5th Grade. Divisibility Rules. Slide 1 / 239 Slide 2 / 239. Slide 3 / 239. Slide 4 / 239. Slide 6 / 239. Slide 5 / 239. Division. Division Unit Topics

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1 Slide 1 / 239 Slide 2 / 239 5th Grade Division Slide 3 / 239 Slide 4 / 239 Division Unit Topics Click on the topic to go to that section Divisibility Rules Patterns in Multiplication and Division Division of Whole Numbers Division of Decimals Divisibility Rules Glossary & Standards Return to Table of Contents Slide 5 / 239 Slide 6 / 239 Divisible Divisible is when one number is divided by another, and the result is an exact whole number. five four two Divisible BUT, 9 is not divisible by 2 because 9 2 is 4 with one left over. three Example: 15 is divisible by 3 because 15 3 = 5 exactly.

2 Slide 7 / 239 Divisibility Slide 8 / 239 Divisibility Rules Look at the last digit in the Ones Place! A number is divisible by another number when the remainder is 0. There are rules to tell if a number is divisible by certain other numbers. 2 Last digit is even-0,2,4,6 or 8 5 Last digit is 5 OR 0 10 Last digit is 0 Check the Sum! 3 Sum of digits is divisible by 3 6 Number is divisible by 3 AND 2 9 Sum of digits is divisible by 9 Look at Last Digits 4 Last 2 digits form a number divisible by 4 Slide 9 / 239 Divisibility Rules Slide 10 / 239 Divisibility Practice Let's Practice! Click for Link Divisibility Rules You Tube song Is 34 divisible by 2? Yes, because the digit in the ones place is an even number. 34 / 2 = 17 Is 1,075 divisible by 5? Yes, because the digit in the ones place is a 5. 1,075 / 5 = 215 Is 740 divisible by 10? Yes, because the digit in the ones place is a / 10 = 74 Slide 11 / 239 Is 258 divisible by 3? Yes, because the sum of its digits is divisible by = 15 Look 15 / 3 = / 3 = 86 Is 192 divisible by 6? Yes, because the sum of its digits is divisible by 3 AND = 12 Look 12 /3 = / 6 = 32 Divisibility Practice Slide 12 / 239 Is 6,237 divisible by 9? Yes, because the sum of its digits is divisible by = 18 Look 18 / 9 = 2 6,237 /9 = 693 Is 520 divisible by 4? Yes, because the number made by the last two digits is divisible by / 4 = 5 Divisibility Practice 520 / 4 = 130

3 1 Is 198 divisible by 2? Yes No Slide 13 / Is 315 divisible by 5? Yes No Slide 14 / Is 483 divisible by 3? Yes No Slide 15 / is divisible by 6. True False Slide 16 / ,926 is divisible by 9. True False Slide 17 / 239 Slide 18 / 239 Divisibility Some numbers are divisible by more than 1 digit. Let's practice using the divisibility rules. 18 is divisible by how many digits? Let's see if your choices are correct. 9 Click Did you guess 2, 3, 6 and 9? 165 is divisible by how many digits? Let's see if your choices are correct. Click Did you guess 3 and 5? 4 6

4 Slide 19 / 239 Divisibility 28 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2 and Click 4? Slide 20 / 239 Divisibility Table Complete the table using the Divisibility Rules. (Click on the cell to reveal the answer) Divisible by2 by 3 by 4 by 5 by 6 by 9 by no yes no no no no no 156 yes yes yes no yes no no 530 is divisible by how many digits? Let's see if your choices are correct. Did you guess 2, 5, Click and 10? 429 no yes no no no no no 446 yes no no no no no no 1,218 yes yes no no yes no no 1,006 yes no no no no no no Now it's your turn... 28,550 yes no no yes no no yes Slide 21 / 239 Slide 22 / What are all the digits 15 is divisible by? 7 What are all the digits 36 is divisible by? Slide 23 / 239 Slide 24 / What are all the digits 1,422 is divisible by? 9 What are all the digits 240 is divisible by?

5 Slide 25 / 239 Slide 26 / What are all the digits 64 is divisible by? Patterns in Multiplication and Division Return to Table of Contents Slide 27 / 239 Number Systems A number system is a systematic way of counting numbers. Slide 28 / 239 Number Systems There are many different number systems that have been used throughout history, and are still used in different parts of the world today. For example, the Myan number system used a symbol for zero, a dot for one or twenty, and a bar for five. Slide 29 / 239 Our Number System Sumerian wedge = 10, line = 1 Roman Numerals Slide 30 / 239 Base Ten Generally, we have 10 fingers and 10 toes. This makes it very easy to count to ten. Many historians believe that this is where our number system came from. Base ten. We have a base ten number system. This means that in a multidigit number, a digit in one place is ten times as much as the place to its right. Also, a digit in one place is 1/10 the value of the place to its left.

6 Slide 31 / 239 Base 10 Slide 32 / 239 Powers of 10 Numbers can be VERY long. $100,000,000,000,000 Wouldn't you love to have one hundred trillion dollars? Fortunately, our base ten number system has a way to make multiples of ten easier to work with. It is called Powers of 10. How do you think things would be different if we had six fingers on each hand? Slide 33 / 239 Powers of 10 Numbers like 10, 100 and 1,000 are called powers of 10. They are numbers that can be written as products of tens. 100 can be written as 10 x 10 or ,000 can be written as 10 x 10 x 10 or Slide 34 / 239 Powers of The raised digit is called the exponent. The exponent tells how many tens are multiplied. Slide 35 / 239 Powers of 10 A number written with an exponent, like 10 3, is in exponential notation. A number written in a more familiar way, like 1,000 is in standard notation. Slide 36 / 239 Powers of 10 Powers of 10 (greater than 1) Standard Product Exponential Notation of 10s Notation x , x 10 x , x 10 x 10 x , x 10 x 10 x 10 x ,000, x 10 x 10 x 10 x 10 x

7 Slide 37 / 239 Powers of 10 Remember, in powers of ten like 10, 100 and 1,000 the zeros are placeholders. Each place holder represents a value ten times greater than the place to its right. Because of this, it is easy to MULTIPLY a whole number by a power of 10. Slide 38 / 239 To multiply by powers of ten, keep the placeholders by adding on as many 0s as appear in the power of 10. Examples: Multiplying Powers of x 10 = 280 Add on one 0 to show 28 tens 28 x 100 = 2,800 Add on two 0s to show 28 hundreds 28 x 1,000 = 28,000 Add on three 0s to show 28 thousands Slide 39 / 239 Multiplying Powers of 10 If you have memorized the basic multiplication facts, you can solve problems mentally. Use a pattern when multiplying by powers of 10. Steps 50 x 100 = 5, Multiply the digits to the left of the zeros in each factor. 50 x x 1 = 5 2. Count the number of zeros in each factor. 50 x Write the same number of zeros in the product. 5, x 400 = steps Slide 40 / 239 Multiplying Powers of Multiply the digits to the left of the zeros in each factor. 6 x 4 = Count the number of zeros in each factor. 3. Write the same number of zeros in the product. 50 x 100 = 5, x 400 = Slide 41 / 239 Multiplying Powers of x 400 = Slide 42 / 239 Multiplying Powers of 10 steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = Count the number of zeros in each factor. 60 x Write the same number of zeros in the product. steps 1. Multiply the digits to the left of the zeros in each factor. 6 x 4 = Count the number of zeros in each factor. 60 x Write the same number of zeros in the product. 60 x 400 = 24,000

8 500 x 70,000 = Slide 43 / 239 Multiplying Powers of x 70,000 = Slide 44 / 239 Multiplying Powers of 10 steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = Count the number of zeros in each factor. 3. Write the same number of zeros in the product. steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = Count the number of zeros in each factor. 500 x 70, Write the same number of zeros in the product. 500 x 70,000 = Slide 45 / 239 Multiplying Powers of 10 Your Turn... Slide 46 / 239 Practice Finding Rule steps 1. Multiply the digits to the left of the zeros in each factor. 5 x 7 = Count the number of zeros in each factor. 500 x 70,000 Write a rule. Input Output 50 15, , ,000 click Rule multiply by Write the same number of zeros in the product. 20 6, x 70,000 = 35,000,000 Slide 47 / 239 Slide 48 / 239 Practice Finding Rule x 10 = Write a rule. Input Output 20 18, ,300 9,000 8,100,000 Rule clickmultiply by ,000

9 Slide 49 / 239 Slide 50 / x 1,000 = x 10,000 = Slide 51 / 239 Slide 52 / x 5,100 = x 8,000 = Slide 53 / 239 Slide 54 / x 500 = 17 1,200 x 3,000 =

10 Slide 55 / 239 Slide 56 / x 1,000 = Dividing Powers of 10 Remember, a digit in one place is 1/10 the value of the place to its left. Because of this, it is easy to DIVIDE a whole number by a power of 10. Take off as many 0s as appear in the power of 10. Example: 42,000 / 10 = 4,200 Take off one 0 to show that it is 1/10 of the value. 42,000 / 100 = 420 Take off two 0's to show that it is 1/100 of the value. 42,000 / 1,000 = 42 Take off three 0's to show that it is 1/1,000 of the value. Slide 57 / 239 Dividing Powers of 10 Slide 58 / 239 Practice Dividing If you have memorized the basic division facts, you can solve problems mentally. Use a pattern when dividing by powers of / 10 = 60 / 10 = 6 steps 1. Cross out the same number of 0's in the dividend as in the divisor. 2. Complete the division fact. More Examples: 700 / / 10 = 70 8,000 / 10 8,000 / 10 = 800 9,000 / 100 9,000 / 100 = 90 Slide 59 / 239 Slide 60 / / / 30 = 4 Practice Dividing This pattern can be used in other problems. 1,400 / 700 1,400 / 700 = 2 44,600 / ,600 / 200 = 223 Your Turn... Practice Dividing Rule Complete. Follow the rule. Rule: Divide by 50 Input ,000 click Output click click

11 Slide 61 / 239 Slide 62 / 239 Practice Dividing Rule / 10 = Complete. Find the rule. Find the rule. Input Output 120 click click 8 2,700 click90 Slide 63 / 239 Slide 64 / ,000 / 100 = 21 1,640 / 10 = Slide 65 / 239 Slide 66 / / 30 = / 40 =

12 Slide 67 / 239 Slide 68 / / 80 = 25 4,500 / 50 = Slide 69 / 239 Remember Powers of 10 (greater than 1) Let's look at Powers of 10 (less than 1) Standard Notation Powers of 10 Powers of 10 (less than 1) Product of x x 0.1 x x 0.1 x 0.1 x x 0.1 x 0.1 x 0.1 x x 0.1 x 0.1 x 0.1 x 0.1 x Slide 71 / 239 Multiplying Powers of 10 Exponential Notation Let's look at how to multiply a decimal by a Power of 10 (greater than 1) Steps 1. Locate the decimal point in the power of Move the decimal point LEFT until you get to the number Move the decimal point in the other factor the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. So, 1,000 x 45.6 = 45,000 Example: 1,000 x 45.6 =? 1,000 = 1, (3 places) Slide 70 / 239 Powers of 10 What if the exponent is zero? (10 0 ) The number 1 is also called a Power of 10, because 1 = ,000s 1,000s 100s 10s 1s 0.1s 0.01s 0.001s s Each exponent is 1 less than the exponent in the place to its left. This is why mathematicians defined 10 0 to be equal to 1. Slide 72 / 239 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 Example: 1,000 x 45.6 =? Steps 1. Locate the decimal point in the power of Move the decimal point LEFT until you get to the number Move the decimal point in the other factor the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. So, 1,000 x 45.6 = 45,000 (greater than 1) 1,000 = 1, (3 places)

13 Slide 73 / 239 Multiplying Powers of 10 Let's look at how to multiply a decimal by a Power of 10 Example: 1,000 x 45.6 =? Steps 1. Locate the decimal point in the power of Move the decimal point LEFT until you get to the number 1. (greater than 1) 3. Move the decimal point in the other factor the same number of places, but to the RIGHT. Insert 0's as needed. That's your answer. 1,000 = 1, (3 places) Let's try some together. 10,000 x 0.28 = $4.50 x 1,000 = 1.04 x 10 = Slide 74 / 239 Practice Multiplying So, 1,000 x 45.6 = 45,000 Slide 75 / 239 Slide 76 / x 3.67 = x 10,000 = Slide 77 / 239 Slide 78 / ,000 x $8.98 = x 10 =

14 Slide 79 / 239 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the power of Move the decimal point LEFT until you get (3 places) to the number Move the decimal point in the other number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 = Dividing Powers of 10 Slide 81 / 239 1,000 = 1, Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the power of Move the decimal point LEFT until you get (3 places) to the number Move the decimal point in the other number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 = / 10 = Dividing Powers of 10 Slide 83 / 239 1,000 = 1, Slide 80 / 239 Let's look at how to divide a decimal by a Power of 10 (less than 1) Example: 45.6 / 1,000 Steps 1. Locate the decimal point in the power of Move the decimal point LEFT until you get (3 places) to the number Move the decimal point in the other number the same number of places to the LEFT. Insert 0's as needed. So, 45.6 / 1,000 = Let's try some together / 10 = 0.47 / 100 = $290 / 1,000 = / 100 = Dividing Powers of 10 Slide 82 / 239 Practice Dividing Slide 84 / 239 1,000 = 1,

15 Slide 85 / 239 Slide 86 / $456 / 1,000 = / 10,000 = Slide 87 / 239 Slide 88 / $89 / 10 = / 100 = Slide 89 / 239 Slide 90 / 239 Review from 4th Grade When you divide, you are breaking a number apart into equal groups. Division of Whole Numbers The problem 15 3 means that you are making 3 equal groups out of 15 total items. Return to Table of Contents Each equal group contains 5 items, so 15 3 = 5

16 Slide 91 / 239 Slide 92 / 239 How will knowing your multiplication facts really well help you to divide numbers? click to reveal Review from 4th Grade Multiplying is the opposite (inverse) of dividing, so you're just multiplying backwards! Find each quotient. (You may want to draw a picture and circle equal groups!) click click click click Review from 4th Grade You will not be able to solve every division problem mentally. A problem like 56 4 is more difficult to solve, but knowing your multiplication facts will help you to find this quotient, too! To make this problem easier to solve, we can use the same Area Model that we used for multiplication. How can you divide 56 into two numbers that are each divisible by 4? (? +? = 56) 4?? 56 Slide 93 / 239 Review from 4th Grade Slide 94 / 239 Area Model Division You can break 56 into and then divide each part by 4.?? Let's try another example. Use the area model to find the quotient of How can you break up 135? Remember... you want the numbers to be divisible by Ask yourself... What is 40 4? What is 16 4? (or 4 x n = 40?) (or 4 x n = 16?) The quotient of 56 4 is equal to the sum of the two partial quotients. Slide 95 / 239 Area Model Division Let's try another example. Use the area model to find the quotient of You can break 135 into and then divide each part by 15.?? Slide 96 / 239 Area Model Division What about remainders? Use the area model to find the quotient = ?? R. Ask yourself... What is 90 15? What is 45 15? (or 15 x n = 90?) (or 15 x n = 45?) 963 The quotient of is equal to the sum of the two partial quotients.

17 Slide 97 / Use the area model to find the quotient = Slide 98 / Use the area model to find the quotient. Write any reminder as a fraction = Slide 99 / Use the area model to find the quotient. Write any reminder as a fraction = Slide 100 / A teacher drew an area model to find the value of 6, Determine the number that each letter in the model represents and explain each of your answers. Write the quotient and remainder for Explain how to use multiplication to check that the quotient is correct. You may show your work in your explanation. From PARCC PBA sample test #15 Slide 101 / 239 Division Key Terms Some division terms to remember... The number to be divided into is known as the dividend. The number which divides the dividend is known as the divisor. Slide 102 / 239 Estimating Estimating the quotient helps to break whole numbers into groups. The answer to a division problem is called the quotient. 4 quotient divisor 5 20 dividend 20 5 = = 4

18 Slide 103 / 239 Estimating: One-Digit Divisor Slide 104 / 239 One-Digit Estimation Practice 8) ) )689 Divide 8) 68 Write 0 in remaining place. Estimate: 9)507 Remember to divide 50 by 9 Then write 0 in remaining place in quotient. 80 is the estimate. Is your estimate 50 or 40? Click Yes, it is 40. Estimate : Slide 105 / 239 One-Digit Estimation Practice Slide 106 / The estimation for 8)241 is 40? True False 5)451 Remember to divide 45 by 5 Then write 0 in remaining place in quotient. Is your estimate 90 or 80? Click Yes, it is 90 Slide 107 / 239 Slide 108 / Estimate Estimate 4)345.

19 Slide 109 / Solve using Estimation. Marta baby-sat fo r four hours and earned $19. ABOUT how much money # did Marta earn each hour that she baby-sat? 26)6,498 Slide 110 / 239 Estimating: Two-Digit Divisor 30)6,498 Round 26 to its greatest place. 2 30) 6,498 Divide 30) Write 0 in remaining places. 30)6, is the estimate. Slide 111 / 239 Two-Digit Estimation Practice Estimate: 31)637 Remember to round 31 to its greatest place 30, then divided 63 by 30. Finally, write 0's in remaining places in quotient. Is your estimate 20 or 30? click to reveal Yes, it is 20. Estimate: 87)9,321 Slide 112 / 239 Remember to round 87 to its greatest place 90, then divide 93 by 90 Finally, write 0's in remaining places in quotient. Is your estimate 100 or 1,000? click to reveal Yes, it is 100. Two-Digit Estimation Practice Slide 113 / 239 Slide 114 / The estimation for 17)489 is 2? 45 Estimate 5, True False

20 46 Estimate 41) 2,130. Slide 115 / Estimate 31)7,264. Slide 116 / 239 Slide 117 / Solve using Estimation. Brandon bought cookies to pack in his lunch. He bought a box with 28 cookies. If he packs five cookies in his lunch each day, ABOUT how many days will the days will the cookies last? Slide 118 / 239 When we are dividing, we are breaking apart into equal groups. Step 1 : Can 3 go into 1, no so can Click for step 1 3 go into 13, yes Step 2 : Bring down the 2. Can 3 Click for step 2 go into 12, yes Division Find x 4 = = 1 Compare 1 < 3 3 x 4 = = 0 Compare 0 < 3 Slide 119 / 239 Division 49 Divide and Check 8)296. Slide 120 / 239 Step 3: Check your answer. 44 x 3 132

21 Slide 121 / 239 Slide 122 / Divide and Check 9) Divide and Check Slide 123 / 239 Slide 124 / Divide and Check Adam has a wire that is 434 inches long. He cuts the wire into 7-inch lengths. How many pieces of wire will he have? Slide 125 / 239 Slide 126 / Bill and 8 friends each sold the same number of tickets. They sold 117 tickets in all. How many tickets were sold by each person? 55 There are 6 outs in an inning. How many innings would have to be played to get 348 outs?

22 Slide 127 / How many numbers between 23 and 41 have NO remainder when divided by 3? A 4 B 5 C 6 Slide 128 / 239 Division Problem John and Lad are splitting the $9 that John has in his wallet. Move the money to give John half and Lad half. D 11 Sometimes, when we split a whole number into equal groups, there will be an amount left over. The left over number Click when is called finished. the remainder. Slide 129 / 239 Long Division Lets look at remainders with long division. For example: 4 7) We say there are 2 left over, because you can not make a group of 7 out of 2. For example: 4 Slide 130 / 239 7) = 4 R Long Division This is the way you may have seen it. The R stands for remainder. Slide 131 / 239 Long Division Another example: 23 15) We say there are 13 left over (R) because you can not make a group of 15 out of 13. Slide 132 / A group of six friends have 83 pretzels. If they want to share them evenly, how many will be left over? = 23 R 13

23 Slide 133 / Four teachers want to evenly share 245 pencils. How many will be left over? Slide 134 / Twenty students want to share 48 slices of pizza. How many slices will be left over, if each person gets the same number of slices? Slide 135 / 239 Slide 136 / Suppose there are 890 packages being delivered by 6 planes. Each plane is to take the same number of packages and as many as possible. How many packages will each plane take? How many will be left over? Fill in the blanks. Each plane will take packages. There will be packages left over. A 149 packages, 2 left over 4 7) Long Division Instead of writing an R for remainder, we will write it as a fraction of the 30 that will not fit into a group of 7. So 2/7 is the remainder. B 148 packages, 2 left over Slide 137 / 239 Slide 138 / 239 Long Division Examples Long Division Example More examples of the remainder written as a fraction: 7 6) The Remainder means that there is 5 left over that can't be put in a group containing 6 To Check the answer, use multiplication and addition. 7 x = = 47 Multiply the quotient and the divisor. Then, add the remainder. The result should be the dividend. Example: 37 7) Check the answer using multiplication and addition.way 1: 37 x = = 264 Way 2: 37 quotient x 7 x divisor remainder 264 dividend

24 Slide 139 / 239 Slide 140 / Divide and Check 4)43 (Put answer in as a mixed number.) 62 Divide and Check 61 3 = (Put answer in as a mixed number.) Slide 141 / 239 Slide 142 / Divide and Check (Put answer in as a mixed number.) 64 Divide and Check 2)811 (Put answer in as a mixed number.) Slide 143 / Divide and Check = (Put answer in as a mixed number.) Slide 144 / 239 Long Division with 2-digit Divisor You can divide by two-digit divisors to find out how many groups there are or how many are in each group. When dividing by a two-digit divisor, follow the steps you used to divide by a one-digit divisor. Repeat until you have divided all the digits of the dividend by the divisor. STEPS Divide Multiply Subtract Compare Bring down next number

25 Step 1 : Can 25 go into 4, no so can 25 go into 45, yes Step 2 : Bring down Click for the step 7. 2Can 25 go into 207, yes Slide 145 / 239 Long Division Practice Find x 1 = = 20 Compare 20 < x 8 = = 7 Compare 7 < 25 Step 3: Check your answer. 183 x 25 Slide 146 / 239 Long Division Practice Step 3 : Bring Click for step 3 down the 5. Can 25 go into 75, yes 25 x 3 = 75 Click for step = 0 Compare 0 < 25 Slide 147 / 239 Long Division Example Slide 148 / 239 Long Division Example Mr. Taylor's students take turns working shifts at the school store. If there are 23 students in his class and they work 253 shifts during the year, how many shifts will each student in the class work? 23)253 Step 1 Compare the divisor to the dividend to decide where to place the first digit in the quotient. Divide the tens. Think: What number multiplies by 23 is less than or equal to 25. Step 2 Multiply the number of tens in the quotient times the divisor. Subtract the product from the dividend. Bring down the next number in the dividend. Step 3 Divide the result by 23. Write the number in the ones place of the quotient. Think: What number multiplied by 23 is less than or equal to 23? Step 4 Multiply the number in the ones place of the quotient by the divisor. Subtract the product from 23. If the difference is zero, there is no remainder ) Each student will work 11 shifts at the school store. Slide 149 / 239 Long Division Slide 150 / 239 Silly Steps Example Division Steps can be remembered using a "Silly" Sentence. David Makes Snake Cookies By Dinner. Divide Multiply Subtract Compare Bring Down What is your "Silly" Sentence to remember the Division Steps? Click boxes to show work Find Step 1 22) 374 Step ) 374 multiply x 22 1 Think 20) 374 divide Step ) subtract less than 22 compare Step ) bring down bring down Step 5 17 repeat 22) repeat Final Step 17 x 22 Check

26 Slide 151 / 239 Slide 152 / A candy factory produces 984 pounds of chocolate in 24 hours. How many pounds of chocolate does the factory produce in 1 hour? A 38 B 40 C 41 D Teresa got a loan of $7,680 for a used car. She has to make 24 equal payments. How much will each payment be? A $230 B $320 C $325 Slide 153 / 239 Slide 154 / Solve 16) Solve Slide 155 / 239 Slide 156 / If 280 chairs are arranged into 35 rows, how many chairs are in each row? 71 There are 52 snakes. There are 13 cages. If each cage contains the same number of snakes, how many snakes are in each cage?

27 Slide 157 / 239 Slide 158 / Solve 46)3, Solve 3, Slide 159 / 239 Slide 160 / Enter your answer. 1, = From PARCC EOY sample test #27 Slide 161 / 239 Let's Practice Remember your Steps: Divide, Multiply, Subtract, Compare, Bring Down, Write the Remainder as a Fraction, Check your work ) Solve CHECK 36 x Divisor x Quotient + Remainder = Dividend Slide 162 / What is the remainder when 402 is divided by 56? A 8 B 7 C 19 D 10

28 Slide 163 / 239 Slide 164 / What is the remainder when 993 is divided by 38? 77 Divide 80) 104 (Put answer in as a mixed number.) A 5 B 8 C 13 D 26 Slide 165 / 239 Slide 166 / Divide (Put answer in as a mixed number.) 79 Divide 45) 1442 (Put answer in as a mixed number.) Slide 167 / 239 Slide 168 / Divide (Put answer in as a mixed number.) 81 Divide 83) 8537 (Put answer in as a mixed number.)

29 Slide 169 / 239 Interpreting the Remainder In word problems, we need to interpret the what the remainder means. For example: Celina has 58 pencils and wants to share them with 5 people. 11 5) people will each get 11 pencils, and there will be 3 left over. Slide 170 / 239 Interpreting the Remainder What does the remainder below mean? Violet is packing books. She has 246 books and, 24 fit in a box. How many boxes does she need? 10 24) The remainder means she would have 6 books that would not fit in the 10 boxes. She would need 11 boxes to fit all the books. Slide 171 / 239 Slide 172 / 239 Slide 173 / 239 Slide 174 / Apples cost $4 for a 5 pound bag. If you have $19, how many bags can you buy? A = 4 R 3 B 3 C 4 D 5

30 Slide 175 / 239 Slide 176 / 239 Slide 177 / Greg is volunteering at a track meet. He is in charge of providing the bottled water. Greg knows these facts. The track meet will last 3 days. There will be 117 athletes, 7 coaches, and 4 judges attending the track meet. Once case of bottled water contains 24 bottles. The table shows the number of bottles of water each athlete coach, and judge will get for each day of the track meet. What is the fewest number of cases of bottled water Greg will need to provide for all the athletes, coaches, and judges at the track meet. Show your work or explain how you found your answer using equations. From PARCC PBA sample test #16 Slide 178 / 239 Dividing Decimals To divide a decimal by a whole number: Use long division. Bring the decimal point up in the answer. Division of Decimals Return to Table of Contents Slide 179 / 239 Decimal Division Examples Match the quotient to the correct problem. Slide 180 / Which answer has the decimal point in the correct location? A 1285 B C D

31 Slide 181 / Which answer has the decimal point in the correct location? Slide 182 / Which answer has the decimal point in the correct location? A 561 B 56.1 C A 51 B 5.1 C D D Slide 183 / 239 Slide 184 / Select the answer with the decimal point in the correct location. 92 Select the answer with the decimal point in the correct location. A B C D A 501 B 50.1 C 5.01 D E 1234 E Slide 185 / 239 Slide 186 /

32 Slide 187 / 239 Slide 188 / Slide 189 / 239 Slide 190 / Zero Place Holder Be careful, sometimes a zero needs to be used as a place holder can not go into 5. So, put a 0 in the quotient, and bring the 6 down. Slide 191 / 239 Slide 192 / What is the next step in this division problem? What is the next step in this division problem? A B C Put a 2 in the quotient. Put a 0 in the quotient. Put a 1 in the quotient. A Put a 0 in the quotient. B Put a 2 in the quotient. C Bring down the 0.

33 Slide 193 / 239 Slide 194 / What is the next step in this division problem? A B C Put a 0 in the quotient. Put a 4 in the quotient. Put a 2 in the quotient. Slide 195 / 239 Slide 196 / Zero Place Holder Be careful! Sometimes there is not enough to make a group, so zero in the quotient Slide 197 / What is the first step in this division problem? Slide 198 / What is the first step in this division problem? A B C Put a 0 in the ones place of the quotient. Put a 0 in the tenths place of the quotient. Put a 7 in the quotient. A B C Put a 0 in the quotient in the tenths and hundredths place. Put a 0 in the quotient in the ones place. Put a 4 in the quotient.

34 Slide 199 / 239 Slide 200 / Another Way to Handle Remainders Instead of writing a remainder, continue to divide the remainder by the divisor (by adding zeros) to get additional decimal points Instead of leaving the 4 as a remainder, add a zero to the dividend. Slide 201 / 239 Slide 202 / 239 Another Way to Handle Remainders Add a zero to the dividend. No remainder now. Slide 203 / 239 Slide 204 /

35 Slide 205 / 239 Slide 206 / Slide 207 / 239 Decimal Division Example Slide 208 / 239 Decimal Division Example When you have a remainder, you can add a decimal point and zeros to the end of a whole number dividend. 56 Example: You want to save $284 over the next 5 months. How much money do you need to save each month? 5 $ $284 5 = Don't leave the remainder 4, or write it as a fraction, add a decimal point and zeros to get the cents. Slide 209 / 239 Slide 210 / 239 Decimal Division Example 56.8 Decimal Division Example $ Since the answer is in money, write the answer as $ $ Since the answer is in money, add a decimal point and 3 zeros. Round the answer to the nearest cent (hundredths place). $82 7 = $11.71

36 Slide 211 / 239 Slide 212 / $ $782 9 = Slide 213 / 239 Slide 214 / $ $352 Slide 215 / 239 Slide 216 / $48 22 = Divisor as a Decimal To divide a number by a decimal: Change the divisor to a whole number by multiplying by a power of 10 Multiply the dividend by the same power of 10 Divide Bring the decimal point up in the answer Divisor Dividend

37 Slide 217 / 239 Divisor as Decimal Examples: Slide 218 / 239 Divisor as Decimal Practice By what power of 10 should the divisor and dividend be multiplied? Multiply by 10, so that 2.4 becomes must also be multiplied by Multiply by 100, so that.64 becomes must also be multiplied by Slide 219 / 239 Slide 220 / 239 Divisor as Decimal Examples 116 By what power of 10 should the divisor and dividend be multiplied? means means Slide 221 / 239 Slide 222 / Divide 118 Enter your answer = = From PARCC EOY sample test #19

38 Slide 223 / 239 Slide 224 / Enter your answer x 0.1 = From PARCC EOY sample test #19 Slide 225 / 239 Slide 226 / divided by Yogurt costs $.50 each, and you have $7.25. How many can you buy? Slide 227 / 239 Slide 228 / 239 Standards for Mathematical Practices Glossary & Standards Return to Table of Contents MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and 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 and make use of structure. MP8 Look for and express regularity in repeated reasoning. Click on each standard to bring you to an example of how to meet this standard within the unit.

39 Slide 229 / 239 Base Ten In a multi digit number, a digit in one place is ten times as much as the place to its right and 1/10 the value of the place to its left. Slide 230 / 239 Dividend The number being divided in a division equation Dividend 24 8 = 3 Dividend Dividend 24 8 = 3 Back to Instruction Back to Instruction Slide 231 / 239 Divisible When one number is divided by another, and the result is an exact whole number. Slide 232 / 239 Divisor The number the dividend is divided by. A number that divides another number without a remainder is divisible by 3 because 15 3 = 5 exactly = 5 R.1 8 Divisor = 3 8 = 3 R1 24 Divisor Must divide evenly. Back to Instruction Back to Instruction Slide 233 / 239 Exponent A small, raised number that shows how many times the base is used as a factor. Slide 234 / 239 Exponential Notation A number written using a base and an exponent. Exponent 3 2 Base "3 to the second power" 3 2 = 3x = x x x x 3 Standard 1,000 Word One Thousand Exponential 10 3 Back to Instruction Back to Instruction

40 Slide 235 / 239 Number System A systematic way of counting numbers, where symbols/digits and their order represent amounts. Slide 236 / 239 Power of 10 Any integer powers of the number ten. (Ten is the base, the exponent is the power). Base Ten Roman Numerals Others 10 = 10x10 = 10x10x10 = 10 1 = = = 1,000 Back to Instruction Back to Instruction Slide 237 / 239 Quotient The number that is the result of dividing one number by another. Slide 238 / 239 Remainder When a number is divided, the remainder is anything that is left over. (Anything in addition to the whole number.) = Quotient 3 4 Quotient = Quotient = 5 R.1 Remainder 2 5 R No remainder 5 Back to Instruction Back to Instruction Slide 239 / 239 Standard Notation A general term meaning "the way most commonly written". A number written using only digits, commas and a decimal point. Standard 3.5 Word Three and five tenths Expanded Back to Instruction

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