Chapter 4 Fractions and Decimals

Chapter 4 Fractions and Decimals
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4 Lesson 4-1 Greatest Common Factor
Fractions and Decimals 4 Lesson 4-1 Greatest Common Factor Lesson 4-2 Problem-Solving Strategy: Make an Organized List Lesson 4-3 Simplifying Fractions Lesson 4-4 Mixed Numbers and Improper Fractions Lesson 4-5 Least Common Multiple Lesson 4-6 Problem-Solving Investigation: Choose the Best Strategy Lesson 4-7 Comparing Fractions Lesson 4-8 Writing Decimals as Fractions Lesson 4-9 Writing Fractions as Decimals Lesson Algebra: Ordered Pairs and Functions Chapter Menu

Greatest Common Factor
4-1 Greatest Common Factor Five-Minute Check (over Chapter 3) Main Idea and Vocabulary California Standards Click here to continue the Lesson Menu Greatest Common Factor Lesson 1 Menu

Greatest Common Factor
4-1 Greatest Common Factor Example 1: Identify Common Factors Example 2: Find the GCF by Listing Factors Example 3: Find the GCF by Using Prime Factors Example 4: Real-World Example Example 5: Real-World Example Greatest Common Factor Lesson 1 Menu

I will find the greatest common factor of two or more numbers.
4-1 Greatest Common Factor I will find the greatest common factor of two or more numbers. common factor greatest common factor (GCF) Lesson 1 MI/Vocab

4-1 Greatest Common Factor Preparation for Standard 6NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Lesson 1 Standard 1

Identify the common factors of 20 and 36.
4-1 Greatest Common Factor Identify the common factors of 20 and 36. First, list the factors by pairs for each number. Answer: The common factors of 20 and 36 are 1, 2, and 4. Lesson 1 Ex1

Identify the common factors of 12 and 18.
4-1 Greatest Common Factor Identify the common factors of 12 and 18. 1, 2, 3, 6 1, 2, 6 1, 2, 4, 6 1, 2, 3, 4, 6 Lesson 1 CYP1

Write the prime factorization.
4-1 Greatest Common Factor Find the GCF of 36 and 48. Write the prime factorization. 36 48 • 12 • 3 2 • 4 • 3 • 3 2 • 3 • 2 2 2 3 • Answer: The GCF of 36 and 48 is 2 × 3 or 6. Lesson 1 Ex2

4-1 Greatest Common Factor Check Use a Venn diagram to show the factors. Notice that the factors 1, 2, 3, 4, 6, and 12 are common factors of 36 and 48 and the GCF is 12. Lesson 1 Ex2

Find the GCF of 14 and 21. 1 2 3 7 4-1 Greatest Common Factor
Lesson 1 CYP2

Answer: The GCF of 21 and 28 is 7.
4-1 Greatest Common Factor Find the GCF of 21 and 28. 21 28 7 • 3 2 • 14 2 • 7 2 • Answer: The GCF of 21 and 28 is 7. Lesson 1 Ex3

4-1 Greatest Common Factor Check Use a Venn diagram to show the factors. Notice that the factors 1 and 7 are common factors of 21 and 28 and the GCF is 7. Lesson 1 Ex3

Find the GCF of 15 and 25. 1 2 5 15 4-1 Greatest Common Factor
Lesson 1 CYP3

4-1 Greatest Common Factor Ana sells bags of different kinds of cookies. She made $27 selling bags of peanut butter cookies, $18 from chocolate chip cookies, and $45 selling bags of oatmeal cookies. Each bag of cookies costs the same amount. What is the most that Ana could have charged for each bag of cookies? Lesson 1 Ex4

factors of 27: 1, 3, 9, 27 factors of 18: 1, 2, 3, 6, 9, 18
4-1 Greatest Common Factor factors of 27: 1, 3, 9, 27 factors of 18: 1, 2, 3, 6, 9, 18 factors of 45: 1, 3, 5, 9, 15, 45 The GCF of 27, 18, and 45 is 9. Answer: So, the most Ana could have charged for each bag of cookies is $9. Lesson 1 Ex4

4-1 Greatest Common Factor Joy bought presents for her three friends. She spent $48 on Jonah, $36 on Louise, and $60 on Brenden. Each gift cost the same amount. What is the most each gift could have cost? $1 $4 $18 $12 Lesson 1 CYP4

There is a total of $27 + $18 + $45 or $90.
4-1 Greatest Common Factor Ana sells bags of different kinds of cookies. She made $27 selling bags of peanut butter cookies, $18 from chocolate chip cookies, and $45 selling bags of oatmeal cookies. How many bags could Ana have sold if each bag cost $9? There is a total of $27 + $18 + $45 or $90. Answer: So, the number of bags of cookies Ana could have sold is $90 ÷ $9 or 10 bags. Lesson 1 Ex5

4-1 Greatest Common Factor If Joy spent $48 on Jonah, $36 on Louise, and $60 on Brenden, and each gift cost $12, how many gifts did she buy? 48 gifts 36 gifts 12 gifts 60 gifts Lesson 1 CYP5

End of Lesson 1

Five-Minute Check (over Lesson 4-1) Main Idea California Standards
4-2 Problem-Solving Strategy: Make an Organized List Five-Minute Check (over Lesson 4-1) Main Idea California Standards Example 1: Problem-Solving Strategy Lesson 2 Menu

I will solve problems by making an organized list.
4-2 Problem-Solving Strategy: Make an Organized List I will solve problems by making an organized list. Lesson 2 MI/Vocab

4-2 Problem-Solving Strategy: Make an Organized List Standard 5MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. Standard 5NS1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors. Lesson 2 Standard 1

4-2 Problem-Solving Strategy: Make an Organized List Jessica is setting up four booths in a row for the school carnival. There will be a dart game booth, a ring toss booth, a face-painting booth, and a virtual football booth. In how many ways can the four booths be arranged for the school carnival? Lesson 2 Ex1

Understand What facts do you know?
4-2 Problem-Solving Strategy: Make an Organized List Understand What facts do you know? There are four different booths: dart game, ring toss, face-painting, and virtual football. The booths will be set up in a row. What do you need to find? Find how many different ways the booth can be arranged. Lesson 2 Ex1

4-2 Problem-Solving Strategy: Make an Organized List Plan Make a list of all the different possible arrangements. Use D for darts, R for ring toss, F for face-painting, and V for virtual football. Organize your list by listing each booth first as shown below. D _ _ _ R _ _ _ F _ _ _ V _ _ _ Lesson 2 Ex1

Plan D _ _ _ R _ _ _ F _ _ _ V _ _ _
4-2 Problem-Solving Strategy: Make an Organized List Plan D _ _ _ R _ _ _ F _ _ _ V _ _ _ Then fill in the remaining three positions with the other booths. Continue this process until all the different arrangements are listed in the second, third, and fourth positions. Lesson 2 Ex1

Solve Listing D first: Listing R first: D R F V D R V F D F R V
4-2 Problem-Solving Strategy: Make an Organized List Solve Listing D first: Listing R first: D R F V D R V F D F R V D F V R D V R F D V F R R F V D R F D V R V D F R V F D R D F V R D V F Lesson 2 Ex1

Solve Listing F first: Listing V first: F V D R F V R D F D R V
4-2 Problem-Solving Strategy: Make an Organized List Solve Listing F first: Listing V first: F V D R F V R D F D R V F D V R F R V D F R D V V D R F V D F R V R F D V R D F V F D R V F R D Answer: There are 24 different ways the booths can be arranged. Lesson 2 Ex1 Lesson 2 Ex1

4-2 Problem-Solving Strategy: Make an Organized List Check Look back. Is each booth accounted for six times in the first, second, third, and fourth positions? Lesson 2 Ex1

End of Lesson 2

Five-Minute Check (over Lesson 4-2) Main Idea and Vocabulary
4-3 Simplifying Fractions Five-Minute Check (over Lesson 4-2) Main Idea and Vocabulary California Standards Example 1: Write Equivalent Fractions Example 2: Write Equivalent Fractions Example 3: Write Fractions in Simplest Form Example 4: Real-World Example Lesson 3 Menu

I will express fractions in simplest form.
4-3 Simplifying Fractions I will express fractions in simplest form. ratio equivalent fractions simplest form Lesson 3 MI/Vocab

4-3 Simplifying Fractions Preparation for Standard 5NS2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form. Lesson 3 Standard 1

Replace the x with a number so the fractions are equivalent.
4-3 Simplifying Fractions Replace the x with a number so the fractions are equivalent. 6 13 x 52 = 6 13 x 52 = Since 13 × 4 = 52, multiply the numerator and denominator by 4. Answer: So, x = 24. Lesson 3 Ex1

Solve for x so the fractions are equivalent. 7 12 x 48 =
4-3 Simplifying Fractions Solve for x so the fractions are equivalent. 7 12 x 48 = 24 28 30 7 Lesson 3 CYP1

Replace the x with a number so the fractions are equivalent.
4-3 Simplifying Fractions Replace the x with a number so the fractions are equivalent. 24 40 3 x = 24 40 3 x = Since 24 ÷ 8 = 3, divide the numerator and denominator by 8. Answer: So, x = 5. Lesson 3 Ex2

Solve for x so the fractions are equivalent. 5 25 1 x =
4-3 Simplifying Fractions Solve for x so the fractions are equivalent. 5 25 1 x = 5 10 20 15 Lesson 3 CYP2

One Way: Divide by common factors.
4-3 Simplifying Fractions Write in simplest form. 14 42 One Way: Divide by common factors. 14 42 7 21 1 3 A common factor of 14 and 42 is 2. = = A common factor of 7 and 21 is 7. Lesson 3 Ex3

Another Way: Divide by the GCF.
4-3 Simplifying Fractions Another Way: Divide by the GCF. factors of 14: 1, 2, 7, 14 factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 The GCF of 14 and 42 is 14. 14 42 1 3 Divide the numerator and denominator by the GCF, 14. = Lesson 3 Ex3

Answer: So, written in simplest form is .
4-3 Simplifying Fractions Answer: So, written in simplest form is . 14 42 1 3 Lesson 3 Ex3

48 Write in simplest form. 50 24 25 9 10 14 15 48 50 4-3
Simplifying Fractions Write in simplest form. 48 50 24 25 9 10 14 15 48 50 Lesson 3 CYP3

Mentally divide both the numerator and denominator by 3.
4-3 Simplifying Fractions Lin practices gymnastics 3 hours each day. There are 24 hours in a day. Express the fraction in simplest form. 3 24 The GCF of 3 and 24 is 3. 1 3 24 1 8 = Mentally divide both the numerator and denominator by 3. 8 Answer: So, Lin spends or 1 out of every hours practicing gymnastics. 1 8 Lesson 3 Ex4

Mark spends $10 of the $50 his mom gave him. Express in simplest form.
4-3 Simplifying Fractions Mark spends $10 of the $50 his mom gave him. Express in simplest form. 10 50 5 10 1 2 1 5 1 25 Lesson 3 CYP4

End of Lesson 3

4-4 Mixed Numbers and Improper Fractions Five-Minute Check (over Lesson 4-3) Main Idea and Vocabulary California Standards Example 1: Mixed Numbers as Improper Fractions Example 2: Improper Fractions as Mixed Numbers Lesson 4 Menu

I will write mixed numbers as improper fractions and vice versa.
4-4 Mixed Numbers and Improper Fractions I will write mixed numbers as improper fractions and vice versa. mixed number proper fraction improper fraction Lesson 4 MI/Vocab

4-4 Mixed Numbers and Improper Fractions Standard 5NS1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. Lesson 4 Standard 1

4-4 Mixed Numbers and Improper Fractions If a spaceship lifts off the Moon, it must travel at a speed of kilometers per second in order to escape the pull of the Moon’s gravity. Write this speed as an improper fraction. Then graph the improper fraction on a number line. 2 5 Lesson 4 Ex1

4-4 Mixed Numbers and Improper Fractions (2 × 5) + 2 5 2 5 = 12 5 = So, = 12 5 2 Lesson 4 Ex1

4-4 Mixed Numbers and Improper Fractions Since is between 2 and 3, draw a number line using increments of one fifth. Then, draw a dot at 12 5 Answer: 12 5 Lesson 4 Ex1

4-4 Mixed Numbers and Improper Fractions The average height of an adult man is feet tall. Choose the answer that shows as an improper fraction. 9 12 59 12 69 60 9 60 69 12 Lesson 4 CYP1

Write as a mixed number. Then graph the mixed number on a number line.
4-4 Mixed Numbers and Improper Fractions Write as a mixed number. Then graph the mixed number on a number line. 23 4 3 4 5 4 23 – 20 So, = 23 4 3 3 Lesson 4 Ex2

4-4 Mixed Numbers and Improper Fractions Since is between 5 and 6, draw a number line from 5 to 6 using increments of one fourth. Then, draw a dot at 3 4 Answer: Lesson 4 Ex2

Choose the answer that shows as a mixed number. 47 6
4-4 Mixed Numbers and Improper Fractions Choose the answer that shows as a mixed number. 47 6 6 5 7 7 5 6 5 6 7 7 8 Lesson 4 CYP2

End of Lesson 4

4-5 Least Common Multiple Five-Minute Check (over Lesson 4-4) Main Idea and Vocabulary California Standards Example 1: Identify Common Multiples Example 2: Find the LCM Example 3: Real-World Example Lesson 5 Menu

I will find the least common multiple of two or more numbers.
4-5 Least Common Multiple I will find the least common multiple of two or more numbers. multiple common multiples least common multiple (LCM) Lesson 5 MI/Vocab

4-5 Least Common Multiple Preparation for Standard 5SDAPS1.3 Use fractions and percentages to compare data sets of different sizes. Lesson 5 Standard 1

Identify the first three common multiples of 3 and 9.
4-5 Least Common Multiple Identify the first three common multiples of 3 and 9. First, list the multiples of each number. multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, … 1 × 3, 2 × 3, 3 × 3, … multiples of 9: 9, 18, 27, 36, 45, 54, … 1 × 9, 2 × 9, 3 × 9, … Lesson 5 Ex1

Notice that 9, 18, and 27 are multiples common to both 3 and 9.
4-5 Least Common Multiple Notice that 9, 18, and 27 are multiples common to both 3 and 9. Answer: So, the first three common multiples of 3 and 9 are 9, 18, and 27. Lesson 5 Ex1

Identify the first three multiples of 6 and 12.
4-5 Least Common Multiple Identify the first three multiples of 6 and 12. 6, 12, 18 6, 12, 24 12, 24, 36 12, 24, 48 Lesson 5 CYP1

Write the prime factorization of each number.
4-5 Least Common Multiple Find the LCM of 8 and 18. Write the prime factorization of each number. 8 18 2 × 4 3 × 6 2 × 2 2 2 × 3 3 Lesson 5 Ex2

Identify all common prime factors.
4-5 Least Common Multiple Identify all common prime factors. 8 = 2 × 2 × 2 18 = 3 × 2 × 3 Find the product of the prime factors using each common prime factor only once and any remaining factors. Answer: The LCM is 2 × 2 × 2 × 3 × 3 or 72. Lesson 5 Ex2

Find the LCM of 7 and 21. 7 42 21 14 4-5 Least Common Multiple
Lesson 5 CYP2

Find the LCM using prime factors.
4-5 Least Common Multiple Liam, Eva, and Bansi each have the same amount of money. Liam has only nickels, Eva has only dimes, and Bansi has only quarters. What is the least amount of money that each of them could have? Find the LCM using prime factors. 5 10 25 5 2 × 5 5 × 5 Answer: The least amount of money each of them could have is 5 × 5 × 2 or $0.50. Lesson 5 Ex3

4-5 Least Common Multiple Samuel, John, and Uma were all paid the same amount of money in one-dollar, five-dollar, and ten-dollar bills, respectively. What is the least amount of money each of them could have been paid? $10 $20 $25 $5 Lesson 5 CYP3

End of Lesson 5

4-6 Problem-Solving Investigation: Choose the Best Strategy Five-Minute Check (over Lesson 4-5) Main Idea California Standards Example 1: Problem-Solving Investigation Lesson 6 Menu

Lesson 6 MI/Vocab/Standard 1
4-6 Problem-Solving Investigation: Choose the Best Strategy I will choose the best strategy to solve a problem. Lesson 6 MI/Vocab/Standard 1

4-6 Problem-Solving Investigation: Choose the Best Strategy Standard 5MR2.6 Make precise calculations and check the validity of the results from the context of the problem. Lesson 6 Standard 1

4-6 Problem-Solving Investigation: Choose the Best Strategy Standard 5SDAP1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets. Lesson 6 Standard 1

4-6 Problem-Solving Investigation: Choose the Best Strategy TROY: This weekend, my family went to the zoo. We spent a total of $42 on admission tickets. We purchased at least 2 adult tickets for $9 each and no more than three children’s tickets for $5 each. YOUR MISSION: Find how many adult and children’s tickets Troy’s family purchased. Lesson 6 Ex1

Understand What facts do you know?
4-6 Problem-Solving Investigation: Choose the Best Strategy Understand What facts do you know? You know that the family spent a total of $42. At least 2 adult tickets were purchased for $9 each. No more than three children’s tickets were purchased for $5 each. Lesson 6 Ex1

Understand What do you need to find?
4-6 Problem-Solving Investigation: Choose the Best Strategy Understand What do you need to find? You need to find how many of each ticket Troy’s family purchased. Lesson 6 Ex1

4-6 Problem-Solving Investigation: Choose the Best Strategy Plan Guess and check to find the number of adult and children’s tickets purchased. Lesson 6 Ex1

4-6 Problem-Solving Investigation: Choose the Best Strategy Solve Answer: So, Troy’s family bought 3 adult and 3 children’s tickets. Lesson 6 Ex1

4-6 Problem-Solving Investigation: Choose the Best Strategy Check Look back. Three adult tickets cost 3 × $9, or $27 and three children’s tickets cost 3 × $5 or $15. Since $27 + $15 = $42, the answer is correct. Lesson 6 Ex1

End of Lesson 6

4-7 Comparing Fractions Five-Minute Check (over Lesson 4-6) Main Idea and Vocabulary California Standards Key Concept: Compare Two Fractions Example 1: Compare Fractions Example 2: Compare Mixed Numbers Example 3: Compare Data Sets Example 4: Real-World Example Lesson 7 Menu

I will compare fractions.
4-7 Comparing Fractions I will compare fractions. least common denominator (LCD) Lesson 7 MI/Vocab

4-7 Comparing Fractions Standard 5SDAP1.3 Use fractions and percentages to compare data sets of different sizes. Lesson 7 Standard 1

4-7 Comparing Fractions Lesson 7 Key Concept

Replace the with <, >, or = to make a true sentence.
4-7 Comparing Fractions Replace the with <, >, or = to make a true sentence. 8 21 3 7 Step 1 The LCM of the denominators is 21. So, the LCD is 21. Lesson 7 Ex1

4-7 Comparing Fractions Step 2 Write an equivalent fraction with a denominator of 21 for each fraction. 8 21 8 21 3 7 9 21 = = Step < , since 8 < 9. 8 21 9 Answer: So, < . 8 21 3 7 Lesson 7 Ex1

4-7 Comparing Fractions Replace the with <, >, or = to make a true sentence. 2 3 4 > < = + Lesson 7 CYP1

4-7 Comparing Fractions Replace the with <, >, or = to make a true sentence. 2 6 1 3 Since the whole numbers are the same, compare and . 1 3 2 6 Step 1 The LCM of the denominators is 6. So, the LCD is 6. Lesson 7 Ex2

4-7 Comparing Fractions Step 2 Write an equivalent fraction with a denominator of 6 for each fraction. 2 6 2 6 1 3 2 6 = = Step = , since 2 = 2. 2 6 Answer: So, = 1 3 2 6 Lesson 7 Ex2

4-7 Comparing Fractions Replace the with <, >, or = to make a true sentence. 4 5 3 8 > < = + Lesson 7 CYP2

Step 1 Write each quantity as a fraction.
4-7 Comparing Fractions Ginny had 3 out of 4 hits in a baseball game. Belinda had 4 out of 6 hits in that game. Who had the greater fraction of hits? Step 1 Write each quantity as a fraction. Ginny: 3 4 Belinda: 4 6 Lesson 7 Ex3

Answer: Since > , the fraction of hits Ginny had is greater. 9 12 8
4-7 Comparing Fractions Step 2 The LCD of the fractions is 12. So, rewrite each fraction with a denominator of 12. 3 4 9 12 4 6 8 12 = = Answer: Since > , the fraction of hits Ginny had is greater. 9 12 8 Lesson 7 Ex3

They got the same fraction. neither
4-7 Comparing Fractions Heidi got 10 out of 12 answers correct on the math quiz. Tiffany got 5 out of 6 correct on her math quiz. Who had the greater fraction of correct answers? Tiffany Heidi They got the same fraction. neither Lesson 7 CYP3

You need to compare the fractions. The LCD of the fractions is 100.
4-7 Comparing Fractions Use the table to answer the following question. What did the fewest number of people say should be done with a penny? You need to compare the fractions. The LCD of the fractions is 100. Lesson 7 Ex4

Rewrite the fractions with the LCD, 100.
4-7 Comparing Fractions Rewrite the fractions with the LCD, 100. 8 25 32 100 3 100 3 100 13 20 65 100 = = = Answer: Since the least number is 3, the fewest number of people were undecided. Lesson 7 Ex4

According to the data in the table, who walked the shortest distance?
4-7 Comparing Fractions According to the data in the table, who walked the shortest distance? Kayla Nora Mercedes They all walked the same distance. Lesson 7 CYP4

End of Lesson 7

4-8 Writing Decimals as Fractions Five-Minute Check (over Lesson 4-7) Main Idea and Vocabulary California Standards Example 1: Write Decimals as Fractions Example 2: Write Decimals as Fractions Example 3: Write Decimals as Fractions Example 4: Write Decimals as Fractions Example 5: Write Decimals as Mixed Numbers Lesson 8 Menu

I will write decimals as fractions or mixed numbers in simplest form.
4-8 Writing Decimals as Fractions I will write decimals as fractions or mixed numbers in simplest form. rational number Lesson 8 MI/Vocab

4-8 Writing Decimals as Fractions Preparation for Standard 5NS1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers. Lesson 8 Standard 1

Write 0.4 as a fraction in simplest form.
4-8 Writing Decimals as Fractions Write 0.4 as a fraction in simplest form. In the place-value chart, the last nonzero digit, 4, is in the tenths place. Say four tenths. 4 Lesson 8 Ex1

4 0.4 = 10 4 = 10 2 = 5 2 Answer: 0.4 = 5 4-8 Write as a fraction.
Writing Decimals as Fractions 4 10 Write as a fraction. 0.4 = 2 4 10 Simplify. Divide the numerator and denominator by the GCF, 2. = 5 2 5 = Answer: 0.4 = 2 5 Lesson 8 Ex1

4-8 Writing Decimals as Fractions Write 0.8 as a fraction in simplest form. 4 5 8 10 6 8 2 3 Lesson 8 CYP1

4-8 Writing Decimals as Fractions Write 0.38 as a fraction in simplest form. In the place-value chart, the last nonzero digit, 8, is in the hundredths place. Say thirty-eight hundredths. 3 8 Lesson 8 Ex2

4-8 Writing Decimals as Fractions 38 100 Write as a fraction. 0.38 = 19 38 100 Simplify. Divide the numerator and denominator by the GCF, 2. = 50 19 50 = 19 50 Answer: So, 0.38 = Lesson 8 Ex2

4-8 Writing Decimals as Fractions Write 0.07 as a fraction in simplest form. In the place-value chart, the last nonzero digit, 7, is in the hundredths place. Say seven hundredths. 7 Lesson 8 Ex3

The GCF is 1, so is in simplest form. 7 100
4-8 Writing Decimals as Fractions 7 100 Write as a fraction. 0.07 = The GCF is 1, so is in simplest form. 7 100 Answer: So, 0.07 = 7 100 Lesson 8 Ex3

4-8 Writing Decimals as Fractions Write as a fraction in simplest form. In the place-value chart, the last nonzero digit, 4, is in the thousandths place. Say two hundred sixty-four thousandths. 2 6 4 Lesson 8 Ex4

4-8 Writing Decimals as Fractions 264 1,000 Write as a fraction. 0.264 = 33 264 1,000 Simplify. Divide by the GCF, 8. = 125 33 125 = Answer: So, = 33 125 Lesson 8 Ex4

4-8 Writing Decimals as Fractions Write as a fraction in simplest form. 246 1,000 123 500 17 40 41 67 Lesson 8 CYP4

4-8 Writing Decimals as Fractions In 1955, Hurricane Diane moved through New England and produced one of the region’s heaviest rainfalls in history. In a 24-hour period, inches of rain were recorded in one area. Express this amount as a mixed number in simplest form. Lesson 8 Ex5

Answer: So, 18 inches of rain were recorded in a 24-hour period. 3 20
4-8 Writing Decimals as Fractions 15 100 Write as a fraction. 18.15 = 18 3 15 100 Simplify. = 18 20 3 20 = 18 Answer: So, inches of rain were recorded in a 24-hour period. 3 20 Lesson 8 Ex5

4-8 Writing Decimals as Fractions Lee Redmond is the world record holder for the longest fingernails. Her thumbnail is 30.2 inches long. Express this length as a mixed number in simplest form. 30 inches 1 5 inches 1 2 inches 3 4 inches 1 4 Lesson 8 CYP5

End of Lesson 8

4-9 Writing Fractions as Decimals Five-Minute Check (over Lesson 4-8) Main Idea California Standards Example 1: Write Fractions as Decimals Example 2: Write Fractions as Decimals Example 3: Fractions as Decimals Example 4: Mixed Numbers Lesson 9 Menu

I will write fractions as decimals.
4-9 Writing Fractions as Decimals I will write fractions as decimals. Lesson 9 MI/Vocab

4-9 Writing Fractions as Decimals Standard 5NS1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number. Lesson 9 Standard 1

4-9 Writing Fractions as Decimals Write as a decimal. 7 10 Since has a denominator of 10, it can be written as a decimal using place value. 7 10 Answer: = 0.7 7 10 Lesson 9 Ex1

Choose the answer below that shows written as a decimal. 29 100
4-9 Writing Fractions as Decimals Choose the answer below that shows written as a decimal. 29 100 0.029 0.29 2.9 0.0029 Lesson 9 CYP1

4-9 Writing Fractions as Decimals Write as a decimal. 1 4 Since 4 is a factor of 100, write an equivalent fraction with a denominator of 100. Lesson 9 Ex2

1 4 = 25 100 = 0.25 Answer: Therefore, = 0.25. 1 4 4-9
Writing Fractions as Decimals 1 4 = 25 100 Since 4 × 25 = 100, multiply the numerator and denominator by 25. = Read 0.25 as twenty-five hundredths. Answer: Therefore, = 0.25. 1 4 Lesson 9 Ex2

4-9 Writing Fractions as Decimals Write as a decimal. 3 8 3 8 0. 3 7 5 8 3.000 – 2 4 6 – 56 4 – 40 Answer: Therefore, = 3 8 Lesson 9 Ex3

Answer: The number of packs is 3.125.
4-9 Writing Fractions as Decimals At a meeting, people drank 25 bottles of water. The water came in packs of 8. This makes packs. Write the number as a decimal. 1 8 3 1 8 1 8 Definition of a mixed number = 3 + Since 8 × 125 = 1,000, multiply the numerator and the denominator by 125. 125 1,000 = 3 + = or 3.125 Answer: The number of packs is Lesson 9 Ex4

4-9 Writing Fractions as Decimals At the party, kids drank 18 juice boxes. The juice came in packs of 10. This makes packs. Choose the answer below that shows the number of packs written as a decimal. 8 10 1.8 packs 1.10 packs 1.18 packs 1.08 packs Lesson 9 CYP4

End of Lesson 9

Ordered Pairs and Functions
4-10 Algebra: Ordered Pairs and Functions Five-Minute Check (over Lesson 4-9) Main Idea and Vocabulary California Standards Click here to continue the Lesson Menu Ordered Pairs and Functions Lesson 10 Menu

Ordered Pairs and Functions
4-10 Algebra: Ordered Pairs and Functions Example 1: Naming Points Using Ordered Pairs Example 2: Graphing Ordered Pairs Example 3: Graphing Ordered Pairs Example 4: Real-World Example Example 5: Real-World Example Ordered Pairs and Functions Lesson 10 Menu

I will use ordered pairs to locate points and organize data.
4-10 Algebra: Ordered Pairs and Functions I will use ordered pairs to locate points and organize data. coordinate plane origin x-axis y-axis ordered pair x-coordinate y-coordinate graph Lesson 10 MI/Vocab

4-10 Algebra: Ordered Pairs and Functions Standard 5SDAP1.5 Know how to write ordered pairs correctly; for example, (x, y). Lesson 10 Standard 1

Write the ordered pair that names the point S.
4-10 Algebra: Ordered Pairs and Functions Write the ordered pair that names the point S. Step 1 Start at the origin. Move right along the x-axis until you are under point S. The x-coordinate of the ordered pair is 1. S Lesson 10 Ex1

Step 2 Now move up until you reach point S. The y-coordinate is 2.
4-10 Algebra: Ordered Pairs and Functions Step 2 Now move up until you reach point S. The y-coordinate is 2. S Answer: So, point S is named by the ordered pair (1, 2). Lesson 10 Ex1

Write the ordered pair that names the point T.
4-10 Algebra: Ordered Pairs and Functions Write the ordered pair that names the point T. (2, 1) (1, 2) (1, 1) (2, 2) Lesson 10 CYP1

Move 2 units to the right on the x-axis.
4-10 Algebra: Ordered Pairs and Functions Graph the point T(2, 2). Start at the origin. Move 2 units to the right on the x-axis. Then move 2 units up to locate the point. Draw a dot and label the dot T. T Lesson 10 Ex2

Which of the graphs shows point N at (4, 3)?
4-10 Algebra: Ordered Pairs and Functions Which of the graphs shows point N at (4, 3)? A. Lesson 10 CYP2

4-10 Algebra: Ordered Pairs and Functions B. Lesson 10 CYP2

4-10 Algebra: Ordered Pairs and Functions C. Lesson 10 CYP2

4-10 Algebra: Ordered Pairs and Functions D. Lesson 10 CYP2

4-10 Algebra: Ordered Pairs and Functions Answer: B. Lesson 10 CYP2

Move 1 units to the right on the x-axis.
4-10 Algebra: Ordered Pairs and Functions Graph the point U(1 , 0). Start at the origin. Move 1 units to the right on the x-axis. Then move 0 units up to locate the point. Draw a dot and label the dot U. U Lesson 10 Ex3

Which of the graphs shows point U at (2, 4 )?
4-10 Algebra: Ordered Pairs and Functions Which of the graphs shows point U at (2, 4 )? A. Lesson 10 CYP3

4-10 Algebra: Ordered Pairs and Functions Answer: D. Lesson 10 CYP3

Answer: The ordered pairs are (1, 2), (2, 4), (3, 6), (4, 8).
4-10 Algebra: Ordered Pairs and Functions Amazi feeds her dog, Buster, 2 cups of food each day. Amazi made this table to show how much food Buster eats for 1, 2, 3, and 4 days. List the information as ordered pairs (days, food). Answer: The ordered pairs are (1, 2), (2, 4), (3, 6), (4, 8). Lesson 10 Ex4

4-10 Algebra: Ordered Pairs and Functions Below is the continuation of the table in Example 4. Choose the answer that shows the information in ordered pairs. (10, 5), (12, 6), (14, 7), (16, 8) (5, 10), (6, 12), (7, 14), (8, 16) (5, 6), (7, 8), (10, 12), (14, 16) (5, 5), (6, 6), (7, 7), (8, 8) Lesson 10 CYP4

Graph the ordered pairs from Example 4. Then describe the graph.
4-10 Algebra: Ordered Pairs and Functions Graph the ordered pairs from Example 4. Then describe the graph. Answer: D C The ordered pairs (1, 2), (2, 4), (3, 6), and (4, 8) correspond to the points A, B, C, and D in the coordinate plane. B A The points appear to lie on a line. Lesson 10 Ex5

4-10 Algebra: Ordered Pairs and Functions Choose the graph that has the ordered pairs (5, 3), (4, 2), (3, 1), and (2, 0) plotted correctly. A. Lesson 10 CYP5

4-10 Algebra: Ordered Pairs and Functions Answer: B. Lesson 10 CYP5

End of Lesson 10

4 Five-Minute Checks Math Tool Chest Image Bank Greatest Common Factor
Fractions and Decimals 4 Five-Minute Checks Math Tool Chest Image Bank Greatest Common Factor Ordered Pairs and Functions CR Menu

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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. IB Instructions

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

(over Chapter 3) Find the sum. 4.1 9.6 0.4 5.1 5Min 1-1

Find the sum. 2.91 + 5.75 8.76 2.84 8.66 7.66 (over Chapter 3)
5Min 1-2

Find the difference. 8.5 – 5.8 2.7 14.3 3.7 3.3 (over Chapter 3)
5Min 1-3

Find the difference. 9.01 – 0.45 9.46 8.66 9.44 8.56 (over Chapter 3)
5Min 1-4

Find the sum. 4.3 + 8.99 8.56 13.29 9.42 12.29 (over Chapter 3)
5Min 1-5

Find the difference. 20 – 11.78 9.32 19.32 8.22 11.98 (over Chapter 3)
5Min 1-6

Identify the common factors of the set of numbers.
(over Lesson 4-1) Identify the common factors of the set of numbers. 9, 15 3 3 and 6 1 and 6 1 and 3 5Min 2-1

Identify the common factors of the set of numbers.
(over Lesson 4-1) Identify the common factors of the set of numbers. 6, 42 1 and 3 1, 2, 3, and 6 1, 2, and 3 1, 3, and 6 5Min 2-2

Find the GCF of the set of numbers.
(over Lesson 4-1) Find the GCF of the set of numbers. 13, 15 3 5 1 2 5Min 2-3

(over Lesson 4-1) Find the GCF of the set of numbers. 22, 104 2 4 1 11 5Min 2-4

(over Lesson 4-1) Find the GCF of the set of numbers. 24, 42, 72 3 2 6 12 5Min 2-5

(over Lesson 4-2) Solve. Use the make an organized list strategy. Luis is displaying sports balls for sale. He has a soccer ball, a baseball, and a basketball. How many different ways can he arrange these balls on a table? 3 ways 6 ways 12 ways 9 ways 5Min 3-1

(over Lesson 4-3) Write in simplest form. If the fraction is already in simplest form, choose simplest form. 18 24 A. 9 12 B. 3 24 C. 3 4 D. simplest form 5Min 4-1

(over Lesson 4-3) Write in simplest form. If the fraction is already in simplest form, choose simplest form. 35 49 15 17 B. 5 7 C. 10 14 D. simplest form 5Min 4-2

Write 4 as an improper fraction. 5 6
(over Lesson 4-4) Write 4 as an improper fraction. 5 6 A. 9 6 B. 24 6 C. 29 6 D. 25 6 5Min 5-1

Write 3 as an improper fraction.
(over Lesson 4-4) Write 3 as an improper fraction. A. 3 B. 3 9 C. 1 3 D. 9 3 5Min 5-2

Write as a mixed number in simplest form. 19 5
(over Lesson 4-4) Write as a mixed number in simplest form. 19 5 A. 3 4 5 B. 2 9 5 C. 2 4 5 D. 1 14 5 5Min 5-3

Write as a mixed number in simplest form. 24 6
(over Lesson 4-4) Write as a mixed number in simplest form. 24 6 A. 12 3 B. 2 12 6 C. 4 D. 3 6 5Min 5-4

Write as a mixed number in simplest form. 17
(over Lesson 4-4) Write as a mixed number in simplest form. 17 A. 1 1 17 B. 1 C. 2 1 7 D. 0 5Min 5-5

Find the LCM of the set of numbers.
(over Lesson 4-5) Find the LCM of the set of numbers. 9, 12 3 72 1 36 5Min 6-1

(over Lesson 4-5) Find the LCM of the set of numbers. 4, 6, 12 24 12 6 36 5Min 6-4

(over Lesson 4-5) Find the LCM of the set of numbers. 2, 4, 7 14 21 56 28 5Min 6-5

(over Lesson 4-6) Solve this problem. A clothing store sells 4 different styles of shoes in 3 different colors. How many combinations of style and color are possible? 24 7 12 4 5Min 7-1

(over Lesson 4-7) Replace the with <, >, or = to make a true sentence. 5 8 6 < > = 5Min 8-1

(over Lesson 4-7) Replace the with <, >, or = to make a true sentence. 7 12 2 3 < > = 5Min 8-2

(over Lesson 4-8) Write 0.55 as a fraction in simplest form. A. 55 100 B. 5 10 C. 11 100 D. 11 20 5Min 9-1

(over Lesson 4-8) Write 0.08 as a fraction in simplest form. A. 8 100 B. 2 25 C. 8 10 D. 4 5 5Min 9-2

Write 3.125 as a mixed number in simplest form.
(over Lesson 4-8) Write as a mixed number in simplest form. A. 3 5 40 B. 3125 1000 C. 3 1 8 D. 3 125 1000 5Min 9-3

Write 4.04 as a mixed number in simplest form.
(over Lesson 4-8) Write 4.04 as a mixed number in simplest form. A. 404 100 B. 4 1 25 C. 4 4 100 D. 4 2 50 5Min 9-4

7 Write as a decimal. 10 0.7 0.07 7.10 0.71 (over Lesson 4-9)
5Min 10-1

11 Write as a decimal. 20 0.505 5.50 0.55 0.055 (over Lesson 4-9)
5Min 10-2

(over Lesson 4-9) Write as a decimal. 5 8 0.625 B C. 31 8 D 5Min 10-3

(over Lesson 4-9) Write as a decimal. 5 11 3.5 B. 38 11 C D 5Min 10-4

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Chapter 4 Fractions and Decimals

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