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PrimePrime 50 40 30 20 10CompositeCompositeGCFGCFLCMLCM MiscMathMiscMath Math 170 – Chapter 5 50 40 30 20 10 50 40 30 20 10 50 40 30 20 10 FINAL 40 30 20 10

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Primes

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CheckWork 2 Go Home Go Home 10 Point Question What is the smallest prime number?

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CheckWork Go Home Go Home Is 209 prime? 20 Point Question No. 209=11*19

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Find the prime factorization of 2008. CheckWork 2*2*2*251 Go Home Go Home 30 Point Question

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CheckWork Any number can be written uniquely as the product of primes Go Home Go Home 40 Point Question What is the fundamental theorem of arithmetic?

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CheckWork 2*2*5*7 Go Home Go Home Find the prime factorization of 140. 50 Point Question

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Composite

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CheckWork Four. Go Home Go Home What is the smallest composite number? 10 Point Question

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CheckWork Go Home Go Home 20 Point Question Is the 36 digit number consisting only of 4’s divisible by 3? Here is the number: 444,444,444,444,444,444,444,444,444,444,444,444 Yes. The sum of the digits will be 144, and 144 is divisible by 3.

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CheckWork Go Home Go Home 30 Point Question How can you tell if a number is divisible by 6? It is divisible by both 2 and 3

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CheckWork Go Home Go Home Suppose that 24|b. What else must divide b? 40 Point Question 1, 2, 3, 4, 6, 8, and 12

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CheckWork Go Home Go Home Show that if a|b and a|c, then a|(b+c). 50 Point Question Since a|b, b can be made out of rods of length a. Since a|c, c can also be made out of rods of length a. By putting these two together, you get b+c, which can also me made of rods of length a. Thus a divides (b+c) aaaaa b aaa c

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GCF

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CheckWork 1, 2, 3, 6, 7, 14, 21, 42 Go Home Go Home List all the factors of 42 10 Point Question

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CheckWork Go Home Go Home Use prime factorization to find the GCF of 12 and 30. 20 Point Question 12 = 2*2*3 30 = 2*3*5 Primes in common: 2& 3. GCF = 2*3=6

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CheckWork GCF(75,120) = GCF(75,45)= GCF(30,45) = GCF(15,30) = GCF(15,15) = 15. Go Home Go Home Use the subtraction method to find the GCF of 75 and 120. 30 Point Question

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CheckWork 6 cookies per tray Go Home Go Home Joe the Baker baked up 84 spice cookies and 90 sugar cookies. Joe is planning on selling the cookies in trays. Each tray should contain only one type of cookie, and each tray, regardless of the type should contain the same number of cookies. Joe wants to use the least number of trays. How many cookies should he put on each tray? 40 Point Question

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CheckWork 2*2*3*7*11 Go Home Go Home Find the GCF of these three numbers: 2*2*2*3*3*5*7*112*2*3*3*3*7*11*17*192*2*2*2*3*5*7*11*19*23 50 Point Question

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LCM

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CheckWork 7, 14, 21, 28, 35, 42 Go Home Go Home 10 Point Question List the first 6 multiples of 7.

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CheckWork Go Home Go Home Carol is laying down rods that are 8 units long. Mike is laying down rods that are 6 units long. If they both started at the same place, when will the ends of their rods line up again? 20 Point Question When they each have reached a length of 24 units.

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Find the LCM of 48 and 40 using the prime factorization of each number. CheckWork 240 Go Home Go Home 30 Point Question

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Go Home Go Home 40 Point Question CheckWork Juan will only by a CD if it has exactly 14 songs on it. Marty will buy a CD only if it has exactly 12 songs on it. If they have the same number of songs in their collection, what is the fewest number of CD’s each owns? Juan owns 6, Marty owns 7. They both have 84 songs in their collection.

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CheckWork Go Home Go Home 50 Point Question Find the LCM of the following numbers 2*2*2*3*3*5*7*11 2*2*3*3*3*7*11*17*192*2*2*2*3*5*7*11*19*23 2*2*2*2*3*3*3*5*7*11*17*19*23

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Misc. Math

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CheckWork The Associative Property of Addition. Go Home Go Home Which property of addition does the following demonstrate? (a + b) + c = a +(b + c) 10 Point Question

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Explain how to do the following problem using mental math. 21X36 + 21X64 Use the distributative property to make it 21X(36+64) Add the compatible numbers, then multiply to get 2100. CheckWork Go Home Go Home 20 Point Question

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CheckWork Go Home Go Home 30 Point Question Use the range method to get estimates for 236+153. Low: 300, high 500.

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Explain how to use the compensation method to find 248+296. CheckWork Go Home Go Home 40 Point Question I would take 4 from the 248 and add it to the 296 so the sum becomes 244 + 300 = 544. I guess you could also take 2 from the 296 and add it to the 248 so the problem becomes 250 + 294, but my way results in an easier sum.

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CheckWork Go Home Go Home Final Question They are perfect squares. For example, 36 has 9 factors: 1, 2, 3, 4, 6, 9, 12, 18, 36 Most numbers have an even number of factors. For example, there are 6 numbers that evenly divide into 12 (1, 2, 3, 4, 6, & 12), 4 numbers that divide evenly into 15 (1, 3, 5, & 15) and only 2 numbers that divide into 19. What is special about numbers with an odd number of factors?

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