Elementary Mathematics

What I show you in the link I have provided is blocks consisting of units, longs, flats, and blocks, representing 1's, 10's,100,1000's.1 unit--> 100 = 1 unit1 long-->101 = 10 units1 flat-->102= 10 longs, or 100 units1 block--> 103= 10 flats, or 100 longs, or 1000 unitshttps://www.youtube.com/watch?v=Ll14bQFGYkk

Problem: How do you write and solve 259 + 354 in Expanded Form? Answer: First you put your place values in. You start with Right to Left. 9 and 4 are both ones. 50 and 50 are both in the tenths place. 200 and 300 are both in the hundredths place. Now you start writing your problem, Putting the Biggest Place Value to Smallest like so: 200 + 40 + 3300 + 20 + 5=500 + 60 + 8 Add the tenths places together (50 and 60) = 560 + 8 Add the ones places together. (0 and 8) Answer = 568 * If still having trouble please go to this hyperlink I have provided for you: https://www.youtube.com/watch?v=4AF7xj7pmWc

Alternative Algorithm  * Left to Right Addition Problem: 342 + 126 First rewrite the problem.  342 + 126Remember define your place values out FIRST before solving. Left Side first. Hundredths place is 300 and 100. Tenths place is 40 + 20.Ones place is 2 + 6Here is how it looks written out:   300 + 40 + 2 Add the hundredths together, the tenths together and the ones together to get”  100 + 20 + 6= 400 + 60 + 8 Add the tenths places together (0 and 60)= 460 + 8    Add the ones together ( 0 + 8) Answer: 468 

*Properties of Multiplication and Addition Distributive Property: 6(5+3)Commutative Property: 3+4 = 4+3Associative Property: 3+(5+9)=(3+5)+9Identity Property for Multiplication and Addition: 5*1 and 5+0* Difference ways to understand and learn the different properties are listed:Distributive Property: You are simply distributing the 6 to the number inside the ()s. This property is very unique and easiest to spot out of all the 4 properties.Commutative Property: Noticed how I underlined mu in the word which stands for- mix up (order).Associative Property: Noticed how I underlined so in the word which stands for- same order.Identity Property for Multiplication and Addition: I underlined the word identity because who you are is who you are or in math language, doing something that does not change the value. 5+0 will always equal the other number being added to 0. Anything times 1 will always equal the number being timed by 1.*If still having trouble please click on this link that also explains the Addition and Multiplication Properties and each rule. https://www.youtube.com/watch?v=QrzF5lDGT9Q

Integers using addition, subtraction, multiplication, and division.Example for Addition:4 + 2 =6This problem is saying 4 positives adding two more positives like shown below.++++ ++ = 7Example for Subtraction:4+(-6) = -2Negatives always go under positives. ( just like thermometers, a number line, ect.) always the SAME! Zero banks- +- means they cancel one another out and become zero. Zero Bank looks like this:https://www.youtube.com/watch?v=sGVF-KfQMfA+/- +/- +/-ALWAYS GO LINEARLY also like so: + + + + + +Example for multiplication:(4) x (2) = 84 positives times 2 positives = 8 positives++++ ++++ or you could even do four groups of 2++ ++ ++ ++Division has not been done yet. Till next time(:Here is a couple of links for how to solve problems with integers for more help!https://www.youtube.com/watch?v=FsKNeU7EFl0https://www.youtube.com/watch?v=hGVm2xs0HEA

*Divisibility Rules for numbers 1 through 10. Rule for 1: Any number will be divisible by 1, therefore 1 will always be a factor of any number.Rule for 2: If the number is even it will always be divisible by 2.Example: 44444 is divisible by 2, but 44445 is not.* Special Note: The number in the one's place will define if the number is odd or even.Rule for 3: If the number in the one's place is odd, then that number is divisible by 3. Therefore, 3 is a factor any odd number.Example: Take the number 44445. 4+4+4+4+5 = 21. The number 21 is divisible by 3.Rule for 4: If the tenth's and one's place are divisible by 4, then the whole number is.Example: Take the number 44444. The last two digits are 44, and 44 is divisible by 4Rule for 5: If the number ends in a 5 or 0, it is divisible by 5.Example: 44445 would be divisible by 5 because its last digit is a 5Rule for 6: If the number is divisible by 2 and 3, then it is also divisible by 6.Example: To find out if a number is divisible by 6, check to see if it is divisible by both 2 and 3 (because 2 x 3 = 6)Rule for 7: DOES NOT HAVE ONE! Rule for 8: If the one's, tenth's, and hundredth's place are divisible by 8, then the whole number is.Example: 57136, 136/8 is 17, therefore 8 is divisible by the whole number 57136. Rule for 9: When adding the digits of numbers, if equals 9 then 9 is a factor of that number.Example: 27, 2+7=9, therefore 9 is divisible by 27. Rule for 10: If the number ends in 0, it is divisible by 10.Example: 44450, since it ends in 0 it would be divisible by 10. *For more help on better understanding Divisibility Rules click on this link below:https://www.youtube.com/watch?v=RIRRJ88rASE

* Adding Integers Note: To show if numbers are less than 10, draw it out. If the numbers are 10 or more then draw diagrams. For example adding integers with numbers that are less then 10 you would do this:-4+ (5)You would first show your negatives which are 4 negatives then add 5 positives on top of the negatives which will give you a zero bank and leave you with only one positive. 2nd example of adding integers with numbers that are more then or equal to 10 is shown below. 40 + -20 Which pile is bigger?The 40 is.... so that will have two positives over its head and -20 will have one negative over its head. Then since you circled a pair you will be subtracting 40 - 20. Which will give you 20 and then you put in your correct sign that is left over and that would give you + 20. * Subtracting Integers Example 1.) Subtracting Integers that have numbers that are less than 10. Keep Change Change... Meaning keep the first number change the second sign and third sign of the third number. Which looks like this Before the KCC: 6 - (-4)After the KCC: 6 + (+4) then you proceed to solving the problem.... ++++++ ++++ = 10 positives Example 2.) Subtracting Integers that have numbers that are greater or equal to 10. KCC Before KCC: -60 - (-32)After KCC: -60 + (+32)Which pile is bigger?-60 is so that will have two negatives above the number, and +32 will only have one positive over above its number. We know that we have to pick one sign from each number which will be one negative and one positive. We will then subtract -60 -32 which will give us. - 92 If still confused look up this link on youtube: https://www.youtube.com/watch?v=_BgblvF90UE

Multiplying a fraction and a whole number together:Example:Make 5 into 5 over 1 or 5/1 :2/3 × 5/1Now just go ahead as normal.Multiply tops and bottoms:2/3 × 5/1 = 2 × 5/3 × 1 = 10/3The fraction is already as simple as it can be.Answer = 10/3Example: Multiplying a whole number and a fraction together, which is a whole different process.Multiply tops and bottoms:3/1  × 2/9 = 3 × 2/9 = 6/9Simplify:6/9 = 2/3

The way we read is the way same way we solve problems. We read from left to right. Than we start by adding the biggest value first whether it be the tenths place or the hundredths place, however big of the number your solving. For example: ALWAYS start from LEFT to RIGHT. So that means you would start with the tenths place first. Which is 20+20- lighter purple = 40 Then the ones place next which is 2+5- darker purple = 7 22+25= 40 + 7 =47 If you still are having trouble understanding even after looking at my example above, HERE is another link that is more detailed and will hopefully help you to better understand this topic. https://www.youtube.com/watch?v=mAvuom42NyY

Equal Value Method:Problem: 24-18 *Special Note: Keep differences between the two numbers the same. Shown Example: I am going to add 2 to the 18 to make 20, which means I need to make sure that I KEEP the same DIFFERENCE with the other number I am taking away from. Now are new problem is: 26-20 Now SOLVE: 26-20 It is a lot easier to solve, than the problem given to us before. If still having trouble please go to this link with a new problem for you to work with to better understand this method.

*Integers Example problem: Build -2 using 8 tiles YOU HAVE A positive square on top of the negative square three times. Then, you have two more negative squares that would = -2.If still having trouble please go to this link that I have provided for further explanation: https://www.youtube.com/watch?v=u69pYSdwugo

Estimating by Rounding and Front-end (hard to show lattice on here). *Example Problem with estimating with Rounding: 34 + 74 Always round up when the ones place is 5 or more. For example: 35... we would round up to 40.... If it were 34 in this case it is... we would round down to 30. Now with knowing that we will look at the ones place. The numbers are both below 5... so we will round both numbers down... like this: 30 + 70 Which equals are estimated answer: 100 *Example Estimate Problem using Front-end: 45 + 74We only look at the tenths place this time, or whatever the front number is, but in this case it is the tenths place. 40 + 70 = 110 *Special Note: If still having trouble solving here is a link to a youtube video to provide you with more example problems: https://www.youtube.com/watch?v=6y4cM43J6-U

*Least Common MultipleList the Multiples of each number,The multiples of 3 are 3, 6, 9, 12, 15, 18, ... etcThe multiples of 5 are 5, 10, 15, 20, 25, ... etcFind the first Common (same) value:The Least Common Multiple of 3 and 5 is 15( 15 is a common multiple of 3 and 5, and is the smallest, or least, common multiple )Youtube Link for more help on learning how to find the LCM: https://www.youtube.com/watch?v=JzDq34ObMHg

Greatest Common Factor of 12 and 16Find all the Factors of each number,Circle the Common factors,Choose the Greatest of thoseYoutube link for more help on finding the GCF: https://www.youtube.com/watch?v=uE9O8N5JYB4

Adding, Subtracting, and Multiplying Fractions Adding Fractions Example: 14 + 14 Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.Step 2. Add the top numbers and put the answer over the same denominator:14 + 14 = 1 + 14 = 24Step 3. Simplify the fraction:24 = 12In picture form it looks like this:14+14=24=12   ... and do you see how 24 is simpler as 12 ? (see Equivalent Fractions.)Subtracting Fractions Example: 12 − 16Step 1. The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we can't subtract them like this:12−16=?   To make the bottom numbers the same, multiply the top and bottom of the first fraction (1/2) by 3 like this:× 312 = 36× 3And now our question looks like this:36−16 The bottom numbers (the denominators) are the same, so we can go to step 2. Step 2. Subtract the top numbers and put the answer over the same denominator:36 − 16 = 3 − 16 = 26In picture form it looks like this:36−16=26  Step 3. Simplify the fraction:26 = 13Multiplying Fractions Example: For more help click this youtube link: https://video.search.yahoo.com/yhs/search?fr=yhs-Lkry-SF01&hsimp=yhs-SF01&hspart=Lkry&p=show+how+to+add%2C+subtract%2C+and+subtract+fractions+together#id=1&vid=4b9ee1fd24ad6c384f45160151a7a2cb&action=view

Always Simplify First when multiplying fractionsExample: 1/2 x 2/5= You can make a one for 2 and 2 since they are across from each other. But that is the only one we can do. Then add across which will give you the answer of 1/5. For more help check out this youtube link: https://youtu.be/pbOtDWiydTo