE 1 Illustrating a Mixed Number with a Diagram 1 whole of a whole shaded parts 1 shaded part whole parts shaded is equivalent to shaded parts. 9 4

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Ch 4 Sec 5: Slide #4 8 5 – 3 5 – Illustrating a Mixed Number with a Number Line EXAMPLE 1 Illustrating Mixed Numbers with a Number Line – 3 5 – 1 is equivalent to

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Ch 4 Sec 5: Slide #5 Mixed Numbers NOTE 1 2 4represents – represents – –, which can also be written as – –

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Ch 4 Sec 5: Slide #6 Mixed Numbers NOTE In algebra we usually work with the improper fraction form of mixed numbers, especially for negative mixed numbers. However, positive mixed numbers are frequently used in daily life, so its important to know how to work with them. For example, we usually say inches rather than inches

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Ch 4 Sec 5: Slide # Writing a Mixed Number as an Improper Fraction Step 1Multiply the denominator of the fraction times the whole number and add the numerator of the fraction to the product. Step 2Write the result of Step 1 as the numerator and keep the original denominator. 4 5 = = =

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Ch 4 Sec 5: Slide #8 Writing a Mixed Number as an Improper Fraction Write as an improper fraction. EXAMPLE 2 Writing a Mixed Number as an Improper Fraction Step = 72 Step 2 = Then = ( 8 9 ) Same denominator

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Ch 4 Sec 5: Slide #9 Writing an Improper Fraction as a Mixed Number To write an improper fraction as a mixed number, divide the numerator by the denominator. The quotient is the whole number part (of the mixed number), the remainder is the numerator of the fraction part, and the denominator remains the same. Divide 38 by Remainder Original denominator

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Ch 4 Sec 5: Slide #10 Writing Improper Fractions as Mixed Numbers (a)Write as a mixed number. EXAMPLE 3 Writing Improper Fractions as Mixed Numbers 28 3 Divide 28 by Remainder Original denominator

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Ch 4 Sec 5: Slide #11 Writing Improper Fractions as Mixed Numbers (b)Write as a mixed number. EXAMPLE 3 Writing Improper Fractions as Mixed Numbers 42 9 Divide 42 by Remainder Original denominator = Write in lowest terms. 6 9

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Ch 4 Sec 5: Slide #12 Estimating Mixed Numbers To estimate answers, first round each mixed number to the nearest whole number. If the numerator is half of the denominator or more, round up the whole number part. If the numerator is less than half the denominator, leave the whole number as it is.

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Ch 4 Sec 5: Slide #13 Rounding Mixed Numbers to the Nearest Whole Number (a)Round EXAMPLE 4 Rounding Mixed Numbers to the Nearest Whole Number rounds up to Half of 7 is is more than 1 2 3

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Ch 4 Sec 5: Slide #14 Rounding Mixed Numbers to the Nearest Whole Number (b)Round EXAMPLE 4 Rounding Mixed Numbers to the Nearest Whole Number rounds to Half of 8 is 4 3 is less than 4

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Ch 4 Sec 5: Slide #15 Multiplying and Dividing Mixed Numbers Step 1Rewrite each mixed number as an improper fraction. Step 2Multiply or divide the improper fractions. Step 3Write the answer in lowest terms and change it to a mixed number or whole number where possible. This step gives you an answer that is in simplest form.

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Ch 4 Sec 5: Slide #16 Estimating the Answer and Multiplying Mixed Numbers EXAMPLE 5 Estimating the Answer and Multiplying Mixed Numbers (a) rounds to 4rounds to 3.and Estimate the answer by rounding the mixed numbers. 4 3 = 12 Estimated answer

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Ch 4 Sec 5: Slide # Estimating the Answer and Multiplying Mixed Numbers EXAMPLE 5 Estimating the Answer and Multiplying Mixed Numbers To find the exact answer, first rewrite each mixed number as an improper fraction. (a) and = = 14 5 Step = Step 2 = =

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Ch 4 Sec 5: Slide #18 Estimating the Answer and Multiplying Mixed Numbers EXAMPLE 5 Estimating the Answer and Multiplying Mixed Numbers Estimate (a) Exact 12 The exact answer is reasonable.

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Ch 4 Sec 5: Slide #19 Estimating the Answer and Multiplying Mixed Numbers EXAMPLE 5 Estimating the Answer and Multiplying Mixed Numbers (b) rounds to 1rounds to 6.and Estimate the answer by rounding the mixed numbers. 1 6 = 6 Estimated answer

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Ch 4 Sec 5: Slide # Estimating the Answer and Multiplying Mixed Numbers EXAMPLE 5 Estimating the Answer and Multiplying Mixed Numbers To find the exact answer, first rewrite each mixed number as an improper fraction. and = = 39 7 Step = Step 2 = = (b)

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Ch 4 Sec 5: Slide #21 Estimating the Answer and Multiplying Mixed Numbers EXAMPLE 5 Estimating the Answer and Multiplying Mixed Numbers Estimate Exact 6 The exact answer is reasonable. (b)

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Ch 4 Sec 5: Slide #22 Estimating the Answer and Dividing Mixed Numbers EXAMPLE 6 Estimating the Answer and Dividing Mixed Numbers (a) ÷ rounds to 8rounds to 2.and Estimate the answer by rounding the mixed numbers. 8 ÷ 2 = 4 Estimated answer

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Ch 4 Sec 5: Slide # Estimating the Answer and Dividing Mixed Numbers EXAMPLE 6 Estimating the Answer and Dividing Mixed Numbers To find the exact answer, first rewrite each mixed number as an improper fraction. and = = 12 5 Step ÷ = 12 5 ÷ 38 5 Step 2 = = (a) ÷ =

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Ch 4 Sec 5: Slide #24 Estimating the Answer and Dividing Mixed Numbers EXAMPLE 6 Estimating the Answer and Dividing Mixed Numbers Estimate Exact 4 The exact answer is reasonable. (a) ÷

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Ch 4 Sec 5: Slide #25 Estimating the Answer and Dividing Mixed Numbers EXAMPLE 6 Estimating the Answer and Dividing Mixed Numbers (b) ÷ Write 2 ÷ 5 using a fraction bar ÷5 First, round the numbers and estimate the answer. 2 ÷5 2 5

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Ch 4 Sec 5: Slide #26 Estimating the Answer and Dividing Mixed Numbers EXAMPLE 6 Estimating the Answer and Dividing Mixed Numbers Now find the exact answer. and = = 5 1 Step ÷ 5 = 5 1 ÷ 7 3 Step 2 = 7 15 = (b) ÷

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Ch 4 Sec 5: Slide # Estimating the Answer and Dividing Mixed Numbers EXAMPLE 6 Estimating the Answer and Dividing Mixed Numbers EstimateExact The estimate and the exact answer are close to one-half. Therefore, the exact answer is reasonable. (b) ÷

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Ch 4 Sec 5: Slide #28 Estimating the Answer and Adding Mixed Numbers EXAMPLE 7 Estimating the Answer and Adding Mixed Numbers (a) rounds to 4rounds to 5.and Estimate the answer by rounding the mixed numbers = 9 Estimated answer

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Ch 4 Sec 5: Slide #29 Estimating the Answer and Adding Mixed Numbers EXAMPLE 7 Estimating the Answer and Adding Mixed Numbers To find the exact answer, first rewrite each mixed number as an equivalent improper fraction. (a) = = = = Rewrite each improper fraction with the LCD of 6.Add the numerators. Keep the common denominator.Write your answer in simplest form.

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Ch 4 Sec 5: Slide #30 Estimating the Answer and Adding Mixed Numbers EXAMPLE 7 Estimating the Answer and Adding Mixed Numbers Estimate Exact 9 The exact answer is reasonable. (a)

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Ch 4 Sec 5: Slide #31 Estimating the Answer and Subtracting Mixed Numbers EXAMPLE 7 Estimating the Answer and Subtracting Mixed Numbers 9 (b) – rounds to 9rounds to 3.and Estimate the answer by rounding the mixed numbers. 9 – 3 = 6 Estimated answer

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Ch 4 Sec 5: Slide #32 Write your answer in simplest form.Rewrite each improper fraction with the LCD of 7.To find the exact answer, first rewrite each mixed number as an equivalent improper fraction. Subtract the numerators. Keep the common denominator. Estimating the Answer and Subtracting Mixed Numbers EXAMPLE 7 Estimating the Answer and Subtracting Mixed Numbers 9 – = 18 7 – 9 1 = = = 18 7 – (b) – 4 7 2

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Ch 4 Sec 5: Slide #33 Estimating the Answer and Subtracting Mixed Numbers EXAMPLE 7 Estimating the Answer and Subtracting Mixed Numbers Estimate Exact 6 The exact answer is reasonable. 9 (b) – 4 7 2

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Ch 4 Sec 5: Slide #34 Using Your Calculator Try these problems using your calculator ) = c A b 215 c A b 9 + c A b 381 c A b

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Ch 4 Sec 5: Slide #35 Using Your Calculator Try these problems using your calculator ) = c A b 564 c A b 5 x c A b

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Ch 4 Sec 5: Slide #36 Using Your Calculator Try these problems using your calculator. = c A b 833 c A b 4 ÷ c A b 111 ÷ ) c A b 2 (-) TI 30X IIS

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Ch 4 Sec 5: Slide #37 Using Your Calculator Try these problems using your calculator. = c A b 833 c A b 4 ÷ c A b 111 ÷ ) c A b 2 TI 30 Xa + –

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Ch 4 Sec 5: Slide #38 Solving Application Problems with Mixed Numbers EXAMPLE 8 Solving Application Problems: Mixed Numbers (a)Mike started his trip with gallons of gas in his car. After his trip, he had gallons remaining. How many gallons of gas did Mike use on his trip? To help understand the mathematical operation needed to solve this problem, read it again using rounded numbers. Mike started his trip with 21 gallons of gas in his car. Afterhis trip he had 6 gallons remaining. How many gallons of gas did Mike use on his trip? 21 – 6 = 15 gallons Estimate

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Ch 4 Sec 5: Slide #39 Solving Application Problems with Mixed Numbers EXAMPLE 8 Solving Application Problems: Mixed Numbers (a)Mike started his trip with gallons of gas in his car. After his trip, he had gallons remaining. How many gallons of gas did Mike use on his trip? To find the exact answer, use the original mixed numbers. = c A b 203 c A b 5 – c A b 51 c A b gallons

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Ch 4 Sec 5: Slide #40 Solving Application Problems with Mixed Numbers EXAMPLE 8 Solving Application Problems: Mixed Numbers (a)Mike started his trip with gallons of gas in his car. After his trip, he had gallons remaining. How many gallons of gas did Mike use on his trip? Mike used gallons of gas on his trip. This result is close to the estimate of 15 gallons

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Ch 4 Sec 5: Slide #41 Solving Application Problems with Mixed Numbers (b)Marys recipe for chocolate chip cookies calls for cups of flour per batch. If she has cups of flour available, how many batches of cookies can Mary make? To help understand the mathematical operation needed to solve this problem, read it again using rounded numbers. Marys recipe for chocolate chip cookies calls for 2 cups of flour per batch. If she has 16 cups of flour available, how many batches of cookies can Mary make? 16 ÷ 2 = 8 batches Estimate EXAMPLE 8 Solving Application Problems: Mixed Numbers

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Ch 4 Sec 5: Slide #42 Solving Application Problems with Mixed Numbers EXAMPLE 8 Solving Application Problems: Mixed Numbers To find the exact answer, use the original mixed numbers. = c A b 153 c A b 4 ÷ c A b 21 c A b 47 batches (b)Marys recipe for chocolate chip cookies calls for cups of flour per batch. If she has cups of flour available, how many batches of cookies can Mary make?

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Ch 4 Sec 5: Slide #43 Solving Application Problems with Mixed Numbers EXAMPLE 8 Solving Application Problems: Mixed Numbers Mary can make 7 batches of cookies. This result is close to the estimate of 8 batches of cookies. (b)Marys recipe for chocolate chip cookies calls for cups of flour per batch. If she has cups of flour available, how many batches of cookies can Mary make?

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Ch 4 Sec 5: Slide #44 Problem Solving: Mixed Numbers and Estimating Chapter 4 Section 5 – Completed Written by John T. Wallace

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