Math Extra Credit

By: Astrid PedrozaPeriod:6November 30-2010

Prime & Composite Numbers

• Prime numbers- A number that has EXACTLY 2 factors, itself and 1.

Example: 2, 3, 5, 7

• Composite numbers- A number that has 2 or more factors.

Example: 10, 9, 8, 6

Simplifying Fractions

• To simplify a fraction you have to divide by the gcf.

Example: 3/6 3/3 = 1/3

8/16 8/8 = 1/8

Converting Fractions & Decimals

• When converting a fraction into a decimal you must divide.

Example: ¼_4/1= 0.25 3/8_8/3= 0.375• Converting a decimal into a fraction you have

to use 10. Examples: 0.3 = 3/10 - 0.29 = 29/100 0.199 = 199/1000

Converting Fraction into Percents

CONVERTING FRACTIONS INTO PERCENTS• Step 1: Divide; Numerator Denominator.• Step 2: Move the decimal point 2 places to the

RIGHT.• Step 3: Add a percent sign (%) Example: 6/20 20/6= 0.3_0.30 30%

Converting Percents into Fractions

• Step 1: Put the number over 100• Step 2: ReduceExamples: 64% = 64/100 2/2 = 32/50 2/2 = 16/50 45% = 45/100 5/5 = 9/2588% = 88/100 5/5 = 44/50 2/2 = 22/25

Converting Percents into Decimals

• Step 1: Remove % sign• Step 2: Move the decimal point 2 places to the

LEFT . Examples: 29% = 29 = 0.29 163% = 163 =1.63 5% = 5 = 0.05

Converting Decimals into Percents

• Step 1: Move the decimal point 2 places to the RIGHT.

• Step 2: Add % sign Example: 0.62 = 62% 0.8 = 80% 1.96 = 169% 15 ½ = 1.55 12.63 = 1263% 0.009 = .9%

Ordering Rational Numbers

• Least to Greatest • 3 Examples 1. -5, -3, -1, 7 2. -6, -4, -2, 0, 8, 12 3. -6, -4, 0, 1/8, 0.3, 9/10, 1

Unit Rate

• Unit Rate is the ratio of two measurements in which the second term is 1.

• Some common unit rates are miles per hour, cost per item, earnings per week, etc.

• Example: If Ximena earns $180 in 20 hours, then unit rate of her earnings is given as: 180/20 = 4 per hr.

Proportions

• Proportions- An equation stating that 2 ratios are equal.

• Examples: 20/5 = 40/10 6/c = 24/28 24c= 6x28 24c= 168 c=7

Percent of a Number

• Every statement of percent involves three numbers. Example,8 is 50% of 16.

• 8 is called the Amount. 50% is the Percent. 16 is called the Base. The Base always follows "of."

• Examples: $300 in 60 hrs = 300/6 = $50 220 miles on 8 gallons = 220/8 = 27.5 mpg Ham Bad Size: 8 Cost: $9.88 = 8/9.88 = $1.23 per lbs

Consumer Math

• Sales Tax- Amount added to original price• List Price- Original price• Total Cost- List price + Sales Tax Formula: LP x Rate = Sales TaxExamples: What is the sales tax on $110 @5% ST? 110 x 0.05 = $5.50What if the total cost of grocery if they are listed at

$74.50 and there is a 7% sales tax? 74.50 x 0.07 = 5.22 $74.500+5.22= $79.72

Consumer Math

• Discount- The amount by which the list price is reduced• Sales Tax: LP-D• Rate of Discount- The % of discount Tent $50 @ 17% discount Skateboard $149 @ 35%

discount What’s the sales price? D= LP x Rate D= LP x D D= 50 x 0.17 D= 149 x 0.35 D= 8.50 D= 52.12 What’s the sales price? SP= LP-D SP= LP-D SP= 149 x 52.12 SP= 50-8.50 SP= $96.85 SP= $41.50

Consumer Math• Using all steps in consumer math. Coat $310 @ 25% discount: 6% sales tax D=LP x R D= 310x0.25 D=$77.50 SP= LP-D SP=310-77.50 SP=232.50 ST= LP x R ST=232.50x0.06 ST=13.95 TC= LP+ST TC= 232.50+13.95 TC= 246.45

Consumer Math• Simple Interest Interest: Principle x Rate x Time in Years Principle: The amount deposited or borrowed Example: Principle= $8000 Rate= 6% Time= 7 years I= PRT I= 8000x06x7 I= 3360

Adding Integers

• Rule 1: If they have the SAME SIGN , ADD them and use their sign.

Examples: -3+-5= -8 6+3=9• Rule 2: If they have different signs subtract

(BIG-Small) and use the sign of the bigger number.

Examples: 16+(-9)=7 -96+36= -61

Subtracting Integers

• Rule: Same Change Change Examples: -9 + -9 = -9 – 9= 0 -32 + 21 = -32 – (-21)= -11

Multiplying and Dividing Integers

• Rule: Positive Negative Examples: Pos. x Pos. Pos. x Neg. 2x3=6 -6x-7=-42 Neg. x Neg. Neg. x Pos. 5(-3)=15 -9x8=-72 Pos./ Pos. Pos./Neg. 25/5 = 5 -32/8=4 Neg./Neg. Neg./Pos.

Integers

• Absolute Value Absolute Value- The distance a number is in the

number line. Example: -9 = 9 -C=C Z=Z• Ordering Integers Example- Least to greatest: -5, -3, -1, 0, 6, 91• Comparing Integers Examples: -15>(-17) -13>0

Order of Operations1. Parenthesis ( )2. Exponents 3. Multiplicative or Divide (Left to Right) 4. Add or Subtract (Left to Right) Example: 100-6x5/3+25 100-30/3+25 100-10+25 90+25 115

One-Step Operations

• Inverse Operation: Opposite operation And & Subtract - Multiply & Divide Examples: 3V/3 = -39/3 V= 13 C-8=3 C= 11 19+e=40 e=21 -19 -19

Two-Step Operations

• Step1: Add or Subtract• Step2: Multiply or Divide Examples: 2g+3= -11 –(-3) 2g= -14 -3 g= -7 5f-1=14 5f/5=15/5 +1 +1 f=3

Coordinate Graphing

Y axis II (+,+) (-,+) I X axis III (+,-) (-,-) IV

Example of coordinate plane

Coordinate Graphing - 10 . TABLE

- 9 RULE: X+3=Y - 8 X Y - 7 7 10 - 6 - 5 - 4 - 3 - 2 - 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 - 4 -5 -6 -7 -8 -9 -10

Example of coordinate graphing

Properties

• Commutative Property: In addition and multiplication, the order doesn’t matter.

Examples: 9x8=72 8x9=72 3+5=8 5+3=8• Associative Property: Grouping numbers

together that are easy to work with (Addition & Multiplication)

Examples: 6x23x10 = (13x10)x6 3+61+7 = (3+7)+61

Properties

• Distribute Property: Distribute your number though the problem using multiplication Example: a(Z x Y) = a (Z) + a (Y) = aZ+aY

• Inverse Property: State that when a number is combined with its inverse, it is equal to its identity.

Example: Inverse of a is - a so that a + (- a) = 0.

Probability

• Probability: The measure of how likely an event is.• Event: One or more outcomes of an experiment.• Experiment: Situation involving chance or probability

that leads to results called outcomes.• Outcome: result of a single trial of an experiment. Example: A spinner has 4 equal sectors colored

yellow, blue, green and red. What are the chances of landing on blue after spinning the spinner? What are the chances of landing on red? Answer: ¼ because there is one red section out of four. And ¼ because there is one blue section out of four.

Venn Diagrams

• Venn Diagrams compare two or more things thing that are different from each other.

Examples: