Math+8

——Math 8

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August 29, 07 Naturals: counting numbers (ex. 1,2,3) Wholes: counting numbers puls zero (ex. 0,1,2,3) Intigers: below zero AND above zero (ex. -4, -3, -2, -1, 0, 1, 2, 3, 4) Rationals: part of a number (ex. 1 1/2, 2 1/2) Irrationals: 3.14, no repeat Complex: imaginary numbers
 * Number Systems:**

August 30, 07 180 <--quotient divisor-->346120<--dividend 34^^ 272^ 272^ 00<--remainder
 * Division:**

August 31,07 million-->6 zeros-->2 000 000 billion-->9 zeros--> 2 000 000 000 behind the decimal you say each number separatly ex: 0.025=zero point zero two five =twenty five thousandths 0 . 0 0 0 ^ones ^decimal ^tenths ^hundredths^thousandths 3 893 000 000 -rounded up to 4 000 000 000 - accurate: 3 893 8.900 8.093 8.09 8.0093 8463 = 8500 14.439 = 14.4 14.983 = 15.0 14.4984 = 14.498 > -- Greater than < -- Less than (ex. 4 > 1 {4 is greater than 1}) (ex. 1 > 4 {1 is less than 4}) (ex. 5 = 5 {5 is equal to 5}) Numbers can be expressed in two ways a) __expanded form__ b) __standard form Standard form__ __Expanded form__ 4352 4000+300+50+2 4x1000+3x100+5x10+2x1 __Exponential notation__ 1000= 10/3 (to the power of 3) 100=10/2 (to the power of 2) 10= 10/1 (to the power of 1) 1= 10/0 (to the power of 0) 1/10=10-1 1/100= 10-2 ex. 72 043 70 000+2000+40+3 7x10 000+2x1000+4x10+3x1 7x10/4+2x10/3+4x10/1+3x10/0 Any powers to 3 last number ends in either 1, 3, 7, 9
 * Biggest to smallest**
 * Rounding to the nearest hundred:**
 * Rounding to the nearest tenth:**
 * Rounding to the nearest thousandth:**
 * Greater than/ less than**
 * Expaning numbers (whole numbers)**
 * hints**:: You dont have to write the 0 in.

12 --> subtrahend __- 12__ --> minuend 10 --> difference
 * Subtraction**

49 __x37__ 343 __+1470__ 1813
 * Multiplication**

__57__ 48| 2736 - __240 ^__ 336 -__336__ 0
 * Division**

This means to be able to divide into a number. __Rules::__ 2: Has to end in an even number or a 0. such as:: 4, 26, 2100, 4126 3: If the sum of the didgits is divisible by 3. such as:: 21, 18, 24 4: If the number represtented by the last two digits is divisible by 4 5: If the ones didgit is 0 or 5. 6: If the number is divisible by 2 and 3 8: If the number represented by the last 3 didgits is divisible by 8 9: If the sum of the digits is divisible by 9
 * Divisibility**

All multiples of 1000 are divisible by 8 such as:: 2000, 7000
 * Multiples**

Surface Area To find surface area of any prism you find all the area for every figure that makes up the prism then add them together. In order to do that we need to find the area of a 2 dimesional figure.

__**Distributive property**__ When you solve problems you have to find the like denomonators when you simplify it. 3(x+4) -2(x-4) 3x+12 -2x+12

4(4x-3y+2)-(2x+5y-4) 4(4x-3y+2)-1(2x+5y-4) ˆ When there is no number after the - sign we just asume that it would be a 1. It could be and x or a 1 16x-12y+8 - 2x-5y+4 We have to find the like denomenators. 16x-2x= -18x when we have used the like denomonators we cross them out so we know we have already used them 12y-5y= 7y +8+4= 12 Now we have to add all the answers up so we can get a simplified equation -18x-7y+12

Since there is no equal sign in the original equation we dont have to solve it because there is no equal sign.

__**Using Division and multiplication tho solve equations** Ex: 1__ Solve the equation 2x=6 __Solution__ Divide both sides of the equation by 2. x x = 6 2x=6 x x = 33 __2x__ = __6__ x = 3 2 = 2 x = 3 the solution of x is 3. __**Solving Equations Containing Numbers EX 1:**__ 0.25x - 5 = 2.75 (multiply them by 100 to get rid of the decimal place) 25x - 500 = 275 25x - 500 (+500) = 275 (+500) ( add 500 to the left and right side to get the x by itself on the left) __25x__ = __775__ 25 25 (divide both numbers by 25 to get the number equal to x) x = 31 **Chk:** 25(31) - 500 = 275 775 - 500 = 275 275 = 275 ALWAYS HAVE YOUR EQUAL SIGNS ALINED! EX 2: 3.14n + 2 = 12.99 314n + 200 = 1299 __314n__ = __1099__ 314 314 n = 3.5 (normally if the question has a decimal the answer with have a decimal as well) Chk: 314(2.5) = 1099 1099 = 1099 EX 3: x/3 - 3x/2 = 1/6 - x (find a denominator each of the fractions can go into in theis case 6 multiply all numers by 6) 2x - 9x = 1 - 6x (Under each of you 6's put one, This makes the 1 and the x cancel each other out) -7x = 1 -6x (do the comon ones with x, (to the left)) -7x (+6x) = 1 -6x (+6x) get the x's over to one side of the equation) -__1x = 1__ 1 = 1 x = -1

==Cube- A=S2 find the area of a 1 side and multiply the number of sides Rectangle- A=lw Polygonal-A=ANS /2 A=altitude N= number of sides S=length of sided Triangle-A=bh /2 Cylinder-A=3.14d of 2 (3.14)r Sphere-A=4(3.14)r2==