Splash Screen Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue. Chapter 6 Multiplying and Dividing Decimals and Fractions Click the mouse or press the space bar to continue.

6 6 Multiplying and Dividing Decimals and Fractions Chapter Menu Lesson 6-1Lesson 6-1Multiplying Decimals by Whole Numbers Lesson 6-2Lesson 6-2Multiplying Decimals Lesson 6-3Lesson 6-3Problem-Solving Strategy: Reasonable Answers Lesson 6-4Lesson 6-4Dividing Decimals by Whole Numbers Lesson 6-5Lesson 6-5Dividing by Decimals Lesson 6-6Lesson 6-6Problem-Solving Investigation: Choose the Best Strategy Lesson 6-7Lesson 6-7Estimating Products of Fractions Lesson 6-8Lesson 6-8Multiplying Fractions Lesson 6-9Lesson 6-9Multiplying Mixed Numbers Lesson 6-10Lesson 6-10Dividing Fractions Lesson 6-11Lesson 6-11Dividing Mixed Numbers

Lesson 1 Menu Five-Minute Check (over Chapter 5) Main Idea and Vocabulary California Standards Example 1: Multiply Decimals Example 2: Multiply Decimals Example 3: Annex Zeros in the Product Example 4: Annex Zeros in the Product Example 5: Scientific Notation 6-1 Multiplying Decimals by Whole Numbers

6-1 Multiplying Decimals by Whole Numbers Lesson 1 MI/Vocab I will estimate and find the product of decimals and whole numbers. scientific notation

6-1 Multiplying Decimals by Whole Numbers Lesson 1 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

Lesson 1 Ex1 6-1 Multiplying Decimals by Whole Numbers One Way: Use estimation. Round 18.9 to × 4 19 × 4 or × 4 6 Since the estimate is 76, place the decimal point after the Find 18.9 × 4.

Lesson 1 Ex1 6-1 Multiplying Decimals by Whole Numbers Another Way: Count decimal places × Answer: 75.6

Lesson 1 CYP1 6-1 Multiplying Decimals by Whole Numbers A.64 B.63.5 C D Find 12.7 × 5.

Lesson 1 Ex2 6-1 Multiplying Decimals by Whole Numbers One Way: Use estimation. Find 0.56 × 7. Round 0.56 to × 7 1 × 7 or × 7 2 Since the estimate is 7, place the decimal point after the

Lesson 1 Ex2 6-1 Multiplying Decimals by Whole Numbers Another Way: Count decimal places × Answer: 3.92

Lesson 1 CYP2 6-1 Multiplying Decimals by Whole Numbers A.8 B.5.76 C.3.76 D Find 0.47 × 8.

Lesson 1 Ex3 6-1 Multiplying Decimals by Whole Numbers × Find 3 × Answer: 0.048

Lesson 1 CYP3 6-1 Multiplying Decimals by Whole Numbers A B.0.52 C D Find × 2.

Lesson 1 Ex4 ALGEBRA Evaluate 5g if g = Multiplying Decimals by Whole Numbers × g = 5 × Replace g with Answer:

Lesson 1 CYP4 6-1 Multiplying Decimals by Whole Numbers ALGEBRA Evaluate 3h if h = A.1.62 B C D

Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers The average distance from Earth to the Sun is 1.5 × 10 8 kilometers. Write the distance in standard form.

Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers One Way: Use order of operations. Evaluate 10 8 first. Then multiply. 1.5 × 10 8 = 1.5 × 10,000,000 = 150,000,000 kilometers

Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers Another Way: Use mental math. Move the decimal point to the right the same number of places as the exponent of 10, or 8 places. 1.5 × 10 8 = = 150,000,000

Lesson 1 Ex5 6-1 Multiplying Decimals by Whole Numbers Answer: The average distance from Earth to the Sun is 150,000,000 kilometers.

Lesson 1 CYP5 6-1 Multiplying Decimals by Whole Numbers A.588,000,000 kilometers B.58,000,000 kilometers C.5,880,000,000 kilometers D.5,800,000 kilometers The average distance from the Sun to the planet Jupiter is 58.8 × 10 7 kilometers. Choose the answer showing the distance written in standard form.

End of Lesson 1

Lesson 2 Menu Five-Minute Check (over Lesson 6-1) Main Idea California Standards Example 1: Multiply Decimals Example 2: Multiply Decimals Example 3: Evaluate an Expression Example 4: Real-World Example 6-2 Multiplying Decimals

6-2 Multiplying Decimals Lesson 2 MI/Vocab I will multiply decimals by decimals.

6-2 Multiplying Decimals Lesson 2 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results. Standard 5MR2.1 Use estimation to verify the reasonableness of calculated results.

Lesson 2 Ex1 6-2 Multiplying Decimals Estimate 8.3 × × 3 or 24 × Find 8.3 × 2.9. one decimal place two decimal places Answer: So, the product is

Lesson 2 Ex1 6-2 Multiplying Decimals Check for Reasonableness Compare to the estimate is about 24.

Lesson 2 CYP1 6-2 Multiplying Decimals Find 4.5 × 3.9. A B.20 C D.19.45

Lesson 2 Ex2 Find 0.12 × Multiplying Decimals Estimate 0.12 × × 5 or 0 × two decimal places one decimal place three decimal places Answer: So, the product is

Lesson 2 Ex2 6-2 Multiplying Decimals Check for Reasonableness Compare to the estimate is about 0.

Lesson 2 CYP2 6-2 Multiplying Decimals Find 0.14 × 3.3. A B C D.0.723

Lesson 2 Ex3 ALGEBRA Evaluate 1.8r if r = Multiplying Decimals 1.8r = 1.8 × Replace r with × one decimal place Annex a zero to make four decimal places. Answer: So, the product is three decimal places

Lesson 2 CYP3 6-2 Multiplying Decimals ALGEBRA Evaluate 2.7x if x = A B C D

Lesson 2 Ex4 Carmen earns $14.60 per hour as a painter’s helper. She worked a total of hours one week. How much money did she earn? 6-2 Multiplying Decimals × $ two decimal places Estimate × × 16 or 240

Compare $ to the estimate. $ is about $240. Lesson 2 Ex4 Answer: So, Carmen earned $ Multiplying Decimals Check for Reasonableness

Lesson 2 CYP4 6-2 Multiplying Decimals Alex went shopping for 6.5 hours and spent $32.50 per hour. How much did she spend? A.$ B.$225 C.$ D.$211.50

End of Lesson 2

Lesson 3 Menu Five-Minute Check (over Lesson 6-2) Main Idea California Standards Example 1: Problem-Solving Strategy 6-3 Problem-Solving Strategy: Reasonable Answers

6-3 Problem-Solving Strategy: Reasonable Answers Lesson 3 MI/Vocab I will solve problems by determining reasonable answers.

6-3 Problem-Solving Strategy: Reasonable Answers Lesson 3 Standard 1 Standard 5MR3.1 Evaluate the reasonableness of the solution in the context of the original situation. Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

Lesson 3 Ex Problem-Solving Strategy: Reasonable Answers For their science project, Stephanie and Angel need to know about how much more a blue whale weighs in pounds than a humpback whale. They have learned that there are 2,000 pounds in one ton. While doing research, they found a table that shows the weights of whales in tons.

Lesson 3 Ex1 Understand What facts do you know? There are 2,000 pounds in one ton. A blue whale weighs tons. A humpback whale weighs 38.1 tons. What do you need to find? A reasonable estimate of the difference in the weight of a blue whale and a humpback whale. 6-3 Problem-Solving Strategy: Reasonable Answers

Lesson 3 Ex1 Plan Estimate to find the weight of each whale in pounds and then subtract to find a reasonable estimate of the difference. 6-3 Problem-Solving Strategy: Reasonable Answers

Lesson 3 Ex1 Solve 6-3 Problem-Solving Strategy: Reasonable Answers Blue whale: Answer: A reasonable estimate for the difference in the weight of a blue whale and a humpback whale is 220,000 pounds. Humpback whale: 2,000 × 151 2,000 × ,000 × 150 2,000 × ,000 80, ,000 – 80,000 = 220,000

Lesson 3 Ex1 Check 6-3 Problem-Solving Strategy: Reasonable Answers Look back at the problem. A blue whale weighs about 150 – 40 or 110 more tons than a humpback whale. This is equal to 110 × 2,000 or 220,000 pounds. So the answer is reasonable.

End of Lesson 3

Lesson 4 Menu Five-Minute Check (over Lesson 6-3) Main Idea and Vocabulary California Standards Example 1: Divide a Decimal by a 1-Digit Number Example 2: Divide a Decimal by a 2-Digit Number Example 3: Real-World Example 6-4 Dividing Decimals by Whole Numbers

6-4 Dividing Decimals by Whole Numbers Lesson 4 MI/Vocab I will divide decimals by whole numbers. quotient

6-4 Dividing Decimals by Whole Numbers Lesson 4 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

6-4 Dividing Decimals by Whole Numbers Lesson 4 Standard 1 Standard 5NS2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

Lesson 4 Ex1 6-4 Dividing Decimals by Whole Numbers Find 7.2 ÷ 3. Estimate 7.2 ÷ 3 6 ÷ 3 or about – 6 12 –12 0

Lesson 4 Ex1 6-4 Dividing Decimals by Whole Numbers Answer: 7.2 ÷ 3 = 2.4 Check Compared to the estimate, the quotient is reasonable.

Lesson 4 CYP1 6-4 Dividing Decimals by Whole Numbers A.8 B.16 C.1.6 D.0.8 Find 6.4 ÷ 4.

Lesson 4 Ex2 6-4 Dividing Decimals by Whole Numbers Find 6.6 ÷ 15. Estimate 6.6 ÷ 15 8 ÷ 16 or about – 0 66 – –60 0

Lesson 4 Ex2 6-4 Dividing Decimals by Whole Numbers Answer: 6.6 ÷ 15 = 0.44 Check Compared to the estimate, the quotient is reasonable.

Lesson 4 CYP2 6-4 Dividing Decimals by Whole Numbers A.5.5 B.0.55 C.0.22 D.2.2 Find 8.8 ÷ 16.

Lesson 4 Ex3 During a science experiment, Nita measured the mass of four unknown samples. Her data is shown below. 6-4 Dividing Decimals by Whole Numbers

Lesson 4 Ex3 First, add all the data together. Answer: So, the mean mass of Nita’s samples is 6.11 grams. 6-4 Dividing Decimals by Whole Numbers Divide by the number of addends to find the mean mass

Lesson 4 CYP3 6-4 Dividing Decimals by Whole Numbers Greta bought 4 pairs of socks for $ If each pair of socks costs the same amount, how much was each pair? A.$6.34 B.$6.00 C.$4.63 D.$3.64

End of Lesson 4

Lesson 5 Menu Five-Minute Check (over Lesson 6-4) Main Idea and Vocabulary California Standards Example 1: Divide by Decimals Example 2: Zeros in the Quotient and Dividend Example 3: Zeros in the Quotient and Dividend Example 4: Round Quotients 6-5 Dividing by Decimals Dividing Decimals

6-5 Dividing by Decimals Lesson 5 MI/Vocab I will divide decimals by decimals. power

6-5 Dividing by Decimals Lesson 5 Standard 1 Standard 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of results.

6-5 Dividing by Decimals Lesson 5 Standard 1 Standard 5NS2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

Lesson 5 Ex1 6-5 Dividing by Decimals Find ÷ 6.4. Estimate 21 ÷ 7 = – – 0 32 – Divide as with whole numbers. Annex a zero to continue. Place the decimal point.

Lesson 5 Ex1 Answer: divided by 6.4 is Dividing by Decimals Compare 3.35 to the estimate. Check 3.35 × 6.4 = 21.44

Lesson 5 CYP1 6-5 Dividing by Decimals Find ÷ 5.5. A.5.9 B.5.09 C.5.90 D.50.9

Lesson 5 Ex2 6-5 Dividing by Decimals Find 72 ÷ – – 00 – Place the decimal point. Answer: So, 72 ÷ 0.4 = 180. Check 180 × 0.4 = 72

Lesson 5 CYP2 6-5 Dividing by Decimals Find 45 ÷ 0.9. A.0.50 B.50 C.5 D.5.0

Lesson 5 Ex3 6-5 Dividing by Decimals Find ÷ – – 24 – Place the decimal point. Answer: So, ÷ 2.4 = Check 0.01 × 2.4 = does not go into 2, so write a 0 in the tenths place.

Lesson 5 CYP3 6-5 Dividing by Decimals A.0.03 B.3 C.0.3 D.1.2 Find ÷ 1.2.

Lesson 5 Ex4 6-5 Dividing by Decimals Ioviano bought a stock at $42.88 per share. If he spent $786.85, how many shares did he buy? Round to the nearest tenth Find ÷

Lesson 5 Ex4 6-5 Dividing by Decimals – – To the nearest tenth, ÷ = – – 20 Answer: So, Ioviano bought about 18.4 shares.

Lesson 5 CYP4 6-5 Dividing by Decimals A department store had one of their televisions on sale for $ If sales of the televisions totaled $21,773.45, about how many televisions were sold? A.88.6 televisions B.88 televisions C.89 televisions D.90 televisions

End of Lesson 5

Lesson 6 Menu Five-Minute Check (over Lesson 6-5) Main Idea California Standards Example 1: Problem-Solving Investigation 6-6 Problem-Solving Investigation: Choose the Best Strategy

6-6 Problem-Solving Investigation: Choose the Best Strategy Lesson 6 MI/Vocab/Standard 1 I will choose the best strategy to solve a problem.

6-6 Problem-Solving Investigation: Choose the Best Strategy Lesson 6 Standard 1 Standard 5MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Standard 5NS2.1 Add, subtract, multiply, and divide with decimals;... and verify the reasonableness of results.

Lesson 6 Ex1 MIGUEL: At the store, I saw the following items: a batting glove for $8.95, roller blades for $39.75, a can of tennis balls for $2.75, and weights for $5.50. I have $15 and I would like to buy more than one item. YOUR MISSION: Find which items Miguel can buy and spend about $ Problem-Solving Investigation: Choose the Best Strategy

Lesson 6 Ex1 Understand What facts do you know? You know the cost of the items and that Miguel has $15 to spend. What do you need to find? You need to find which items Miguel can buy. 6-6 Problem-Solving Investigation: Choose the Best Strategy

Lesson 6 Ex1 Plan Make an organized list to see the different possibilities and use estimation to be sure he spends about $ Problem-Solving Investigation: Choose the Best Strategy

Lesson 6 Ex1 Solve 6-6 Problem-Solving Investigation: Choose the Best Strategy Since the roller blades cost more than $15, you can eliminate the roller blades. The batting glove is about $9, the weights are about $6, and the can of tennis balls is about $3. Start with the batting glove: 1 glove + 1 weights ≈ $9 + $6 or $15 1 glove + 2 cans of tennis balls ≈ $9 + $6 or $15

Lesson 6 Ex1 Solve 6-6 Problem-Solving Investigation: Choose the Best Strategy List other combinations that contain the weights: 2 weights + 1 can of tennis balls ≈ $12 + $3 or $15 1 weights + 3 cans of tennis balls ≈ $6 + $9 or $15 List the remaining combinations that contain only tennis balls: 5 cans of tennis balls ≈ $15

Lesson 6 Ex1 Check 6-6 Problem-Solving Investigation: Choose the Best Strategy Check the list to be sure that all of the possible combinations of sporting good items that total no more than $15 are included.

End of Lesson 6

Lesson 7 Menu Five-Minute Check (over Lesson 6-6) Main Idea and Vocabulary California Standards Example 1: Estimate Using Compatible Numbers Example 2: Estimate Using Compatible Numbers 6-7 Estimating Products of Fractions Example 4: Estimate With Mixed Numbers Example 3: Estimate by Rounding to 0,, or 1 1 2

6-7 Estimating Products of Fractions Lesson 7 MI/Vocab I will estimate products of fractions using compatible numbers and rounding. compatible numbers

6-7 Estimating Products of Fractions Lesson 7 Standard 1 Standard 5MR2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Lesson 7 Ex1 6-7 Estimating Products of Fractions Find a multiple of 5 that is close to 16. × × 16 means of Estimate × × × 15 = Answer: So, × 16 is about and 5 are compatible numbers since 15 ÷ 5 = ÷ 5 = 3

Lesson 7 CYP1 6-7 Estimating Products of Fractions A.2 Estimate × B.3 C D.2 1 4

Lesson 7 Ex2 6-7 Estimating Products of Fractions Find a multiple of 4 that is close to 23. × Estimate × 23 first. 1 4 Estimate × × × 24 = Use 24 since 24 and 4 are compatible numbers. 24 ÷ 4 = 6

Lesson 7 Ex2 6-7 Estimating Products of Fractions Answer: So, of 23 is about If of 24 is 6, then of 24 is 6 × 3 or

Lesson 7 CYP2 6-7 Estimating Products of Fractions Estimate × B.18 C.17 A D.20

Lesson 7 Ex3 6-7 Estimating Products of Fractions × × 1 6 Estimate × × 1 6 = 1 6 Answer: So, × is about

Lesson 7 CYP3 6-7 Estimating Products of Fractions Estimate × B.2 A D C. 1 2

Lesson 7 Ex4 6-7 Estimating Products of Fractions Estimate the area of the rectangle. Round each mixed number to the nearest whole number.

Lesson 7 Ex4 6-7 Estimating Products of Fractions × 7 × 2 = 14 Answer: So, the area is about 14 square inches

Lesson 7 CYP4 6-7 Estimating Products of Fractions Estimate the area of a rectangle with a width of 9 in. and a length of 3 in A.30 in 2 B.27 in 2 C.40 in 2 D.36 in 2

End of Lesson 7

Lesson 8 Menu Five-Minute Check (over Lesson 6-7) Main Idea California Standards Key Concept: Multiply Fractions Click here to continue the Lesson Menu 6-8 Multiplying Fractions

Lesson 8 Menu Example 1: Multiply Fractions Example 2: Multiply Fractions and Whole Numbers Example 3: Simplify Before Multiplying Example 4: Evaluate Expressions 6-8 Multiplying Fractions

6-8 Multiplying Fractions Lesson 8 MI/Vocab I will multiply fractions.

6-8 Multiplying Fractions Lesson 8 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Lesson 8 Key Concept 6-8 Multiplying Fractions

Lesson 8 Ex1 6-8 Multiplying Fractions Find × × 1 6 = 1 × 1 5 × 6 Multiply the numerators. Multiply the denominators. = 1 30 Simplify.

Lesson 8 CYP1 6-8 Multiplying Fractions Find × C. 1 2 A D B. 1 7

Lesson 8 Ex2 6-8 Multiplying Fractions Find × Estimate × 7 = × 7 = 5 8 × 7 1 Write 7 as. 7 1 = 5 × 7 8 × 1 Multiply. = 35 8 or Simplify.

Lesson 8 Ex2 6-8 Multiplying Fractions Check for Reasonableness 4 is about

Lesson 8 CYP2 6-8 Multiplying Fractions Find × C.9 A.8 B D.8 1 9

Lesson 8 Ex3 6-8 Multiplying Fractions Find × Estimate × 0 = × 2 9 = 3 × 2 7 × 9 Multiply. = 6 63 or 2 21 Simplify.

Lesson 8 Ex3 6-8 Multiplying Fractions Check for Reasonableness is about

Lesson 8 CYP3 6-8 Multiplying Fractions Find × D.1 A B. 2 7 C. 6 26

Lesson 8 Ex4 6-8 Multiplying Fractions ALGEBRA Evaluate pq if p = and q = pq = × Replace p with and q with = 3 × 8 4 × 9 The GCF of 3 and 9 is 3. The GCF of 4 and 8 is 4. Divide the numerator and the denominator by 3 and = 2 3 Simplify. Answer: So, × =

Lesson 8 CYP4 6-8 Multiplying Fractions ALGEBRA Evaluate gh if g = and h = B. 1 5 A. 1 2 C D. 5 50

End of Lesson 8

Lesson 9 Menu Five-Minute Check (over Lesson 6-8) Main Idea California Standards Key Concept: Multiply Mixed Numbers Example 1: Multiply a Fraction and a Mixed Number Example 2: Multiply Mixed Numbers Example 3: Evaluate Expressions 6-9 Multiplying Mixed Numbers

6-9 Multiplying Mixed Numbers Lesson 9 MI/Vocab I will multiply mixed numbers.

6-9 Multiplying Mixed Numbers Lesson 9 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Lesson 9 Key Concept 6-9 Multiplying Mixed Numbers

Lesson 9 Ex1 6-9 Multiplying Mixed Numbers Find × × Estimate × 3 = × 10 8 × 3 = Write 3 as = 3 8 × 3 = 5 4 or Divide 10 and 8 by their GCF, 2. Divide 3 and 3 by their GCF, 3. Simplify. Compare to the estimate Answer: 1 1 4

Lesson 9 CYP1 6-9 Multiplying Mixed Numbers Find × C.3 A D.3 B.2 1 2

Lesson 9 Ex2 6-9 Multiplying Mixed Numbers Belinda lives 1 times farther from school than Elena does. If Elena lives 4 miles from school, how far from school does Belinda live? Elena lives 4 miles from school. Multiply 4 ×

Lesson 9 Ex2 6-9 Multiplying Mixed Numbers 4 × × 3 5 × 2 = First, write mixed numbers as improper fractions. = 3 2 × 21 5 Then, multiply the numerators and multiply the denominators. Simplify. = or Answer: So, Belinda lives 6 miles from school. 3 10

Lesson 9 CYP2 6-9 Multiplying Mixed Numbers Mariah is making 4 times the recipe for crispy treats. If the recipe calls for 1 cups of butter, how much butter will she need? A. cups B.5 cups 1 5 C.5 cups 5 16 D. cups 25 16

Lesson 9 Ex3 6-9 Multiplying Mixed Numbers ALGEBRA If y = 3 and w = 2, what is the value of wy? = Divide the numerator and denominator by 2 and 5. Simplify wy = 2 × Replace w with 2 and y with × 15 4 = or

Lesson 9 CYP3 6-9 Multiplying Mixed Numbers ALGEBRA If m = 4 and n = 2, what is the value of mn? C D.13 A B

End of Lesson 9

Lesson 10 Menu Five-Minute Check (over Lesson 6-9) Main Idea and Vocabulary California Standards Key Concept: Divide Fractions Example 1: Find Reciprocals Example 2: Find Reciprocals Example 3: Divide by a Fraction Example 4: Divide by a Fraction Example 5: Real-World Example 6-10 Dividing Fractions

6-10 Dividing Fractions Lesson 10 MI/Vocab I will divide fractions. reciprocal

6-10 Dividing Fractions Lesson 10 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Lesson 10 Key Concept Dividing Fractions

Lesson 10 Ex1 Find the reciprocal of Dividing Fractions Answer: Since, 8 × = 1, the reciprocal of 8 is

Lesson 10 CYP Dividing Fractions Find the reciprocal of 6. A.6 B.0.6 C. 6 1 D. 1 6

Lesson 10 Ex Dividing Fractions Find the reciprocal of. 3 5 Answer: Since, × = 1, the reciprocal of is

Lesson 10 CYP Dividing Fractions C. 2 2 D. 3 3 Find the reciprocal of. 2 3 A. 3 2 B. 2 3

Lesson 10 Ex Dividing Fractions 1 3 ÷ × 6 3 × 5 = Multiply by the reciprocal. 6 5 = 2 5 Divide 3 and 6 by the GCF, 3. Multiply numerators. Multiply denominators. 2 1 Find ÷ = 1 3 × Answer:

Lesson 10 CYP Dividing Fractions C. 7 9 D. 9 7 A. 4 7 B Find ÷

Lesson 10 Ex Dividing Fractions Find 5 ÷ ÷ 1 6 Multiply by the reciprocal. 6 1 Simplify. = 5 1 × 6 1 = or Answer: 30

Lesson 10 CYP Dividing Fractions C. 3 4 D.14 A.48 Find 6 ÷. 1 8 B. 6 8

Lesson 10 Ex Dividing Fractions A relay race is of a mile long. There are 4 runners in the race. What portion of a mile will each racer run? 3 4 Divide into 4 equal parts. 3 4

Lesson 10 Ex Dividing Fractions Answer: So, each runner ran of a mile Simplify. = 3 16 ÷ Multiply by the reciprocal. = 3 4 × 1 4

Lesson 10 CYP Dividing Fractions Three ladies decided to knit the world’s longest scarf. It was of a mile long. If each lady knit the same amount, what portion of a mile did each lady knit? 1 4 A. 3 4 mile B mile C. 1 8 mile D. 2 4 mile

End of Lesson 10

Lesson 11 Menu Five-Minute Check (over Lesson 6-10) Main Idea California Standards Key Concept: Dividing by Mixed Numbers Example 1: Divide by a Mixed Number Example 2: Evaluate Expressions Example 3: Real-World Example 6-11 Dividing Mixed Numbers

6-11 Dividing Mixed Numbers Lesson 11 MI/Vocab I will divide mixed numbers.

6-11 Dividing Mixed Numbers Lesson 11 Standard 1 Standard 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Lesson 11 Key Concept Dividing Mixed Numbers

Lesson 11 Ex Dividing Mixed Numbers Find 6 ÷ ÷ Estimate 6 ÷ 3 = 2 Write mixed numbers as improper fractions. = 25 4 ÷ 5 2 Multiply by the reciprocal. = 25 4 × 2 5

Lesson 11 Ex Dividing Mixed Numbers Divide 2 and 4 by the GCF, 2, and 25 and 5 by the GCF, 5. = 25 4 × Simplify. = or Check for Reasonableness 2 is about Answer: 2 1 2

Lesson 11 CYP Dividing Mixed Numbers Find 3 ÷ C D.2 B A

Lesson 11 Ex Dividing Mixed Numbers ALGEBRA Find a ÷ b if a = 2 and b = a ÷ b Write the mixed number as an improper fraction. = 21 8 ÷ 2 3 = 2 ÷ Multiply by the reciprocal. = 21 8 × 3 2 Replace a with 2 and b with Simplify. = or

Lesson 11 CYP Dividing Mixed Numbers ALGEBRA Find f ÷ g if f = 3 and g = D A C B

Lesson 11 Ex Dividing Mixed Numbers Estimate 180 ÷ 4 = ÷ Write mixed numbers as improper fractions. A team took 3 days to complete 180 miles of an adventure race consisting of hiking, biking, and river rafting. How many miles did they average each day? 3 4 = ÷

Lesson 11 Ex Dividing Mixed Numbers = 48 Multiply by the reciprocal. = × Divide 15 and 180 by the GCF, 15. Simplify. Compare to the estimate. Answer: So, the team averaged 48 miles each day. = ×

Lesson 11 CYP Dividing Mixed Numbers A cross country skier took 4 days to travel 240 miles. How many miles did he average each day? 2 3 D.52 miles 1 2 A.51 miles 3 7 B.51 miles 6 14 C.50 miles 3 4

End of Lesson 11

6 6 Multiplying and Dividing Decimals and Fractions 6 6 CR Menu Five-Minute Checks Math Tool Chest Image Bank Dividing Decimals Multiplying Fractions

6 6 Multiplying and Dividing Decimals and Fractions IB Instructions To use the images that are on the following four slides in your own presentation: 1.Exit this presentation. 2.Open a chapter presentation using a full installation of Microsoft ® PowerPoint ® in editing mode and scroll to the Image Bank slides. 3.Select an image, copy it, and paste it into your presentation.

6 6 Multiplying and Dividing Decimals and Fractions IB 1

6 6 Multiplying and Dividing Decimals and Fractions IB 2

6 6 Multiplying and Dividing Decimals and Fractions IB 3

6 6 Multiplying and Dividing Decimals and Fractions IB 4

6 6 Multiplying and Dividing Decimals and Fractions 6 6 5Min Menu Lesson 6-1Lesson 6-1(over Chapter 5) Lesson 6-2Lesson 6-2(over Lesson 6-1) Lesson 6-3Lesson 6-3(over Lesson 6-2) Lesson 6-4Lesson 6-4(over Lesson 6-3) Lesson 6-5Lesson 6-5(over Lesson 6-4) Lesson 6-6Lesson 6-6(over Lesson 6-5) Lesson 6-7Lesson 6-7(over Lesson 6-6) Lesson 6-8Lesson 6-8(over Lesson 6-7) Lesson 6-9Lesson 6-9(over Lesson 6-8) Lesson 6-10Lesson 6-10(over Lesson 6-9) Lesson 6-11Lesson 6-11(over Lesson 6-10)

6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-1 (over Chapter 5) Find 6 – C D.4 A B.8 3 4

6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-2 (over Chapter 5) Find 5 – C A B D.2 6 9

6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-3 (over Chapter 5) Find the value of n. n + 1 = A B.6 D.5 C.4 3 5

6 6 Multiplying and Dividing Decimals and Fractions 5Min 1-4 (over Chapter 5) Find the value of n. C. 2 5 A.3 B D n + 10 =

6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-1 (over Lesson 6-1) Find 3.8 × 2. A.5.8 B.7.6 C.5.6 D.5

6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-2 Find 0.6 × 25. A.15 B.25 C.10 D.4 (over Lesson 6-1)

6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-3 Find × 15. A.0.63 B.1.35 C.0.57 D.1 (over Lesson 6-1)

6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-4 Find × 17. A B C D.0.21 (over Lesson 6-1)

6 6 Multiplying and Dividing Decimals and Fractions 5Min 2-5 Mercury is approximately 3.6 × 10 7 miles from the Sun. How far is this? A.360 mi B.1,800,000 mi C.36,000,000 mi D.3,000,000 mi (over Lesson 6-1)

6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-1 (over Lesson 6-2) Find 75.4 × 2.9. A B C.125 D

6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-2 (over Lesson 6-2) Find 0.05 × A.0.15 B C D.1

6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-3 (over Lesson 6-2) Evaluate 2.5y if y = 4.8. A.4.8 B C.8.5 D.12

6 6 Multiplying and Dividing Decimals and Fractions 5Min 3-4 (over Lesson 6-2) Selam makes $6.75 an hour. Last week, she worked 12.4 hours. How much did she earn? A.$36.75 B.$48.55 C.$48.50 D.$83.70

6 6 Multiplying and Dividing Decimals and Fractions 5Min 4-1 (over Lesson 6-3) Determine a reasonable answer. Mr. Nieto has yards of fencing. How many feet of fencing is that? A ft B ft C.255 ft D ft

6 6 Multiplying and Dividing Decimals and Fractions 5Min 4-2 Cafeteria workers made 23.5 gallons of punch for an awards banquet. They are serving the punch in 1-quart pitchers. How many containers do they need for all the punch? (1 gal = 4 qt) A pitchers B.40 pitchers C.4 pitchers D.94 pitchers (over Lesson 6-3)

6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-1 (over Lesson 6-4) Find ÷ 9. Round to the nearest tenth if necessary. A.7.09 B.4 C.3.01 D.7

6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-2 (over Lesson 6-4) Find ÷ 5. Round to the nearest tenth if necessary. A.75.7 B.75 C.35.5 D.102

6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-3 (over Lesson 6-4) Find ÷ 7. Round to the nearest tenth if necessary. A.35.4 B.24 C D.23.5

6 6 Multiplying and Dividing Decimals and Fractions 5Min 5-4 (over Lesson 6-4) Find the mean for the following set of data: 7.8, 9.02, A.4.5 B.4.45 C.6.48 D.5.55

6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-1 (over Lesson 6-5) Find ÷ 4.2. A.5.8 B.5.66 C.4 D.6.18

6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-2 (over Lesson 6-5) Find ÷ A B.3 C.12 D.307.8

6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-3 (over Lesson 6-5) Find ÷ A.0.85 B.1.48 C.5.4 D.5.6

6 6 Multiplying and Dividing Decimals and Fractions 5Min 6-4 (over Lesson 6-5) Find ÷ 3.4. A.0.23 B C.4 D.12

6 6 Multiplying and Dividing Decimals and Fractions 5Min 7-1 (over Lesson 6-6) Choose the best strategy to solve the problem. The sum of three consecutive numbers is 42. What are the three numbers? A.12, 14, 16 B.15, 12, 9 C.13, 14, 15 D.12, 13, 14

6 6 Multiplying and Dividing Decimals and Fractions C.1 × 36 = 6 5Min 8-1 (over Lesson 6-7) Estimate the product. A. × 38 = × B. × 36 = D. × 48 = 8 1 6

6 6 Multiplying and Dividing Decimals and Fractions 5Min 8-2 (over Lesson 6-7) Estimate the product. A.1 × 45 = 45 C. × 45 = × B. × 45 = D. × 44 =

6 6 Multiplying and Dividing Decimals and Fractions 5Min 8-3 (over Lesson 6-7) Estimate the product. × B. × 45 = C. × 45 = A. × 1 = D. × 1 =

6 6 Multiplying and Dividing Decimals and Fractions 5Min 8-4 (over Lesson 6-7) B.25 × 40 = 1,000 ft 2 C.26 × 40 = 1,040 ft 2 A.25 × 40 = 975 ft 2 A pool is 25 feet wide and 39 feet long. Estimate the area D.25 × 4 = 100 ft 2

6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-1 (over Lesson 6-8) Multiply. Write in simplest form. × B. C D. 3 5 A. 4 5

6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-2 (over Lesson 6-8) Multiply. Write in simplest form. × B. D. 2 5 A. 2 3 C.1 1 3

6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-3 (over Lesson 6-8) Evaluate n if n =. Write in simplest form B. 1 3 D. 3 9 A. 4 5 C. 2 3

6 6 Multiplying and Dividing Decimals and Fractions 5Min 9-4 (over Lesson 6-8) Evaluate 10n if n =. Write in simplest form. 3 4 B D. 1 3 A C. 7 9

6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-1 (over Lesson 6-9) Multiply. Write in simplest form. × B D.2 C A.3 3 5

6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-2 (over Lesson 6-9) Multiply. Write in simplest form. B C A × D

6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-3 (over Lesson 6-9) The length of a square sandbox is 4 feet. What is the area of the sandbox? 2 3 B.23 ft C.21 ft A.21 ft D.9 ft 2 1 3

6 6 Multiplying and Dividing Decimals and Fractions 5Min 10-4 (over Lesson 6-9) ALGEBRA If a = 4 and t = 1, what is the value of at? C D.6 A B. 3 16

6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-1 (over Lesson 6-10) Divide. Write in simplest form. ÷ D.8 C.4 B. 1 2 A. 5 10

6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-2 (over Lesson 6-10) ÷ Divide. Write in simplest form. B.4 D.2 C.3 A.3 1 2

6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-3 (over Lesson 6-10) 6 ÷ 2 3 Divide. Write in simplest form. B.3 D.9 C.8 A. 2 3

6 6 Multiplying and Dividing Decimals and Fractions 5Min 11-4 (over Lesson 6-10) ÷ Divide. Write in simplest form. C.1 A. 2 3 B. 1 2 D. 1 3

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