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Prime vs. Composite Numbers

Prime vs. Composite Numbers. A prime number is a whole number greater than 1 that has exactly two factors 1 and itself. 2,3,5,7 are whole prime numbers Ex: The number 17 has only two factors 1 and itself, so its prime. Prime vs. Composite Numbers.

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Prime vs. Composite Numbers

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  1. Prime vs. Composite Numbers A prime number is a whole number greater than 1 that has exactly two factors 1 and itself. 2,3,5,7 are whole prime numbers Ex: The number 17 has only two factors 1 and itself, so its prime.

  2. Prime vs. Composite Numbers • Prime Factorization is a composite number that can be written as a product of prime numbers. Factor Trees are used to find the prime factorization. 60 6 x 10 2 x 3 x 2 x 5 The prime factorization of 60 is 2x2x3x5.

  3. Prime vs. Composite Numbers • A Composite Number is a whole number grater than 1 that has more than 2 factors. • 4,6,8,9,10 are whole composite numbers Ex: The number 12has six factors:1,2,3,4,6 and 12, so its composite.

  4. Simplifying Factions • A fraction is simplest form when the GCF of the numerator and denominator is 1. • Equivalent fractions have the same value. Method 1: 6 over 24 divided by the CF which is 2 will bring you to 3/12 which is simplified but not in simplest form so you’d divide again by 3 and you’d get and get ¼.

  5. Simplifying Fractions Method 2: First find the GCF of the numerator and denominator. Factors of 6:1,2,3,6 The GCF of 6 and Factors of 24:1,2,3,4,6 24 is 6. Then divide the numerator and denominator by the GCF,6. 6/24 divided by 6 which equals ¼

  6. Converting between percents, decimals, fractions • Percents, decimals, and fractions can all be turned into each other. They all came from whole numbers. • Percents are basically out of 100. • Fractions are out of what ever the denominator is and the numerator should never be bigger than the denominator. • Decimals are whole numbers with extra left over.

  7. Converting between Percents, Decimals and Fractions • Percents turned into fractions: 190%=190/100 then take off the extra zero’s and make it 19/10 or 1 9/10 this is called an improper fractions • Fractions turned into percents: ¼ =25%, ½ =50%,3/4 =75%

  8. Converting between Percents, Fractions, and Decimals Fractions turned into decimals: 89/100,000 = n/100 8,900=100,000n 8,900/00,000 = 100,000n/100,000 n=0.089 Write a proportion, find the cross products, divide each side by 100,000 Fractions turned into decimals: ¼ = 0.25 ¾ = 0.75 ½ = 0.5

  9. Ordering Rational Numbers • A rational number is a number that can be expressed as a fractions. Least to Greatest: -5,3,-3,7,-1 = -5,-3,-1,3,7 6.8,7.2,1,0.94,6 = -6,0.94,1,6.8,7.2 Greatest to Least: 12,6,-4,0,-5,-3 = 12,6,0,-3,-4,-5 10,6.8,4.9,-0.1,0.1,10.6=10.6,10,6.8,4.9,0.1, -0.1

  10. Unit Rate • Unit Rate-the quantity per 1 unit (30mph) • To find the unit rate ,your denominator must be 1. Ex:$280 a week, what is your hourly wage if you work 40 hrs per week? $280 divided by $40=$7hr

  11. Proportions • Proportion- an equation stating that 2 ratios are equal. Ex:2/3= 10/15 • Cross product-to multiply diagonally. Ex:20 40 20x10=200 y = 5x40=200 5 10

  12. Proportions Ex: 6 24 7x24=168 y = 6x29=174 no 7 29 Ex: 5 x 6x=18.5 multiply y = 6x=90 divide 6 18 6 6 (x=15 solution) Ex:6/c=24/28 24c=6x28=168 24 divided by 7=168 24c=7x2 c=7

  13. Percent of a Number To find 5% of 300, you can use either method. Method 1:Write the percent as a fraction 5%=5/100 or 1/20 1/20 of 300=1/20x300 or 15 Method 2:Write the percent as a decimal 5%=5/100 or 0.05 0.05 of 300=o.05x300 or 15 so 5% of 300 is 15

  14. Consumer Mathematics List price-Original prize Sales tax-Amount added to the original price Total price-LP+ Sales tax Sales Tax Sales tax= LP x rate What is the sales tax?, on $110 @ 5% sales tax? $110x0.05=$5.50 In Arizona the sales tax is 6.5%. What is the sales tax on a $239 DVD player? 239x0.065=$15.535=$15.54

  15. Consumer Mathematics Total Cost: What is the total cost the of groceries if they are listed @ $74.50 and there is a 7% sales tax? $74.50x7=52.150=52.2 74.50+52.2=$79.72 Discount-The amount by which the list is reduced Sales price-LP-D Rate of Discount-the percent of discount Tent-$50 @ 17% discount. D=LP x Rate D=50 x 0.17 D=$8.50

  16. Consumer Mathematics $310 @ 25% discount; 6% sales tax D=LP x R ST=LP x R D=310x0.25 ST=232.50x0.06 D=$77.50 ST=$13.95 SP=LP-D TC=LP + ST SP=310-77.50 TC=23.50 + 13.95 SP=$232.50 TC=$246.45

  17. Integers Integers are numbers that are either positive or negative. Positive integers are numbers above zero. 012345678910 Negative integers are numbers below zero. -1-2-3-4-5-6-7-8-9-10

  18. Integers Add and Integers Rule 1: If they have the same sign, add them and use their sign. Ex: 3+1=4 -3+(-1)=-4 Rule 2: If they have different signs, subtract (big-small) and use the sign of the bigger number Ex:15+-35=-20

  19. Integers Absolute value-the distance a number is from zero on the number line. *Absolute value is always positive. Ex: -9 =9 Compare and order Integers -100,35,-32,-33,-1=-100,-33,-32,-1,35 Subtracting Integers Rule: Keep, change, flip

  20. Integers Multiply and Divide Integers Positive: Pos x Pos, Negative x Negative, Pos divided by a Pos, Negative divided by a Negative Negative: Pos x Negative, Negative x Pos, Pos divided by a Negative, Negative divided by a Pos. 2x3=6 -2x-3=6 5x-2=-10 -5x2=10 20 divided by -2=10 -20 divided by 2=-10

  21. Order of Operations • Parenthesis ( ) • Exponents • Multiplication or Division (left to right) • Add or Subtract (left to right) Ex:5(3-1)+6 to the second power 1.(3-1) 2.6 to the second power 3.5x2 4.36+10

  22. One and Two Step Operation Inverse Operations- Opposite Operation, add/subtract; multiply/divide. Ex: a+4= 7 c-8=3 -4 -4 +8 +8 a=3 c=11

  23. One and Two Step Operation Step 1-Add or Subtract Step 2-Multiply or divide Ex: 2a+4=16 -4 -4 2a=12 2 2 a=6

  24. Coordinate Graphing PointCoordinateQuadrant II (-,+) (+,+)I v -8,0 x-axis v X-AXIS III (-,-) (+,-)IV Y-AXIS Middle- origin Order pair=(x, y)

  25. Properties Commutative Property-In addition and multiplication, the order dose not matter. Ex:9x8=72 3+5=8 a+ b= b+ a 8x9=72 5+3=8 ax b= b x a Associative Property-Grouping numbers together that are easy to work with. (t and x) Ex:3+61+7=(3+7)+61

  26. Properties Distribute Properties-Distribute your number through the problem using multiplication. Ex:5(8x3)=5x8+5x3=40+15=55 Identity Properties-The sum of an addend and 0 is the addend. The product of a factor and 1 is the factor. A + 0=A

  27. Probability Simple Events: Probability-number of successful outcomes divided by a total number outcomes Event: Roll a number cube P(5)=1/6 not likely P (not 1)=5/6 likely P (odd)=3/6=1/2 equal P(6)=6/6=1 definite P(9)=0/6=0 impossible

  28. Probability Sample Space and Probability Sample space-the set of all possible outcomes in a probability experiment. Tree diagram-used to display the sample space. A couple decided to have two children. Find the sample space of the children's gender if having a boy is equally likely as having a girl. Answer: girl, girl, girl, boy, boy, boy, girl, boy.

  29. Probability Sample space and Probability Amy has two choices of bread and 3 choices for lunchmeat. Ham Outcomes=6 Wheat Turkey Roast beef Ham Sourdough Turkey Roast beef

  30. Fundamental Counting Principle We use the FCP to determine how many out comes there are in an event. Ex: Day of the week then month of a year. 84 Toss a coin roll a cube choose a letter in math. 48 Pants Shirt Shoes Socks Pink skinnies Hello kitty Boots Knee highs School pants Halter top Boots w/ fur dirty socks Short shorts Toga 54

  31. Probability Permutations-in a permutation the order is not important. How many different ways can 5 people line up. 5x4x3x2x1=120 Combinations-not important number Ex: 2 toppings Method 1: Make a list ham hp ph sh bh oh pineapple hs ps sp bp op salami hb pb sb bs os bacon ho po so bo ob onion 10 choices

  32. Probability Combinations: Method 2-Formula 5x4/2x1=20/2=10 Ex: You choose 3 out of 7 stickers 7x6x5/3x2x1=35

  33. Probability Compound Events- two or more simple events. Independent Events-the outcome of one event doses NOT affect the next outcome. (with replacement) 2 Ex: flip a coin and roll a cube

  34. Probability Compound Events: Dependent Event-The outcome of the first event will affect the probability of the next event. (without replacement) Ex: P (g, b)=4/105

  35. Venn diagrams Sprite-5 Both-10 Pepsi-8 Neither-2 10 represents the people that like both Sprit and Pepsi. 2 represents the people who do not like either Sprite or Pepsi. 5 represents the people who like Sprite only. 8 represents the people who like Pepsi only.

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