Elementary Math (MTE280)

Convert to base ten: 23 five(.....)(.....) ...5 + 5 + 3 = 13In order to convert to base 10 with 23 base five you have to put 2 longs and 3 units each long is equal to five since the base is five and there are only 3 units.

Convert to base 5 : 8(.....) ... = 13 basefiveSince we are converting to base five using 8 there is only one long because since it is base five only 5 could fit into a long and there are 3 left over making it 13.

Flats: A collection of longs depending on the base that is how many longs will be in a flatEx; Base five there will be five longs in a flatFlats are the first numbers when putting together a number if there are 2 flats than the number is 200

Longs: a collection of units, depending on the base that is how many units will make up a longEx; base five means 5 units will make a longLongs are the middle number when putting together the number if there are 2 flats and 5 longs the number is 250

Units: the number of individual unitsUnits are the last number when putting together the number if there are 2 flats and 5 longs and 7 units the number would be 257

12 base five + 22 base five(.....)(.....).. + (.....)(.....)(.....)(.....).. 22 + 42 = 64 base five In order to use addition you have to fine the base five of each number first. You get 2 longs and 2 units for 12 base five making it equal to 22. You get 4 longs and 2 units for 22 base five making it equal to 42. You then have to add 22+42 to get 64 base five.

5+(-3)+++++---The green and red indicate the Zero bank meaning there is 2 positives left over

7-4+++++++The red indicates 4 being taken away from the 7 positives

When the signs are the same the answer is positiveWhen the signs are the opposite the answer is negative10 (-15)+ - = -150 (-7)(-20) - -= 140

Keep Change ChangeK C C 3 -(-4) 3+(+4) = 7

The smallest number that goes into two or more numbersWhen factorizing use the small numbers, only use the same numbers and use the lowest exponentEx: 18=  (1x18),(2x9), (3x6) GCF=6

The greatest number that two or more numbers are divisible byEx: a) 3^2 x 5^4 x 7 b) 2 x 3^7 x 5^2 x 11GCF: 3^2 x 5^2 LCM: 2 x 3^7 x 5^4 x 7 x 11

Factor Tree45= 9x5, 9= 3x3Factors= 5,3,3Prime factorization = 3^2 x 5Upside down division

When adding denominators must be the sameIf they're not the same find the GCF to get the denominators the sameEx: (5) 5/12 + 2/15 (4)Get the denominators the same When multiplying, multiply both the numerator and denominator 25/60 + 8/60 = 33/66 (simplify) = 11/20

When subtracting denominators must be the sameIf they're not the same find the GCF to get the denominators the sameEx: 7/8- 5/8 = 2/8 (can simplify down) = 1/4

When a numerator and denominator are the same they are considered whole fractionsEx: 11/11When adding a whole number and a fraction you can pair them together Ex: 8+ 5/17 =8 5/17

an alternative way for long multiplication and is a method constructed to fit numbers being multiplied.Add the numbers diagonallyGet to write down the tens first than onesanswer is read from left to rightEx:(26)(38)6*3=182*3=66*8=488*2=16Add numbers diagonally in diagram making it equal 988

A alternative way to solve multiplication problems where the length and width are usedA square is drawn out and the one set of numbers is written on top (Horizontally) while the other set is written straight down on the side of the box (vertically)Flats, longs, and units are separated in order to simplifyEx: (253)(346)200 x 300 = 60,000200 x 40 = 8,000200 x 6 = 1,20050 x 300 = 15,00050 x 40 = 2,00050 x 6 = 3003 x 300 = 9003 x 40 = 1203 x 6 = 18(60,000+15,000+900)+(8,000+2,000+120)+(1,200+300+18) = 87,538

 Allows you to create simpler multiplication problems and add them together by breaking down one of the factors into smaller numbersseparates flats, long, and unitsEx: (43)(56)(40 + 3) x (50 + 6)(40)(50) = 2000(50)(3) = 150(40)(60) = 240(3)(6) = 182000+150+240+18 = 2408

an easier way to add by changing numbers to a 0 so changing it to become a factor of 10.You subtract from one set of number and add it onto the other to make it a factor of 10They are called friendly because once the rule for adding 0 is understood, that understanding can now be used to larger numbers that end in 0ex: 36+25 = 36(+4) + 25(-4) 40+21= 61

This method is also similar to the friendly numbers, but is wrote down vertically downWant to get pairs of factor numbers of 10ex: 53 + 78 = 53(-2) + 78(+2) = 131 51+80=131

 An Addition Strategy where you start from the left side of the problem rather than the right side and Switching the order so that we begin with the largest values place a zero for the other place numbers when adding Ex : 342 + 156 400 90 8 498

The lattice method of addition is an alternative way of adding numbers that eliminates the need to carry tens over to the next columnAdd the digits diagonallyEx: 243+4293+9=124+2=62+4=6 = 672

Cross of the number as you reach the base value you are looking forEvery time you count up to ten you cross off the number and if there is a reminder you start counting again from that reminder but if there is no number after the reminder the number goes straight downEx: 3 6 4 R 3 3 + 5 R 1 8 2 R 1 1 4 36

Allows you to create simpler addition problems and add them together by breaking down one of the factors into smaller numbersseparates flats, long, and unitsEx: 243 + 429 + 200+40+3 400+20+9  600+60+12 = 672

The associative property states that you can add or multiply regardless of how the numbers are grouped Ex: 5+(7+1)= (5+7)+1

a math rule that says that the order in which we multiply numbers does not change the product Ex: 5+7+1=1+7+5

The distributive property lets you multiply a sum by multiplying each addend separately and then add the products Ex: 5(7+1)

An easier way than long divisionEx: 52 6 52 - 48 = 8 4/6 6

2- End in even number 3- Sum of digits divides into 34- Last 2 digits divide into 45- Ends in 0 or 5 6- If 2 & 3 work than 6 works 8- last 3 digits divide into 8 9- sum of digits divide into 910- ends in 0

a fraction whose denominator is a power of ten and whose numerator is expressed by figures placed to the right of a decimal point Make sure the decimals are lined up and numbers lined up in the same value34.5 + 6.32 34.50+ 6.32 40.82

GEMDAS G- Groups E- Exponents M- MultiplicationD- DivisionA- AdditionS- SubtractionThe same as Pemdas but instead of parenthesis use groups, separate groups by addition and subtraction symbols

When adding denominators must be the sameIf they're not the same find the GCF to get the denominators the same

When subtracting denominators must be the sameIf they're not the same find the GCF to get the denominators the same

Simplify the fractions Multiply the numerators of the fractions to get the new numeratorMultiply the denominators of the fractions to get the new denominator.

What is 60% of 80? 6 6 X 10 X 8 60 48 = 48%

A alternative way to solve multiplication problems where the length and width are usedAlgebra way would be using variables Ex: 5(32) Ex: Let x=10 5(3x+2)