Elementary Mathematics

Math in other bases (Notes/practice down below)https://docs.google.com/document/d/1iSCe8ShmuRuwxXJt1wWFhQXsyQNaibmzEweVwnvW8uY/edit?usp=sharing

place value : the value of a digit based on its place within a numbervalue : how much a digit is worthtenths, hundredths, thousandths = less than 1digit : a single numerical symbolnumber : one or more digits togetherEx. in the number 74.892, the 8 is in which place? Answer : tenths

Powers of 10490 = 49 tens490 / 10 = 4936,000 / 9 = 4,000each place is 10 times larger than the place to its right1 x 10 = 10 (one zero)1 x 10 x 10 = 100 (2 zeroes)1 x 10 x 10 x 10 = 1000 (3 zeroes)

Different types of multiplication strategiesarrayequal groupsnumber linerepeated additionskip counting

Math Properties NotesCommutative Property of Addition - Changing the order of the addends doesn't change the sumEx. 26 + 7 = 7 + 26Commutative Property of Multiplication - Changing the order of the factors doesn't change the productEx. 5 x 3 = 3 x 5Associative Property of Addition - Changing the grouping 3 or more addends doesn't change the sumEx. (6+2) + 4 = 6 + (2+4)Associative Property of Multiplication - Changing the grouping of factors doesn't change the productEx. 6 x (3x8) = (6x3) x 8Distributive Property - You can multiply each number in an addition problem or subtraction problem, then add or subtract their sum or differenceEx. 8 x (20+3) = 8 x 20 + 8 x 3Identity Element of Addition - If you add zero to any number, you get the original numberEx. 5 + 0 = 5Identity Element of Multiplication - If you multiply 1 to any number, you get the original numberEx. 6 x 1 = 6Zero Property - If you multiply zero to any number, you get zeroEx. 10 x 0 = 0

Decimals Notes : Steps for Adding Decimals:(1) Line up the decimals vertically(2) Fill in the zero (placeholders) to the right as needed(3) Add from right to left(4) Bring down the decimalEx. 1 : 8.266 + 1.540= 9.806Steps for Subtracting Decimals:(1) Line up the decimals vertically(2) Fill in the zero (placeholders) to the right as needed(3) Subtract from right to left(4) Bring down the decimalEx. 2 : 28.830 - 4.229 = 24.601

Multiplying/Dividing Decimals Notes : Steps for Multiplying Decimals:(1) Take decimal out(2) Count how many digits are to the right of the decimal(3) Place decimal back into answerEx. 1 : 1.3 x 0.513 x 5 = 65two digits behind the decimalAnswer = 0.65 Dividing Decimals:Can use traditional or partial quotient method of divisionconvert outside number to a whole numberhowever many places you move the outside number, do the same to the inside numberEx. 2 : 1.518 divided by 0.60.6 = 61.518 = 15.1815.18 / 6Answer = 2.53

Intro to Fraction Skills Notes : Fractions are PART of a wholeNumerator = # on the topDenominator = # on the bottomDenominator represents the WholeNumerator represents the PARTSUnit Fraction = numerator is oneBenchmark Fraction = regularly used fractions (1/4, 1/2, 3/4, 1/3)

Adding Fractions : With Like Denominators:Denominator stays the same all the way acrossEx. 1/4 + 2/4 = 3/4Ex. 3/6 + 2/6 = 5/6With Different Denominators:Convert the fractions into fractions that have a common denominatorEx. 3/4 + 4/63/4 = 9/124/6 = 8/129/12 + 8/12 = 17/12 = 1 5/12Fractions in a Mixed Number (with common denominator):Add the whole numbers first and then the fractions3 5/9 + 1 3/9 = 4 8/9Fractions in a Mixed Number (without a common denominator)Change the fractions to have a common denominator. Then, add the whole numbers and the fractions after.Ex. 5 1/6 + 3 1/81/6 = 4/241/8 = 3/245 + 3 = 84/24 + 3/24 = 7/24Answer = 8 7/24

Division Strategies :Array = representing multiplication/division using rows and columnsEqual Groups = Putting objects/things in groups where each group has the same amountNumber Line = Plotting the multiples of the divisor starting from 0 up to the dividendRepeated Subtraction = Subtracting the same number from a large number until the end result is zeroStrip Diagram = A visual rectangular model cut into "strips" to solve the division problem.Fact Family = A set of 4 related multiplication and division facts that use the same 3 numbers

Partial Quotients (BIG 7) : (1) Write easy facts for the divisor (ex. 3x1 = 3, 3x8 = 24, 3x11 = 33, 3x30 = 90, 3x50 = 150, 3x100 = 300(2) Subtract an easy multiple of the divisor from the dividend(3) Repeat the subtraction until the number is less than the divisor (4) Add the multipliers (right side) of the divisor

Division Practice HW Problems :*these are only a few problems from the homeworkEx. 1 : Show 24 divided by 6 as repeated subtraction.Answer : 424 - 6 = 1818 - 6 = 1212 - 6 = 66 - 6 = 0 Ex. 2 : Write the fact families (4 equations) to show 32 divided by 4.Answer : 4 x 8 = 328 x 4 = 3232/4 = 832/8 = 4Ex. 3 : Jada had 24 cookies. She gave 5 cookies to each friend. How many friends did she give cookies to?Answer : Jada gave 4 friends cookies. Since she gave each friend an equal amount, the greatest amount of friends she could have given cookies to is 4. For this problem, you simply ignore the remainder.

Factors and Factors and MultiplesF x F = MEx. 1 : Find all the factors of 12Answer : 1, 2, 3, 4, 6, 1240 = composite numberEx. 2 : Find the factors of 40Answer : 1, 2, 4, 5, 8, 10, 20, 40Ex. 3 : Find the factors of 7Answer : 1, 77 = prime numberEx. 4 : Find all the factors of 45Answer : 1, 3, 5, 9, 15, 45

Prime factorization : getting a number only down to its prime numbersEx. 1 : Prime factorization of 12Answer : 2 x 2 x 3Ex. 2 : Prime factorization of 18Answer : 2 x 3 x 3Ex. 3 : Prime factorization of 48Answer : 3 x 2 x 2 x 2 x 2Ex. 4 : Prime factorization of 60Answer : 5 x 2 x 3 x 2

Divisibility Rules : A number is divisible by 2 : if the last digit is 0, 2, 4, 6, or 8.3 : if the sum of the digits is divisible by 3.4 : if the last two digits is a number divisible by 4.5 : if the last digit is 5 or 0.6 : if the number is divisible by 2 and 3.9 : if the sum of all the digits is divisible by 910 : if the number ends in 0.