Chapter 6 Multiplying and Dividing Decimals and Fractions

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

Five-Minute Check (over Chapter 5) Main Idea and Vocabulary
6-1 Multiplying Decimals by Whole Numbers Five-Minute Check (over Chapter 5) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Example 4 Example 5 Lesson 1 Menu

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

6-1 Multiplying Decimals by Whole Numbers 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 Standard 1

One Way: Use estimation.
6-1 Multiplying Decimals by Whole Numbers Find 18.9 × 4. One Way: Use estimation. Round 18.9 to 19. 18.9 × × 4 or 76 3 3 18.9 Since the estimate is 76, place the decimal point after the 5. × 4 7 5 6 . Lesson 1 Ex1

Another Way: Count decimal places.
6-1 Multiplying Decimals by Whole Numbers Another Way: Count decimal places. 3 3 18.9 × 4 7 5 6 . Lesson 1 Ex1

6-1 Multiplying Decimals by Whole Numbers Find 12.7 × 5. 64 63.5 60.35 63.35 Lesson 1 CYP1

One Way: Use estimation.
6-1 Multiplying Decimals by Whole Numbers Find 0.56 × 7. One Way: Use estimation. Round 0.56 to 1. 0.56 × × 7 or 7 3 4 0.56 Since the estimate is 7, place the decimal point after the 3. × 7 3 . 9 2 Lesson 1 Ex2

Another Way: Count decimal places.
6-1 Multiplying Decimals by Whole Numbers Another Way: Count decimal places. 3 4 0.56 × 7 3 . 9 2 Lesson 1 Ex2

6-1 Multiplying Decimals by Whole Numbers Find 0.47 × 8. 8 5 4.76 0.392 Lesson 1 CYP2

6-1 Multiplying Decimals by Whole Numbers Find 3 × 1 0.016 × 3 0. 4 8 Lesson 1 Ex3

6-1 Multiplying Decimals by Whole Numbers Find × 2. 0.052 0.52 0.0052 0.502 Lesson 1 CYP3

ALGEBRA Evaluate 5g if g = 0.0091.
6-1 Multiplying Decimals by Whole Numbers ALGEBRA Evaluate 5g if g = 5g = 5 × Replace g with 4 0.0091 × 5 0. 4 5 5 Lesson 1 Ex4

ALGEBRA Evaluate 3h if h = 0.0054.
6-1 Multiplying Decimals by Whole Numbers ALGEBRA Evaluate 3h if h = 1.62 0.162 0.0162 Lesson 1 CYP4

One Way: Use order of operations.
6-1 Multiplying Decimals by Whole Numbers The average distance from Earth to the Sun is 1.5 × 108 kilometers. Write the distance in standard form. One Way: Use order of operations. Evaluate 108 first. Then multiply. 1.5 × 108 = 1.5 × 10,000,000 = 150,000,000 kilometers Lesson 1 Ex5

Another Way: Use mental math.
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 × 108 = = 150,000,000 Lesson 1 Ex5

6-1 Multiplying Decimals by Whole Numbers The average distance from the Sun to the planet Jupiter is 58.8 × 107 kilometers. Choose the answer showing the distance written in standard form. 588,000,000 kilometers 58,000,000 kilometers 5,880,000,000 kilometers 5,800,000 kilometers Lesson 1 CYP5

End of Lesson 1

Five-Minute Check (over Lesson 6-1) Main Idea California Standards
6-2 Multiplying Decimals Five-Minute Check (over Lesson 6-1) Main Idea California Standards Example 1 Example 2 Example 3 Example 4 Lesson 2 Menu

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

6-2 Multiplying Decimals 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 2 Standard 1

Answer: So, the product is 24.07.
6-2 Multiplying Decimals Find 8.3 × 2.9. Estimate × × 3 or 24 one decimal place 8.3 × 2.9 one decimal place 747 + 166 24.07 two decimal places Answer: So, the product is Lesson 2 Ex1

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

Find 4.5 × 3.9. 17.55 20 18.44 19.45 6-2 Multiplying Decimals
Lesson 2 CYP1

Answer: So, the product is 0.636.
6-2 Multiplying Decimals Find 0.12 × 5.3. Estimate × × 5 or 0 two decimal places 0.12 × 5.3 one decimal place 36 + 60 0.636 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 Ex2

Find 0.14 × 3.3. 0.636 0.543 0.462 0.723 6-2 Multiplying Decimals
Lesson 2 CYP2

ALGEBRA Evaluate 1.8r if r = 0.029.
6-2 Multiplying Decimals ALGEBRA Evaluate 1.8r if r = 1.8r = 1.8 × 0.029 Replace r with 0.029 three decimal places × 1.8 one decimal place 232 + 29 0.0522 Annex a zero to make four decimal places. Answer: So, the product is Lesson 2 Ex3

ALGEBRA Evaluate 2.7x if x = 0.038.
6-2 Multiplying Decimals ALGEBRA Evaluate 2.7x if x = 2.738 0.1026 0.0126 0.2106 Lesson 2 CYP3

6-2 Multiplying Decimals 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? Estimate × × 16 or 240. two decimal places $14.60 × 15.75 two decimal places 7300 10220 7300 + 1460 Lesson 2 Ex4

Answer: So, Carmen earned $229.95.
6-2 Multiplying Decimals Answer: So, Carmen earned $ Check for Reasonableness Compare $ to the estimate. $ is about $240. Lesson 2 Ex4

6-2 Multiplying Decimals Alex went shopping for 6.5 hours and spent $32.50 per hour. How much did she spend? $211.25 $225 $250.25 $211.50 Lesson 2 CYP4

End of Lesson 2

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

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

6-3 Problem-Solving Strategy: Reasonable Answers 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 Standard 1

6-3 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 Ex 1

Understand What facts do you know? There are 2,000 pounds in one ton.
6-3 Problem-Solving Strategy: Reasonable Answers 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. Lesson 3 Ex1

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

Solve Blue whale: Humpback whale: 2,000 × 151 2,000 × 150 2,000 × 38.1
6-3 Problem-Solving Strategy: Reasonable Answers Solve Blue whale: Humpback whale: 2,000 × 151 2,000 × 2,000 × 38.1 2,000 × 300,000 80,000 300,000 – 80,000 = 220,000 Answer: A reasonable estimate for the difference in the weight of a blue whale and a humpback whale is 220,000 pounds. Lesson 3 Ex1

6-3 Problem-Solving Strategy: Reasonable Answers Check 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. Lesson 3 Ex1

End of Lesson 3

6-4 Dividing Decimals by Whole Numbers Five-Minute Check (over Lesson 6-3) Main Idea California Standards Example 1 Example 2 Example 3 Lesson 4 Menu

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

6-4 Dividing Decimals by Whole Numbers 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 4 Standard 1

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

Find 7.2 ÷ 3. Estimate 7.2 ÷ 3 7 ÷ 3 or about 2. 2 . 4 3 7.2 – 6 1 2 –
6-4 Dividing Decimals by Whole Numbers Find 7.2 ÷ 3. Estimate 7.2 ÷ ÷ 3 or about 2. 2 . 4 3 7.2 – 6 1 2 – 1 2 7.2 ÷ 3 = 2.4 Compared to the estimate, the quotient is reasonable. Lesson 4 Ex1

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

Find 6.6 ÷ 15. Estimate 6.6 ÷ 15 7 ÷ 15 or about 0.5. . 4 4 15 6.6 – 6
6-4 Dividing Decimals by Whole Numbers Find 6.6 ÷ 15. Estimate 6.6 ÷ ÷ 15 or about 0.5. . 4 4 15 6.6 – 6 6 – 6 6 – 60 6.6 ÷ 15 = 0.44 Compared to the estimate, the quotient is reasonable. Lesson 4 Ex2

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

6-4 Dividing Decimals by Whole Numbers During a science experiment, Nita measured the mass of four unknown samples. Her data is shown below. Sample 1: g Sample 2: g Sample 3: g Sample 4: g Lesson 4 Ex3

First, add all the data together.
6-4 Dividing Decimals by Whole Numbers First, add all the data together. Divide by the number of addends to find the mean mass. 6.22 6.00 6.11 6.11 4 24.44 + 24.44 Answer: So, the mean mass of Nita’s samples is 6.11 grams. Lesson 4 Ex3

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? $6.34 $6.00 $4.63 $3.64 Lesson 4 CYP3

End of Lesson 4

6-5 Dividing by Decimals Five-Minute Check (over Lesson 6-4) Main Idea California Standards Example 1 Example 2 Example 3 Example 4 Dividing Decimals Lesson 5 Menu

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

6-5 Dividing by Decimals 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 5 Standard 1

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

6-5 Dividing by Decimals Find ÷ 6.4. Estimate 21 ÷ 7 = 3 3 . 3 4 Place the decimal point. 6.4 21.44 64 214.4 Divide as with whole numbers. – 192 22 4 – 19 2 Annex a zero to continue. 3 2 – 3 2 Lesson 5 Ex1

6-5 Dividing by Decimals 21.44 divided by 6.4 is 3.34. Compare to the estimate. Check 3.34 × 6.4 = 21.44 Lesson 5 Ex1

Find 25.45 ÷ 5.5. 5.9 5.09 5.90 50.9 6-5 Dividing by Decimals
Lesson 5 CYP1

6-5 Dividing by Decimals Find 72 ÷ 0.4. 1 8 . Place the decimal point. 0.4 72.0 4 720. – 4 3 2 – 32 – Answer: So, 72 ÷ 0.4 = 180. Check × 0.4 = 72 Lesson 5 Ex2

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

6-5 Dividing by Decimals Find ÷ 2.4. . 1 Place the decimal point. 2.4 0.024 24 0.24 24 does not go into 2, so write a 0 in the tenths place. – 2 – 2 4 – 24 Answer: So, ÷ 2.4 = 0.01. Check × 2.4 = 0.024 Lesson 5 Ex3

Find 0.036 ÷ 1.2. 0.03 3 0.3 1.2 6-5 Dividing by Decimals
Lesson 5 CYP3

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

6-5 Dividing by Decimals 1 8 . 3 5 42.88 – 4288 3580 5 – 34304 1501 – 1286 4 2146 – 2144 20 Answer: So, to the nearest tenth, ÷ = So, Ioviana bought about 18.4 shares. Lesson 5 Ex4

6-5 Dividing by Decimals Oprah bought televisions for everyone in her audience at $ per TV. If she spent $21, about how many people were in the audience? Round to the nearest whole number. 88.6 people 88 people 89 people 90 people Lesson 5 CYP4

End of Lesson 5

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

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

6-6 Problem-Solving Investigation: Choose the Best Strategy 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 Standard 1

YOUR MISSION: Find which items Miguel can buy and spend about $15.
6-6 Problem-Solving Investigation: Choose the Best Strategy 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 $15. Lesson 6 Ex1

Understand What facts do you know?
6-6 Problem-Solving Investigation: Choose the Best Strategy 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. Lesson 6 Ex1

6-6 Problem-Solving Investigation: Choose the Best Strategy Plan Make an organized list to see the different possibilities and use estimation to be sure he spends about $15. Lesson 6 Ex1

6-6 Problem-Solving Investigation: Choose the Best Strategy Solve 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 List other combinations that contain the weights:
6-6 Problem-Solving Investigation: Choose the Best Strategy Solve 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

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

End of Lesson 6

Five-Minute Check (over Lesson 6-6) Main Idea and Vocabulary
6-7 Estimating Products of Fractions Five-Minute Check (over Lesson 6-6) Main Idea and Vocabulary California Standards Example 1 Example 2 Example 3 Lesson 7 Menu

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

6-7 Estimating Products of Fractions 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 Standard 1

Find a multiple of 5 that is close to 16.
6-7 Estimating Products of Fractions Estimate × 16. 1 5 × 16 means of 16. 1 5 Find a multiple of 5 that is close to 16. 15 and 5 are compatible numbers since 15 ÷ 5 = 3 1 5 1 5 × 16 × 15 1 5 × 15 = 3 15 ÷ 5 = 3 Answer: So, × 16 is about 3. 1 5 Lesson 7 Ex1

1 Estimate × 19. 9 2 3 2 2 6-7 1 1 4 Estimating Products of Fractions
Lesson 7 CYP1

Find a multiple of 4 that is close to 23.
6-7 Estimating Products of Fractions Estimate × 23. 3 4 Estimate × 23 first. 1 4 Find a multiple of 4 that is close to 23. Use 24 since 24 and 4 are compatible numbers. 1 4 1 4 × 23 × 24 1 4 × 24 = 6 24 ÷ 4 = 6 Lesson 7 Ex2

6-7 Estimating Products of Fractions If of 24 is 6, then of 24 is 6 × 3 or 18. 3 4 1 Answer: So, of 23 is about 18. 3 4 Lesson 7 Ex2

6-7 Estimating Products of Fractions Estimate × 29. 3 5 17 2 5 18 17 20 Lesson 7 CYP2

6-7 Estimating Products of Fractions Estimate × . 4 5 1 6 4 5 1 6 1 6 × 1 × 1 6 1 6 1 × = Answer: So, × is about 4 5 1 6 Lesson 7 Ex3

6-7 Estimating Products of Fractions Estimate × . 5 6 2 3 1 3 2 1 2 1 3 Lesson 7 CYP3

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

Answer: So, the area is about 14 square inches.
6-7 Estimating Products of Fractions 7 8 6 1 4 2 × 7 × 2 = 14 Answer: So, the area is about 14 square inches. Lesson 7 Ex4

6-7 Estimating Products of Fractions Estimate the area of a rectangle with a width of 9 in. and a length of 3 in. 4 5 1 8 30 sq. in. 27 sq. in. 40 sq. in. 36 sq. in. Lesson 7 CYP4

End of Lesson 7

Multiplying Fractions
6-8 Multiplying Fractions Five-Minute Check (over Lesson 6-7) Main Idea California Standards Key Concept: Multiply Fractions Example 1 Example 2 Example 3 Example 4 Multiplying Fractions Lesson 8 Menu

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

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

6-8 Multiplying Fractions Lesson 8 Key Concept

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

Find × . 1 7 2 2 14 1 7 1 2 1 14 6-8 Multiplying Fractions
Lesson 8 CYP1

Find × 7. 5 8 Estimate × 7 = 3 . 1 2 5 8 5 8 7 1 × 7 = × 5 × 7 8 × 1 =
6-8 Multiplying Fractions Find × 7. 5 8 Estimate × 7 = 1 2 5 8 5 8 7 1 Write 7 as . 7 1 × 7 = × 5 × 7 8 × 1 = Multiply. 35 8 or 4 3 8 = Simplify. Lesson 8 Ex2

6-8 Multiplying Fractions Check for Reasonableness 4 is about 3 8 1 2 Lesson 8 Ex2

6-8 Multiplying Fractions Find × 9. 7 8 8 7 9 9 8 1 9 Lesson 8 CYP2

6-8 Multiplying Fractions Find × . 3 7 2 9 Estimate × 0 = 0. 1 2 3 7 2 9 3 × 2 7 × 9 × = Multiply. 6 63 2 21 = or Simplify. Lesson 8 Ex3

6-8 Multiplying Fractions Check for Reasonableness is about 0. 2 21 Lesson 8 Ex3

Find × . 4 6 3 7 3 13 12 42 6 26 1 6-8 Multiplying Fractions
Lesson 8 CYP3

ALGEBRA Evaluate pq if p = and q = . 3 4 2
6-8 Multiplying Fractions ALGEBRA Evaluate pq if p = and q = . 3 4 2 pq = × 3 4 2 Replace p with and q with . 3 4 2 1 1 The GCF of 2 and 4 is 2. The GCF of 3 and 3 is 3. Divide the numerator and the denominator by 2 and 3. 3 × 2 4 × 3 = 2 1 1 2 = Simplify. Answer: So, × = . 3 4 2 1 Lesson 8 Ex4

ALGEBRA Evaluate gh if g = and h = . 2 5 10
6-8 Multiplying Fractions ALGEBRA Evaluate gh if g = and h = 2 5 10 1 2 1 5 10 50 5 50 Lesson 8 CYP4

End of Lesson 8

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

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

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

6-9 Multiplying Mixed Numbers Lesson 9 Key Concept

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

Find × 2 . 4 5 2 3 2 2 3 3 6-9 15 1 1 2 Multiplying Mixed Numbers
Lesson 9 CYP1

Elena lives 4 miles from school. Multiply 4 × 1 . 1 5 2
6-9 Multiplying Mixed Numbers Belinda lives 1 times farther from school than Elena does. If Elena lives miles from school, how far from school does Belinda live? 1 2 5 Elena lives miles from school. Multiply 4 × 1 5 2 Lesson 9 Ex2

Answer: So, Belinda lives 6 miles from school. 3 10
6-9 Multiplying Mixed Numbers 4 × 1 1 5 2 = 3 2 × 21 5 First, write mixed numbers as improper fractions. Then, multiply the numerators and multiply the denominators. 21 × 3 5 × 2 = = or 6 63 10 3 Simplify. Answer: So, Belinda lives miles from school. 3 10 Lesson 9 Ex2

6-9 Multiplying Mixed Numbers Mariah is making times the recipe for crispy treats. If the recipe calls for 1 cups of butter, how much butter will she need? 1 4 85 16 5 1 5 16 25 16 Lesson 9 CYP2

ALGEBRA If y = 3 and w = 2 , what is the value of wy? 3 4 5
6-9 Multiplying Mixed Numbers ALGEBRA If y = and w = 2 , what is the value of wy? 3 4 5 wy = × 3 4 5 3 Replace w with 2 and y with 4 5 3 3 7 Divide the numerator and denominator by 2 and 5. 15 4 14 5 = × 2 1 = or 10 1 2 21 Simplify. Lesson 9 Ex3

ALGEBRA If m = 4 and n = 2 , what is the value of mn? 5 8 6 7
6-9 Multiplying Mixed Numbers ALGEBRA If m = 4 and n = 2 , what is the value of mn? 5 8 6 7 185 14 180 14 13 3 14 13 Lesson 9 CYP3

End of Lesson 9

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

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

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

6-10 Dividing Fractions Lesson 10 Key Concept 1

Since, 8 × = 1, the reciprocal of 8 is . 1 8
6-10 Dividing Fractions Find the reciprocal of 8. Since, 8 × = 1, the reciprocal of 8 is . 1 8 Answer: 1 8 Lesson 10 Ex1

Find the reciprocal of 6. 6 0.6 6-10 6 1 1 6 Dividing Fractions
Lesson 10 CYP1

Since, × = 1, the reciprocal of is . 3 5
6-10 Dividing Fractions Find the reciprocal of . 3 5 Since, × = 1, the reciprocal of is . 3 5 Answer: 5 3 Lesson 10 Ex2

2 Find the reciprocal of . 3 6-10 3 2 2 3 2 3 Dividing Fractions
Lesson 10 CYP2

6-10 Dividing Fractions Find ÷ . 1 3 5 6 1 3 ÷ 5 6 = 1 3 × 6 5 Multiply by the reciprocal . 6 5 2 1 × 6 3 × 5 = Divide 3 and 6 by the GCF, 3. 1 Multiply numerators. Multiply denominators. = 2 5 Lesson 10 Ex3

Find ÷ . 2 3 6 7 6-10 4 7 12 21 7 9 9 7 Dividing Fractions
Lesson 10 CYP3

6-10 Dividing Fractions Find 5 ÷ . 1 6 5 ÷ 1 6 = 5 1 × 6 Multiply by the reciprocal . 6 1 = or 30 30 1 Simplify. Lesson 10 Ex4

6-10 Dividing Fractions Find 6 ÷ . 1 8 48 6 8 3 4 14 Lesson 10 CYP4

Divide into 4 equal parts. 3 4
6-10 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 Ex5

Answer: So, each runner ran of a mile. 3 16
6-10 Dividing Fractions ÷ 4 3 4 3 4 × 1 = Multiply by the reciprocal. 3 4 × 1 = Multiply. 3 16 = Simplify. Answer: So, each runner ran of a mile. 3 16 Lesson 10 Ex5

6-10 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 3 4 1 8 1 12 2 4 Lesson 10 CYP5

End of Lesson 10

6-11 Dividing Mixed Numbers Five-Minute Check (over Lesson 6-10) Main Idea California Standards Key Concept: Dividing by Mixed Numbers Example 1 Example 2 Example 3 Lesson 11 Menu

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

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

6-11 Dividing Mixed Numbers Lesson 11 Key Concept 1

6-11 Dividing Mixed Numbers Find ÷ 1 4 2 Estimate 6 ÷ 3 = 2 Write mixed numbers as improper fractions. 6 ÷ 2 1 4 2 = 25 4 ÷ 5 2 Multiply by the reciprocal. = 25 4 × 2 5 Lesson 11 Ex1

Check for Reasonableness 2 is about 3.
6-11 Dividing Mixed Numbers 5 1 Divide 2 and 4 by the GCF, 2, and 25 and 5 by the GCF, 5. = 25 4 × 2 5 2 1 Simplify. = or 2 1 2 5 Check for Reasonableness is about 3. 1 2 Lesson 11 Ex1

Find 3 ÷ 1 . 3 4 1 2 2 2 2 2 6-11 6 12 1 3 4 Dividing Mixed Numbers
Lesson 11 CYP1

ALGEBRA Find a ÷ b if a = 2 and b = . 5 8 2 3
6-11 Dividing Mixed Numbers ALGEBRA Find a ÷ b if a = and b = . 5 8 2 3 Replace a with 2 and b with . 5 8 2 3 = 2 ÷ 5 8 2 3 a ÷ b Write the mixed number as an improper fraction. = 21 8 ÷ 2 3 = 21 8 × 3 2 Multiply by the reciprocal. = 63 16 or 3 15 Simplify. Lesson 11 Ex2

ALGEBRA Find f ÷ g if f = 3 and g = . 2 3 5 8
6-11 Dividing Mixed Numbers ALGEBRA Find f ÷ g if f = and g = . 2 3 5 8 5 3 2 7 24 5 13 15 2 1 6 Lesson 11 CYP2

6-11 Dividing Mixed Numbers A team took 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 Estimate 180 ÷ 4 = 45 Write mixed numbers as improper fractions. 180 ÷ 3 3 4 = ÷ 180 1 15 4 Lesson 11 Ex3

Answer: So, the team averaged 48 miles each day.
6-11 Dividing Mixed Numbers = × 180 1 4 15 Multiply by the reciprocal. = 720 15 Simplify. = 48 Compare to the estimate. Answer: So, the team averaged 48 miles each day. Lesson 11 Ex3

6-11 Dividing Mixed Numbers A cross country skier took days to travel 240 miles. How many miles did he average each day? 2 3 51 miles 3 7 miles 6 14 50 miles 3 4 52 miles 1 2 Lesson 11 CYP3

End of Lesson 11

Five-Minute Checks Dividing Decimals Multiplying Fractions CR Menu

Lesson 6-1 (over Chapter 5) Lesson 6-2 (over Lesson 6-1)
5Min Menu

(over Chapter 5) Find – 1 4 3 3 1 2 8 3 4 4 1 2 4 5Min 1-1

(over Chapter 5) Find – 1 3 5 9 2 4 9 1 7 9 8 6 9 2 6 9 5Min 1-2

Find the value of n. 3 n + 1 = 8 5 6 6 4 5 2 5 3 5 (over Chapter 5)
5Min 1-3

(over Chapter 5) Find the value of n. n = 12 1 2 3 3 5 13 2 5 1 5 6 5Min 1-4

(over Lesson 6-1) Find 3.8 × 2. 5.8 7.6 5.6 5 5Min 2-1

(over Lesson 6-1) Find 0.6 × 25. 15 25 10 4 5Min 2-2

(over Lesson 6-1) Find × 15. 0.63 1.35 0.57 1 5Min 2-3

(over Lesson 6-1) Find × 17. 0.0021 0.0034 0.0051 0.21 5Min 2-4

(over Lesson 6-1) Mercury is approximately 3.6 × 107 miles from the Sun. How far is this? 360 mi 1,800,000 mi 36,000,000 mi 3,000,000 mi 5Min 2-5

(over Lesson 6-2) Find 75.4 × 2.9. 150.36 77.36 125 218.66 5Min 3-1

(over Lesson 6-2) Find 0.05 × 0.15 1 5Min 3-2

(over Lesson 6-2) Evaluate 2.5y if y = 4.8. 4.8 10.48 8.5 12 5Min 3-3

(over Lesson 6-2) Selam makes $6.75 an hour. Last week, she worked 12.4 hours. How much did she earn? $36.75 $48.55 $48.50 $83.70 5Min 3-4

(over Lesson 6-3) Determine a reasonable answer. Mr. Nieto has yards of fencing. How many feet of fencing is that? ft ft 255 ft 33.75 ft 5Min 4-1

(over Lesson 6-3) 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) 11.75 pitchers 40 pitchers 4 pitchers 94 pitchers 5Min 4-2

Find 27.09 ÷ 9. Round to the nearest tenth if necessary.
(over Lesson 6-4) Find ÷ 9. Round to the nearest tenth if necessary. 7.09 4 3.01 7 5Min 5-1

(over Lesson 6-4) Find ÷ 5. Round to the nearest tenth if necessary. 75.7 75 35.5 102 5Min 5-2

(over Lesson 6-4) Find ÷ 7. Round to the nearest tenth if necessary. 35.4 24 35.04 23.5 5Min 5-3

Find the mean for the following set of data: 7.8, 9.02, 2.62.
(over Lesson 6-4) Find the mean for the following set of data: 7.8, 9.02, 2.62. 4.5 4.45 6.48 5.55 5Min 5-4

(over Lesson 6-5) Find ÷ 4.2. 5.8 5.66 4 6.18 5Min 6-1

(over Lesson 6-5) Find ÷ 0.05. 128.5 3 12 307.8 5Min 6-2

(over Lesson 6-5) Find ÷ 0.12. 0.85 1.48 5.4 5.6 5Min 6-3

(over Lesson 6-5) Find ÷ 3.4. 0.023 0.015 4 12 5Min 6-4

(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? 12, 14, 16 15, 12, 9 13, 14, 15 5Min 7-1

Estimate the product. 1 × 38 6 × 38 = 8 × 36 = 6 1 × 36 = 6 1 6 1 6
(over Lesson 6-7) Estimate the product. × 38 1 6 × 38 = 8 1 6 × 36 = 6 1 6 1 × 36 = 6 5Min 8-1

Estimate the product. 2 × 44 3 1 × 45 = 45 × 45 = 45 × 45 = 30 2 3 2 3
(over Lesson 6-7) Estimate the product. × 44 2 3 1 × 45 = 45 × 45 = 45 2 3 × 45 = 30 2 3 5Min 8-2

Estimate the product. × 3 8 4 5 × 1 = × 45 = 30 × 45 = 17 1 2 3 8 1 2
(over Lesson 6-7) Estimate the product. × 3 8 4 5 × 1 = 1 2 × 45 = 30 3 8 × 45 = 17 1 2 5Min 8-3

A pool is 25 feet wide and 39 feet long. Estimate the area. 1 4 5 6
(over Lesson 6-7) A pool is feet wide and feet long. Estimate the area. 1 4 5 6 25 × 40 = 975 ft2 25 × 40 = 1,000 ft2 26 × 40 = 1,040 ft2 5Min 8-4

Multiply. Write in simplest form.
(over Lesson 6-8) Multiply. Write in simplest form. × 2 3 9 10 4 5 1 3 9 10 3 5 5Min 9-1

(over Lesson 6-8) Multiply. Write in simplest form. × 4 5 6 2 3 4 5 1 3 2 5 5Min 9-2

Evaluate n if n = . Write each product in simplest form. 8 9 3 4
(over Lesson 6-8) Evaluate n if n = . Write each product in simplest form. 8 9 3 4 4 5 1 3 2 3 3 9 5Min 9-3

Evaluate 10n if n = . Write each product in simplest form. 3 4
(over Lesson 6-8) Evaluate 10n if n = . Write each product in simplest form. 3 4 7 1 2 4 2 3 7 9 1 3 5Min 9-4

(over Lesson 6-9) Multiply. Write in simplest form. × 1 2 3 9 10 3 5 2 3 1 2 2 5Min 10-1

(over Lesson 6-9) Multiply. Write in simplest form. 5 × 4 5 6 1 10 1 5 24 1 2 21 1 2 31 1 2 5Min 10-2

(over Lesson 6-9) The length of a square sandbox is feet. What is the area of the sandbox? 2 3 ft2 7 9 ft2 5 9 ft2 5 9 5Min 10-3

ALGEBRA If a = 4 and t = 1 , what is the value of at? 4 5 1 16
(over Lesson 6-9) ALGEBRA If a = 4 and t = , what is the value of at? 4 5 1 16 5 16 3 16 5 3 6 5Min 10-4

Divide. Write in simplest form.
(over Lesson 6-10) Divide. Write in simplest form. ÷ 4 5 1 10 5 10 1 2 4 8 5Min 11-1

(over Lesson 6-10) Divide. Write in simplest form. ÷ 7 8 1 4 3 1 2 4 3 2 5Min 11-2

(over Lesson 6-10) Divide. Write in simplest form. 6 ÷ 2 3 2 3 3 8 9 5Min 11-3

(over Lesson 6-10) Divide. Write in simplest form. ÷ 1 2 3 4 2 3 1 2 1 1 3 5Min 11-4

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Chapter 6 Multiplying and Dividing Decimals and Fractions

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Chapter 6 Multiplying and Dividing Decimals and Fractions

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