2014 Fall Semester

A=(c,e,j,k)D=(8,3,6,9)G=(4,6)B=(x,y,z,w)E= weird circle slash thingH=(6,4)C=(j,k,e,c)F=(weird circle slash thing)J= ( )True or FalseA=C TrueE=F FalseC=D FalseE=J TrueG=H TrueA=B False

Find the greatest common divisor (GCD) and the least common multiple (LCM) of the following.a. 20,15b. B. 250, 100a. GCD (20,15)=b. 20=(1*20, 2*10, 4*5, 5*4, 10*2, 20*1)c. 15= (1*15, 3*5, 5*3, 15*1)d. Look for commons (GREATEST COMMON)e. Answer= 5LCM (20, 15)a. 20, 40, 60, 80, 100, 120, 140, 160b. 15, 30, 45, 60c. BOTH HAVE 60 for the least they have in common!GCD (250, 100)= 50YESa. 250=1*250, 2*125, 5*50, 10*25, CHECKED OUT b. 100=1*100, 2*50, 4*25, 5*20, 10*10, 20*5 CHECKED OUT c. WHAT IS THE MOST COMMON FOR BOTHd. Answer= 50LCM (250, 100)a. 250, 500, 750, 1,000b. 100, 200, 300, 400, 500 CHECKED OUT c. Answer=5002. Calvin has three alarm clocks which sound at different intervals. Clock A goes off every 15 minutes, clock B every 20 minutes, and clock C every 25 minutes.The three clocks sound together every____ minutes.a. Use the prime factorization method.b. 15=5*3c. 20=5*4= 2 squared *5d. 25=5*5THE LCM (15, 20, 25)(2 squared) ( three) (five squared) SINCE THERE ARE REPEATS BY THEMSELVES OF FIVE YOU HAVE FOUR ORIGINALLY AND YOU DELETE HALF? YOU DELETED TWO.=300The three clocks sound together every 300 minutes.5-4 Prime and Composite NumbersFind the prime factorization of 2,205.The prime factorization is ____a. Use a factor treeb. 2,205=5*441c. FIVE IS PRIMEd. 441=3*147e. THREE IS PRIMEf. 3*49g. THREE IS PRIMEh. SEVEN SQUAREDi. (FIVE)(THREE)(THREE)(SEVEN)(SEVEN)2. Find the prime factorization of 33 fifths* 39 * 4 twelthsa. 2 twelths* 3 sixths * eleven fifths* 13b. 2 twenty fourths* 3 sixths * 11* 13c. 2 twenty fourths* 3 sixths* 11 fifths* 13d. 2 twenty fourths* 3 fifths* 11 fifths* 1333 fifths = (11x3) fifths so (11x11x11x11x11)(3x3x3x3x3)39=13x34 twelths is 2 twenty fourthsSo the answer should be2 twenty fourths x 13 x 3 sevenths x 11 sixthsTake away one eleven and one 3Answer is C(Still confused why you take away certain numbers)5-3 DivisibilityUsing the divisibility tests, answer each of the following.Can 148 passengers be assigned to 3 flights so that each flight has the same number of passengers? (Yes or No)No (Dividing 3 into 148 does not come out evenly)Can a parking lot designed to accommodate 4916 cars be divided into 11 equal rows?No (does not divide equally)Can a theater charging six dollars per person for admission to a play take in exactly 1476 dollars for a night’s performance?1479/6=246YES2. Use divisibility tests to determine whether 4,805,235 is divisible by 15(YES OR NO?)Just divide the number by 15 to check and see if it works outYES IT DOES

For practice on 5-1 and 5-2 click the hyperlink attached to 5-1.

Find two fractions equivalent to the following fraction. 2/7Answer: 4/14 and 12/42Why:Multiply 2/7 by 2/2 to get 4/14Multiply 2/7 by 6/6 to get 12/42Write the fraction in lowest terms: 24/42Answer: 4/7Why: Take 24/42 and divide the numerator and denominator by 2 and then by 3 to reduce the fraction to 4/7.Determine if the following pairs are equal by changing both to the same denominator: 15/24 and 20/21Answer: Not EqualWhy: They are not equal because you can't reduce them to the same fraction. They do not equal the same even if they are reduced or are given common denominators.

Subtract 61/75 from 27/35Answer: 22/525Why?Basically we are trying to find a common denominator. Lots of guessing, but what you find is that both the denominators have a common denominator of 525.(75x7)=525 and (35x15)=525With both of these what you do to the bottom you have to do to the top.(61x7)=427 and (27x15)=405What we have now...427/525-405/525=22/525This can't be reduced so it's our answer.Change the following fraction to a mixed number. 23/3Answer: 7 and 2/3Why?How many 3's can go into 23. The answer is 7.7x3=2123 is our total so 23-21=2 we have 2 left over.So therefor that 2 is part of the thirds so it is our left over 2/3So our whole number 7And our fraction 2/3Our answer is 7 and 2/3

Multiply. Write the answer in the simplest form.4/25x5/24Answer: 1/30Why?You do not have to find common denominators so you can just multiply right across to get your answer. You reduce 20/600 to 1/30 to get your answer by dividing by 20.Solve using the multiplication principle2/15t=-1/4Answer: t=-15/8Why?Just cross multiply everything together. If you do it successfully you will get.8t=-15Divide both sides by 8 to get t by itself and you will get the answer t=-15/8Perform the proper calculations. Reduce your answer whenever possible.14x1 and 1/2Answer: 21Why?Take 1 and 1/2Take 2x1+1 to get 3/2 This changes the number and fraction to just a fractionYou can then just multiply 14/1 by 3/2 to get 42/2 Reduce this to get your answer of 21

Write the following as a sum, using powers of 10 to show place value: 0.279=2x10 to the -1st +7x10 to the -2nd +9x10 to the -3rdWithout performing the actual division determine whether the following represents a terminating decimal. 19/40Yes! It is a terminating decimal.Why?You can't reduce it any farther.Write as a decimal 1/8Answer: 0.125Why?To get this answer divide 8 into 1 adding .000

Hannah went to the store and bought a chair for 6.18, a rake for 12.45, a spade for 11.12, a mower for 141.03, and two six packs of water for 2.02 each. What was the bill?Answer: $184.82Why?Add up all the different prices to get this answer. Careful to make sure you add 2.02 twice since you are buying two packs instead of one.The water in a tank weighs 693.75 lb. One cubic foot of water weighs 62 lb. How many cubic feet of water does the tank hold.Answer: 11.1 cubic feet of waterWhy?Divide 693.75 by 62 to get 11.189.In this instance we do not round up because it the tank can not hold any more than that. So we round down to 11.1 cubic ft to be safe.Convert to decimal notation 8.6x10 to the -7thAnswer=.00000086Why?go back 7 places from the decimal point like the question says to get your answer.

Find a decimal representation of 2/3Answer: 0.6 foreverWhy?Do 3 divided by 2 .000 to get your answer.Find a rational number between 2/5 and 0.40 foreverAnswer: 0.4022Why? Divide 5 by 2 to get .4 which is equivalent to 2/5We now know that the third number right of the decimal point has to be between 0 and 4 to work.Find a decimal representation of 1/9Answer: 0.1 foreverWhy?Just divide 9 into 1 and you will get the answer.

Express the number as a percent3.53Answer 353%Why?Just move the decimal point to to the right to get this answer.What is 8% of 24Answer: 1.92Why?Take .08 and multiply it by 24We got the .08 by moving the decimal point to to the right to make it a number.A real estate commission rate is 6% what is the commission on the state of a 93,000 dollar home.Answer 5,580 dollarsWhy?Take 93,000 and multiply it by 0.06See above for explanation on how to change a percent to a number.

Find the 9th term of the sequence-2, 2, -2, 2The ninth term of the sequence is -2The nth term of the sequence is:an=a1r ^n-1an is the nth terma1 is the first termr is the common ratio-2 * (-1) ^n-1

a. 1+2+3+4+ ... +999b. 1+3+5+7+ ...+ 101A. S= 1 + 2 + 3 + ... +997 +998 + 999 S=999+998+997 ...+ 3 + 2 + 12S=1,000 + 1,000 + 1,000 ... +1,000+ 1,0000 + 1,00002S = 999 * 1,000=2S= 999,000S=999,000/2S=499,500The sum of the sequence for a is 499,500The sum of the sequence for b is 2,601

http://www.mathsisfun.com/associative-commutative-distributive.htmlAssociative, Communitive, and Distributive properties.There is also the property that has to do with 0 and 1Anything times 0 equals 0Anything multiplied by 1 equals that number for example 8x1=8