Slide / 6 Slide / 6 6th Grade Fraction & Decimal Computation 05-09-4 www.njctl.org Fraction and Decimal Computation Slide 3 / 6 Fraction Division Long Division Review Adding Decimals Subtracting Decimals Distributive Property & Product of Decimals Multiplying Decimals Dividing Decimals Glossary & Standards Click on the topic to go to that section
Slide 4 / 6 Fraction Division Return to Table of Contents Recall from 5th grade: Modeling Division Slide 5 / 6 When we are dividing, we are breaking apart into equal groups. Dividend Divisor = Quotient The model below represents: 8 4 = groups of 4 Applying to Fractions The previous example used whole numbers and grouped the dividend according to the divisor. Slide 6 / 6 The same strategy can be applied when dividing with fractions. Use the model below to demonstrate: 8 = 8 The pink rectangle represents. See how many you can fit in the 8 squares.
Example Use the model below to demonstrate = 3 Slide 7 / 6 3 Evaluate the following problem using the model below. Slide 8 / 6 3 = 4 3 4 Evaluate the following problem using the model below. 5 = Slide 9 / 6 5
Visual Model A fraction can be divided by a whole number using the following visual model. 3/5 4 3 4 Slide 0 / 6 Divide into 4 groups Word Problem Slide / 6 The previous expression can be represented by the following word problem: How much will each person receive if 4 friends share a 3/5 pound bag of popcorn? 3 4 Each friend will receive 3/0 lb. of popcorn. Slide / 6
Slide 3 / 6 Slide 4 / 6 Slide 5 / 6
Slide 6 / 6 Slide 7 / 6 Slide 8 / 6
Vocabulary Review Slide 9 / 6 Complex Fraction: A fraction with another fraction in the numerator, denominator or both. Reciprocal: The inverse of a number/fraction. Original Number 4 Reciprocal Patterns Slide 0 / 6 Do you notice a pattern between the division of fractions and their solution? Slide / 6 If you think about it, we are dividing by a fraction which creates a complex fraction. You need to eliminate the fraction in the denominator in order to solve the problem. To do this, multiply the numerator and denominator of the complex fraction by the reciprocal of the denominator (making the denominator = ). You can then simplify the fraction by rewriting it without the denominator of and solve the new multiplication problem.
Example Slide / 6 3 = 3 = 3 x 3 x 3 = x 3 = x 3 Original Problem Complex Fraction Multiply by Reciprocal Simplify Denominator Rewrite Without There are rules that can be applied to fraction division problems to eliminate steps from this lengthy procedure. source - http://www.helpwithfractions.com/dividing-fractions.html Dividing Fractions Algorithm Slide 3 / 6 Algorithm Step : Leave the first fraction the same. Step : Multiply the first fraction by the reciprocal of the second fraction. Step 3: Simplify your answer. = 5 5 x = x 5 x = 5 Dividing Fractions Algorithm Slide 4 / 6 Some people use the saying " Keep Change Flip" to help them remember the algorithm. Change Keep Flip Changed Kept Flipped 3 5 7 8 = 3 5 x 8 7 = 3 x 8 5 x 7 = 4 35
Slide 5 / 6 Checking Your Answer Slide 6 / 6 To check your answer, use your knowledge of fact families. 3 5 7 = 8 4 35 3 5 = 7 4 8 x 35 3 5 is 7 8 of 4 35 Slide 7 / 6 7 ) 4 5 8 0 = 5 4 x 8 0 True False
Slide 8 / 6 8 ) 3 4 7 = 7 8 True False Slide 9 / 6 9 ) 4 5 8 0 = A B 39 40 C 40 4 0 ) Slide 30 / 6
) Slide 3 / 6 Simplify Slide 3 / 6 Sometimes you can cross simplify prior to multiplying. without cross simplifying with cross simplifying 5 3 Can this problem be cross simplified? Slide 33 / 6 Yes No
3 Can this problem be cross simplified? Slide 34 / 6 Yes No 4 Can this problem be cross simplified? Slide 35 / 6 Yes No 5 Can this problem be cross simplified? Slide 36 / 6 Yes No
6 ) Slide 37 / 6 7 ) Slide 38 / 6 8 ) Slide 39 / 6
9 ) Slide 40 / 6 Visual Model A mixed number can be divided by a mixed number using the following visual model. Slide 4 / 6 First find the least common denominator (LCD) which is 6. If every 6 lines represents a whole, then how many lines should we draw to make sure both mixed numbers fit? Visual Model Slide 4 / 6 Since our LCD is 6, every 6 lines is considered a whole. / is equivalent to 9 sections on the number line. / 3 4 5 6 7 8 9 0 3 4 5 6 7 8 /3 /3 is equivalent to 6 sections on the number line. So / /3 = 9/6
Visual Model Slide 43 / 6 What if the problem were written as? /3 3 4 5 6 7 8 9 0 3 4 5 6 7 8 / / How many times does / divide into /3? Dividing Mixed Numbers Algorithm Slide 44 / 6 Step : Rewrite the Mixed Number(s) as an improper fraction(s). (write whole numbers / ) Step : Follow the same steps for dividing fractions 6 = 6 3 = 6 x = = 4 3 3 Example Slide 45 / 6 Evaluate: 3 3 = 5 3 7 = 5 3 x 7 = 0
Slide 46 / 6 0 ) 3 = Slide 47 / 6 ) 5 = Slide 48 / 6 ) 4 5 5 =
Slide 49 / 6 3 ) 3 3 8 = Application Problem Slide 50 / 6 Winnie needs pieces of string for a craft project. How many /6 yd pieces of string can she cut from a piece that is /3 yd long? 3 6 3 x 6 = 3 = 4 4 pieces or 3 x 6 = 4 = 4 pieces Application Problem Slide 5 / 6 One student brings / yd of ribbon. If 3 students receive an equal length of the ribbon, how much ribbons will each student receive? 3 x 3 = 6 yards of ribbon
Application Problem Slide 5 / 6 Kristen is making a ladder and wants to cut ladder rungs from a 6 ft board. Each rung needs to be 3/4 ft long. How many ladder rungs can she cut? 6 3 4 6 3 4 6 x 4 3 = 4 3 8 = = 8 rungs Application Problem Slide 53 / 6 A box weighing 9 /3 lb contains toy robots weighing /6 lb apiece. How many toy robots are in the box? 9 3 6 8 3 7 6 4 8 3 x 6 7 = 8 = 8 robots 4 Robert bought 3/4 pound of grapes and divided them into 6 equal portions. What is the weight of each portion? Slide 54 / 6 A 8 pounds B 4 / pounds C /5 pounds D /8 pound
5 A car travels 83 7/0 miles on /4 gallons of fuel. Which is the best estimate of the number miles the car travels on one gallon of fuel? Slide 55 / 6 A 84 miles B 6 miles C 4 miles D 38 miles 6 One tablespoon is equal to /6 cup. It is also equal to / ounce. A recipe uses 3/4 cup of flour. How many tablespoons of flour does the recipe use? Slide 56 / 6 A 48 tablespoons B 4 tablespoons C tablespoons D 6 tablespoons 7 A bookstore packs 6 books in a box. The total weight of the books is 4 /5 pounds. If each book has the same weight, what is the weight of one book? Slide 57 / 6 A 5/ pound B /5 pounds C 8 /5 pounds D 86 /5 pounds
8 There is gallon of distilled water in the Slide 58 / 6 class science supplies. If each pair of students doing an experiment uses gallon of distilled water, there will be gallon left in the supplies. How many students are doing the experiments? 9 Carol makes cups of snack mix. She Slide 59 / 6 puts all the snack mix into plastic bags. She puts cup of the snack mix in each bag. How many plastic bags does Carol need? Enter your answer in the box. bags From PARCC EOY sample test non-calculator #9 30 Part A A group of hikers buy 8 bags of trail mix. Slide 60 / 6 Each bag contains cups of trail mix. The trail mix is shared evenly among hikers. How many cups of trail mix will each hiker receive? Show your work or explain your answer. From PARCC PBA sample test calculator #0
3 Part B The hikers plan to visit a scenic lookout. They will rest after they hike miles. Then they will hike the remaining miles to the lookout. The trail the hikers will use to return from the lookout is mile shorter than the trail they will use to go to the lookout. Each hiker will bring gallon of water for each mile to and from the lookout. Determine the total distance each hiker will hike. Show your work or explain your answer. Slide 6 / 6 From PARCC PBA sample test calculator #0 3 Part B (continued) Determine the total number of gallons of water each hiker will bring. Show your work or explain your answer. Slide 6 / 6 From PARCC PBA sample test calculator #0 33 This diagram shows a number line. Slide 63 / 6 Part A James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each /8 foot long. How many pieces can James cut from the board? Explain how James can use the number line diagram to determine the number of pieces he can cut from the board. From PARCC PBA sample test calculator #8
34 Part B Slide 64 / 6 Write an equation using division that represents how James can find the number of pieces he can cut from the board. From PARCC PBA sample test calculator #8 Slide 65 / 6 Long Division Review Return to Table of Contents Some division terms to remember... The number to be divided into is known as the dividend Slide 66 / 6 The number which divides the other number is known as the divisor The answer to a division problem is called the quotient 0 5 = 4 4 quotient divisor 5 0 dividend 0 5 = 4
When we are dividing, we are breaking apart into equal groups Slide 67 / 6 EXAMPLE Find 3 3 Step : Can 3 go into, no so can Click for step 3 go into 3, yes Step : Bring down the. Can 3 Click for step go into, yes 4 4 3 3 - - 0 3 x 4 = 3 - = Compare < 3 3 x 4 = - = 0 Compare 0 < 3 Step 3: Check your answer. Slide 68 / 6 44 x 3 3 Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track. Slide 69 / 6 357 5 What place value should we round to? Round to the largest place value. 357 rounds to 5 rounds to Our answer should approximately be... 0
EXAMPLE (change pages to see each step) Slide 70 / 6 Step : Can 5 go into 3, no so can 5 go into 35, yes 5 357-30 5 5 x = 30 35-30 = 5 Compare 5 < 5 EXAMPLE (change pages to see each step) Slide 7 / 6 Step : Bring down the 7. Can 5 go into 07, yes 3 5 357-30 57-45 5 x 3 = 45 57-45 = Compare < 5 EXAMPLE (change pages to see each step) Slide 7 / 6 Step 3: You need to add a decimal and a zero since the division is not complete. Bring the zero down and continue the long division. 3.8 5 357.0-30 57-45 0-0 0 5 x 8 = 0 0-0 = 0 Compare 0 < 5 Is our answer close to our estimate?
Check your answer. Slide 73 / 6 3.8 x 5 357 Estimate the following problems. Discuss your answers with your group. Slide 74 / 6 35 300 5 0 Now solve the following problems. Discuss your answers with your group. Slide 75 / 6 4 34 9.5 3.
35 Estimate the quotient. Slide 76 / 6 779 9 36 Compute. Slide 77 / 6 779 9 = 37 Estimate the quotient. Slide 78 / 6,55 55
38 Compute. Slide 79 / 6,55 55 = 39 Estimate the quotient. Slide 80 / 6,88 35 40 Compute. Slide 8 / 6,88 35 =
4 The school concert hall contains 3 chairs in rows. Estimate how many chairs are in each row. Slide 8 / 6 4 The school concert hall contains 3 chairs in rows. How many chairs are in each row? Slide 83 / 6 43 Compute. Slide 84 / 6 4706 04 =
44 The local Italian restaurant receives the same number of visitors every day. If 343 people visit the restaurant over the course of one week, how many visitors visit each day? Slide 85 / 6 45 Compute. Slide 86 / 6 03 4 = 46 Compute. Slide 87 / 6 49 9 =
47 Enter your answer in the box. Slide 88 / 6 34,99 8 = From PARCC EOY sample test non-calculator #8 Slide 89 / 6 Adding Decimals Return to Table of Contents Adding Decimals Slide 90 / 6 If you know how to add whole numbers then you can add decimals. Just follow these few steps. Step : Step : Step 3: Put the numbers in a vertical column, aligning the decimal points. Add each column of digits, starting on the right and working to the left. Place the decimal point in the answer directly below the decimal points that you lined up in Step.
Adding Decimals Slide 9 / 6 When adding or subtracting decimals, always remember to align the decimals vertically... 0.5 0.5 0.5 0.5.00 + Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track. Slide 9 / 6 5. +.5 + 0.04 +.99 What place value should we round to? Round to the nearest whole number. 5. rounds to.5 rounds to 0.04 rounds to.99 rounds to Our answer should approximately be... 8 Adding Decimals Slide 93 / 6 Now, try this - Don't forget - LINE THEM UP 5. +.5 + 0.04 +.99 + 5.0.5 0.04.99 You can add a zero as a place holder to help line your numbers up. 8.38
TRY THESE. Estimate the following sums in your notebook. Check with the rest of your group. Slide 94 / 6 ) 8.3 + 4.5 + 0.89 ) 3.78 +.8 + 9 8 + 4 + 0 = 3 + + 9 = 4 3) 7.009 +.965 + 8.4 4) 9.999 + 3.567 + 4.5656 7 + 3 + 8 = 8 0 + 3 + 5 = 8 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 95 / 6 ) 8.3 + 4.5 + 0.89 ) 3.78 +.8 + 9 8.3 3.78 4.5.8 + 0.89 + 9..4739 4.458 3) 7.009 +.965 + 8.4 4) 9.999 + 3.567 + 4.5656 7.009 9.999.965 3.567 + 8.4 + 4.5656 8.374 7.73 48 Add the following: Slide 96 / 6 0.6 + 0.55 = A 6. B 0.5 C.5 D 0.6
49 Joanne and Peter are working together to solve the problem 0.6 + 0.55. Joanne says that the sum should be approximately. Peter disagrees and says the sum should be approximately 0. Who is correct? Why? Slide 97 / 6 A Joanne B Peter 50 Find the sum. Slide 98 / 6.05 + 0.03 + 4.000 = 5 Franco went to buy new video games. He bought MaxRush for $9.95, Duplo Race for $3.95 and Garage Mate for $.95. Estimate how much Franco spent on the video games. Slide 99 / 6
5 Franco went to buy new video games. He bought MaxRush for $9.95, Duplo Race for $3.95 and Garage Mate for $.95. How much did he spend on video games? Slide 00 / 6 53 What is the sum of Slide 0 / 6.034 and 0.004? A.344 B.0444 C.38 D.0444 54 Estimate the sum. Slide 0 / 6 8.5 + 0.04 +.3 A 0 B C D 3
55 Find the sum. Slide 03 / 6 8.5 + 0.04 +.3 = A 3.58 B.3 C 0.85 D 0.4 56 Five students collected paper to be recycled. Shelly's stack was.008 cm. thick; Ken's stack was.5 cm. thick; Joe's stack was.50 cm. thick; Betty's stack was.85 cm. thick; Mary's stack was.005 cm. thick. What was the thickness of the papers collected to be recycled? Slide 04 / 6 A.56 cm. B.45 cm. C.480 cm. D.473 cm. Slide 05 / 6 57 Find the sum. 5 + 00.45 + 57.896 +.3 =
58 What is the sum of 74.835 and.67? Slide 06 / 6 Enter your answer in the box. From PARCC EOY sample test non-calculator #9 Web Link Slide 07 / 6 Let's go to Cool Math and practice addition. Cool Math Link Slide 08 / 6 Subtracting Decimals Return to Table of Contents
Subtracting Decimals If you know how to subtract whole numbers then you can subtract decimals. Just follow these few steps. Slide 09 / 6 Step : Step : Step 3: Put the numbers in a vertical column, aligning the decimal points.. - 0.3 Subtract the numbers from right to left using the same rules as whole numbers. 0. - 0.3 0.8 Place the decimal point in the answer directly below the decimal points that you lined up in Step. Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track. Slide 0 / 6.7-8. What place value should we round to? Round to the nearest whole number..7 rounds to 8. rounds to Our answer should approximately be... 4 Subtracting Decimals Slide / 6 What do we do if there aren't enough decimal places when we subtract?.7-8. Don't forget...line Them Up!.7 8. What goes here? 6.70 8. 3.49
TRY THESE. Estimate the following differences in your notebook. Then check with the rest of your group. Slide / 6 ) 8.3-0.89 ).83-9.05 8-0 = 8-9 = 3 3) 7.009-8.4 4) 9.999-4.5656 7-8 = 9 0-5 = 5 TRY THESE. Complete in your notebook then check with the rest of your group. Slide 3 / 6 ) 8.3-0.89 ).83-9.05 8.3.83-0.89-9.05 8. 3.58 3) 7.009-8.4 4) 9.999-4.5656 7.009 9.999-8.4-4.5656 8.609 5.4334 59 ) 5-0.38 = Slide 4 / 6
60 ).809-4 = Slide 5 / 6 6 Sally won $5.00 for her science fair project. Her project cost $.57 to prepare. What is the estimate of Sally's profit? Slide 6 / 6 A $0 B $8 C $3 D $ 6 Sally won $5.00 for her science fair project. Her project cost $.57 to prepare. How much profit? did Sally actually make as a Slide 7 / 6 A $37.57 B $.43 C $3.57 D $.00
63 ) 897. - 0.647 = Slide 8 / 6 64 The Johnson twins raced each other in the 00-meter dash. Jordan finished in 3.48 seconds, and Max finished in 6.3 seconds. How much faster was Jordan than Max? Slide 9 / 6 65 Timothy is working on the problem 4. - 0.094. He estimates his answer before solving and rounds the numbers to the nearest tenths. He uses 4. and 0. to estimate the answer. Is he correct in doing so? Why or why not? Yes No Slide 0 / 6
66 ) 4. - 0.094 = Slide / 6 67 ) 7-3.008 = Slide / 6 68 Which problem below would give you two different estimates when you either round to the nearest whole or round to the nearest tenths? A 7.85 -.9 B 4.7-8. C 7.9-3.88 D.5-8.6 Slide 3 / 6
69 If you buy two movie tickets for $8.5 each, what will your change be from $0? Slide 4 / 6 Web Link Slide 5 / 6 Let's go to Cool Math and practice subtraction. Cool Math Link Slide 6 / 6 The Distributive Property and the Product of Decimals Return to Table of Contents
Multiplication Slide 7 / 6 If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step : Ignore the decimal points. Step : Multiply the numbers using the same rules as whole numbers. Step 3: Count the total number of digits to the right of the decimal point. Put that many digits to the right of the decimal point in your answer. Distributive Property Slide 8 / 6 Evaluate 00 x 4.5 8,300 We can also use the distributive property to calculate the product. Separate 4.5 into an addition expression with two addends Apply the distributive property Apply the order of operations 00 x 4.5 00 x (4 + 0.5) (00 x 4) + (00 x 0.5) 8,00 + 00 = 8,300 Distributive Property Slide 9 / 6 Evaluate 400 x 8.33 400 x ( + ) (400 x ) + (400 x ) + = 733 This method is known as partial products.
Distributive Property Slide 30 / 6 How can we use partial products to calculate the area of the rectangle shown below? 5858.6 ft ft 0.6 ft 00 x 58.6 00 ft ft 00 x ( + ) (00 x ) + (00 x ) + =,70 Click to reveal 70 ) (43) = (40) x (3) Slide 3 / 6 True False 7 Use the distributive property to rewrite the expression. Slide 3 / 6 3(76.8) Students type their answers here
7 Calculate the product using partial products. Slide 33 / 6 5(48) 73 Calculate the product using partial products. Slide 34 / 6 3(5.) 74 Calculate the product using partial products. Slide 35 / 6 300(7.4)
75 Calculate the product using partial products. Slide 36 / 6 00(6.5) 76 Calculate the area of the rectangle using partial products. Slide 37 / 6 300 units 43.9 units Slide 38 / 6 Multiplying Decimals Return to Table of Contents
Multiplication Slide 39 / 6 Convert the following decimal numbers into fractions. 0.7 x 0.09 What is the product? 63 000 We multiplied seven tenths by nine hundredths. What place value will the last digit in the product be in if we convert it into a decimal number? Thousandths Try These! Slide 40 / 6 What place value will the last digit be in for the following problems? Don't forget to convert them to fractions first. Fractions Product Place Value ) 0.3 x 0.7 ) 0. x 0.3 3) 0.08 x 0.3 Multiplication Slide 4 / 6 Do you notice a pattern for multiplying decimals? 3.5 x.7 3 5 x 0 7 00 35 0 x 7 00 600 000 Where does the decimal point go? Drag the decimal point. 6 0 0
Multiplication Slide 4 / 6 If you know how to multiply whole numbers then you can multiply decimals. Just follow these few steps. Step : Step : Step 3: Ignore the decimal points. Multiply the numbers using the same rules as whole numbers. Count the total number of digits to the right of the decimal points in both numbers. Put that many digits to the right of the decimal point in your answer. Multiplication Slide 43 / 6 3. x.04 } digits } digits.84 There are a total of four digits to the right of the decimal points. There must be four digits to the right of the decimal point in the answer. Estimate Your Answer Before any calculations, estimate your answer to make sure you are on the right track. Slide 44 / 6 3. x 4.04 What place value should we round to? Round to the nearest whole number. 3. rounds to 4.04 rounds to Our answer should approximately be... 9
Exact Answer 3. x 4.04 98 0000 9800 93.78 } digit } digits Slide 45 / 6 There are a total of three digits to the right of the decimal points. There must be three digits to the right of the decimal point in the answer. Estimating helps us recognize where the decimal point belongs! Estimate Your Answer Estimate your answer for the following problem by rounding the numbers to the nearest whole number. Slide 46 / 6 9.5 x 0.05 9.5 rounds to What is your estimate? 0.05 rounds to For problems like these, use your number sense! You are multiplying 9.5 by 0.05 which means you are taking a part (fraction) of 9.5. So your answer must be smaller than 9.5! TRY THESE. Estimate the following products in your notebook then check with the rest of your group. Slide 47 / 6 ) 4.5 ) 8.3 x 4. x.008 5 x 4 = 60 8 x = 8 3) 7.0045 4) 3.4 x 5. x 0.0034 7 x 5 = 35 smaller than 3.4
TRY THESE. Complete in your notebook then check with the rest of your group. Slide 48 / 6 ) 4.5 ) 8.3 x 4. x.008 45 6648 9040 5804800 6.0955 0000 00000 83000 8.37648 3) 7.0045 4) 3.4 x 5. x 0.0034 40090 35050 36.4340 856 9640 0.00976 77 Estimate the product. Slide 49 / 6 0.4 x 0.03 A The product will be less than B The product will be equal to C The product will be greater than 78 The product of 0.4 x 0.03 will have 4 digits to the right of the decimal point. Slide 50 / 6 True False
79 Multiply 0.4 x 0.03 Slide 5 / 6 80 Multiply 3.45 x. Slide 5 / 6 8 You need to buy 6 notebooks that cost $0.87 each. If you have $5, do you have enough money? Slide 53 / 6 Estimate to determine your answer. Do not solve. Yes No
8 You need to buy 6 notebooks that cost $0.87 each. How much will this cost? Slide 54 / 6 83 Multiply 53.4 x 0.089 Slide 55 / 6 84 The regular price of a pair of jeans is $9.99. Mrs. Jones has four children for whom she must buy new jeans. The jeans are on sale for $.50. Slide 56 / 6 What would the total cost be of four pairs of jeans on sale? A $9.96 B $90.00 C $86.00 D $5.49
85 How many digits will be to the right of decimal point the product for the problem 4.056 x 7.8? A B 3 C 4 D 5 Slide 57 / 6 86 Multiply 4.056 x 7.8 Slide 58 / 6 87 Multiply 0.0 x 0. Slide 59 / 6
88 Enter your answer in the box. Slide 60 / 6 8.3 x 4.39 = From PARCC EOY sample test non-calculator #7 89 Thomas buys a case of bottled water. A case contains 36 bottles of water and costs $4.69. Thomas will sell each bottle of water for $0.75 at a school event. Slide 6 / 6 How much profit, in dollars, will Thomas earn if he sells all the bottles of water? Enter your answer in the box. $ From PARCC EOY sample test non-calculator #7 Slide 6 / 6 Dividing Decimals Return to Table of Contents
Divide Decimals by Whole Numbers Slide 63 / 6 Step : Step : Use long division. Bring the decimal point up into the quotient. 8 04 56.08 Try This! Slide 64 / 6.45 5 = 0 The Power of Ten Multiplying by a power of ten makes dividing by decimals easier! Slide 65 / 6 ) 3 x 0 = ) 94 x 00 = 3) 8 x 000 = 4) 6. x 0 = 5) 4.78 x 00 = 6) 5.93 x 000 = Do you see a pattern for multiplying by a power of ten? The decimal point moves to the right depending on the number of zeros Click in the to power of ten! Reveal
Divide by Decimals Slide 66 / 6 Step : Change the divisor to a whole number by multiplying by a power of 0. Step : Multiply the dividend by the same power of 0. Step 3: Step 4: Use long division. Bring the decimal point up into the quotient. Divisor Quotient Dividend Power of Ten Slide 67 / 6 Try rewriting these problems so you are ready to divide! 5.6 6.4 56 6.4 Multiply by 0, so that 5.6 becomes 56 6.4 must also be multiplied by 0.34 3.4 34 3400 Multiply by 000, so that.34 becomes 34 3.4 must also be multiplied by 000 Power of Ten Slide 68 / 6 Rewrite each problem after multiplying by a power of 0. ) 50. 4.5 45 500 ).008 4. 008 400 3) 0.9 678.9 09 6789. 4) 68.34. 683.4
Estimating Your Answer Before any calculations, estimate your answer to make sure you are on the right track. Slide 69 / 6 3. 4.04 What place value should we round to? Round to the nearest whole number. 3. rounds to 4.04 rounds to Our answer should approximately be... 5 Try This! Be sure to round your answer to the thousandths. Slide 70 / 6 4.04 3. 5.743 Estimate Slide 7 / 6 Estimate your answer for the following problem by rounding the numbers to the nearest whole number. 9.5 0.05 9.5 rounds to What is your estimate? 0.05 rounds to For problems like these, use your number sense! If you are dividing 9.5 by 0.05, then does that mean the quotient will be smaller than 9.5 or greater than 9.5? Your answer must be greater than 9.5!
90 Divide Slide 7 / 6 0.78 0.0 = 9 Use estimation to figure out if the quotient will be 4.866 0.6 Slide 73 / 6 A less than 4.866 B around 4.866 C greater than 4.866 9 Slide 74 / 6 0.6 4.866
93 ) 0 divided by 0.5 = Slide 75 / 6 94 ).03 0.04 = Slide 76 / 6 95 Slide 77 / 6 0.0 4.6
96 Estimate. 36. Slide 78 / 6 97 Evaluate. 36. = Slide 79 / 6 98 Estimate. 9.6. Slide 80 / 6
99 Evaluate. 9.6. = Slide 8 / 6 00 Enter your answer in the box. 33.8 3.5 = Slide 8 / 6 From PARCC EOY sample test # non-calculator Terminating and Repeating Slide 83 / 6 There are two types of decimals - terminating and repeating. A terminating decimal is a decimal that ends. All of the examples we have completed so far are terminating. A repeating decimal is a decimal that continues forever with one or more digits repeating in a pattern. To denote a repeating decimal, a line is drawn above the numbers that repeat. However, with a calculator, the last digit is rounded.
Terminating or Repeating Slide 84 / 6 Let's consider the following... Click to Reveal Repeating Example Slide 85 / 6 63 48 45 39 Click 36 to Reveal 3 7 5 45 60 54 6 Repeating Example Slide 86 / 6 6600 34 00 400 Click 300 to Reveal 0000 8800 000 000 0000 8800 000 000
0 ) 5.5 0.3 Slide 87 / 6 0 ) 0.8 0.003 = Slide 88 / 6 03 You need to put some gas in your car. Regular gasoline is $3.59 per gallon. You only have a $0 bill on you. How many gallons can you buy? Slide 89 / 6
04 ) 5. = Slide 90 / 6 A.7 B.73 C.7 D.7 05 Slide 9 / 6 06 If 6 people are on an elevator and together they weigh 93.56 pounds, find the average weight of each person. Slide 9 / 6
07 ) 0.007 0.9 = Slide 93 / 6 08 Heather has 5.5 lbs of jelly beans. She will put them in 8.5 bags. How much will be in each bag? Slide 94 / 6 09 Slide 95 / 6
0 ) 9.84 4.8 = Slide 96 / 6 Texas suffered through a heat wave in August 0. The highest four temperatures (in degrees Fahrenheit) were 03.4, 0.8, 0.9 and 0.5. What was the average temperature for those four days? Slide 97 / 6 For your sewing project at school, you need to purchase 3.5 yards of fabric. You spend $9.0 on one pattern and $8.40 on another. How much does one yard cost? Slide 98 / 6
3 ) 9 0. Slide 99 / 6 A 40.9 B 40.90 C 40.9 D 40.9 Slide 00 / 6 Glossary & Standards Return to Table of Contents Inverse Operation The operation that reverses the effect of another operation. Slide 0 / 6 Back to Instruction
Algorithm Slide 0 / 6 A step-by-step process to find a solution. How to... Step : Step : Step 3: 4 + = Add the ones then add the tens It's like a cooking recipe for mathematics. Back to Instruction Average The value/amount of each item when the total is distributed across each item equally. Slide 03 / 6 3 + 4 + = 9 = 9 3 = 3 Back to Instruction Complex Fraction Slide 04 / 6 A fraction whose numerator or denominator or both contain fractions. 3 5 3 5 = 3 5 = 3 5 3 5 Must be written as a fraction. Back to Instruction
Cross Simplify Slide 05 / 6 Used to make operations with fractions easier. Divide the numerator of one fraction and the denominator of another fraction by their GCF. 5 5 + 0 GCF of 5 and 5 is 5. 3 5 + 5 0 = 3 + 0 Back to Instruction Distributive Property Multiplying a sum by a number is the same as multiplying each addend in the sum by the same number and then adding the products. Slide 06 / 6 5 3 (3 + ) 3x5=3(3+) 3 4 (3+4)= (x3)+(x4) also applies to subtraction a(b-c)=ab-ac a(b+c)=ab +ac Back to Instruction Dividend Slide 07 / 6 The number being divided in a division equation. 8 3 4 Dividend 4 8 = 3 Dividend Dividend 4 8 = 3 Back to Instruction
Divisor The number the dividend is divided by. A number that divides another number without a remainder. Slide 08 / 6 3 8 4 Divisor 4 8 = 3 Divisor 5 8 = 3 R Must divide evenly. Back to Instruction Power of 0 Slide 09 / 6 Any integer powers of the number ten. (Ten is the base, the exponent is the power.) 0 = 0x0 = 0x0x0 = 0 = 0 0 = 00 0 3 =,000 Back to Instruction Profit Slide 0 / 6 The difference between the amount earned and the amount spent. Earned - Spent Profit $30 Washing Cars $ - Supplies $8 Profit Back to Instruction
Quotient Slide / 6 The number that is the result of dividing one number by another. 3 = 4 3 4 Quotient Quotient 3 = Quotient 4 Back to Instruction Reciprocal Slide / 6 One of two numbers whose product is one. x = is the reciprocal of. Number x = Reciprocal r x r = Back to Instruction Repeating Decimal Slide 3 / 6 A decimal with a digit or group of digits that repeats endlessly..333... 3.0 00-9 0 9-0 - 9 3 =.3 7 33 =. (...) Back to Instruction
Terminating Decimal Slide 4 / 6 A decimal that ends and doesn't go on forever. / =.5 3/8 =.375.333... 3.0 00-9 0 9-0 - 9 Back to Instruction Vertical Slide 5 / 6 In an up-down position. vertical horizontal diagonal Back to Instruction Standards for Mathematical Practice Slide 6 / 6 MP: Making sense of problems & persevere in solving them. MP: Reason abstractly & quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for & make use of structure. MP8: Look for & express regularity in repeated reasoning. Additional questions are included on the slides using the "Math Practice" Pull-tabs (e.g. a blank one is shown to the right on this slide) with a reference to the standards used. If questions already exist on a slide, then the specific MPs that the questions address are listed in the Pull-tab.