Math 9 Notes. Grade 6 8 Review. Multiplication and Division: Slide show and Table. M9 Intro Notes 2017.notebook. June 12, 2017.

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1 Math 9 Notes Grade 6 8 Review Sep 11:32 AM Multiplication and Division: Slide show and Table Sep 11:34 AM 1

2 Long Division 11 Sept Sep 11:34 AM Find the first number that 6 divides into Divide 6 into 41 Multiply 6 x 6 and put the answer below the 41 Subtract Sep 11:43 AM 2

3 Drop the next number down Divide 54 by 6 Multiply 9 x 6 and put the answer below the 54 Sep 27:59 AM Subtract Sep 27:02 AM 3

4 Sep 14:12 AM Integers Ugg the Caveman story Natural Numbers 1, 2, 3,... Whole Numbers 0, 1, 2, 3,... Real Numbers...,,,, 0, 1, 2, 3,... and all the fractions, and terminating/repeating decimals in between ex. 0.5,.79 and all the irrational numbers ex. π, 2 Integers...,,,, 0, 1, 2, 3,... Rational Numbers...,,,, 0, 1, 2, 3,... and all the fractions, and terminating/repeating decimals in between ex. 0.5,.79, ½, ¾ Sep 15:31 AM 4

5 Ordering and Comparing Integers 15 Sept Negative #s are smaller than positive #s > The "bigger" a negative number looks, the smaller it is. Sep 15:33 AM Sep 27:06 AM 5

6 Adding Integers You are used to adding some types of integers already: ex Notice that you are going the number line? ex Sep 15:21 PM You try *Hint: Start at the first number and move to the right the amount of the second number Sep 15:34 PM 6

7 Commutative Property of Addition The order of numbers in an addition question doesn't matter because: a + b = b + a ex = = = 7 Sep 16:25 AM Adding a negative number Remember, winking men are all bad. ex. 8 + ( 4) Doesn't it look like a winking man? A negative and a positive directly beside each other on the other side of a bracket (or with no bracket), are always negative. so 8 + ( 4) is the same thing as 8 4 Try ( 2) Sep 15:23 PM 7

8 You try ( 4) *Hint: Start at the first number and move to the left the amount of the second number ( 3) ( 1) Sep 15:10 PM Subtracting Integers You are used to subtracting some integers already: ex. 5 3 Notice that you are going the number line? ex. 5 (+ 3) Winking men are always bad!!! Sep 15:30 PM 8

9 You try (+ 4) 2. 2 (+ 3) 3. 8 (+ 1) Sep 15:06 PM Subtracting a negative number Remember, kill the sleeping man. Not literally. It's a metaphor. A math metaphor. ex. 8 ( 4) Doesn't it look like a sleeping man? A negative and another negative directly beside each other on the other side of a bracket (or with no bracket), are always positive. so 8 ( 4) is the same thing as Try... 9 ( 2) Sep 15:07 PM 9

10 You try ( 4) 2. 2 ( 3) 3. 8 ( 1) Sep 15:14 PM The two math metaphors we are using (winking men are always bad and kill the sleeping man) are based on multiplication laws. Any number directly beside another number indicates multiplication. ex. mn means m x n When we are adding integers, (+3) means ( 1)(+3). The 1 is just not written. This brings us to multiplication! Sep 15:20 PM 10

11 Multiplying Integers Often considered "easier" than addition and subtraction of integers. Use the Superhero Blind Date Rule! > 2 superheroes go on a date = + experience > 2 villains go on a date = + experience > 1 superhero and 1 supervillain = very experience ex. 3 x 5 ex. ( 3) x 5 ex. ( 3) x ( 5) ex. 3 x ( 5) Sep 17:57 AM Practice Questions Sep 29:39 AM 11

12 Dividing Integers Often considered "easier" than addition and subtraction of integers. Also uses the Superhero Blind Date Rule! > + x + = + > x = + > + x = > x + = ex ex. ( 15) 5 ex. ( 15) ( 5) ex. 15 ( 5) Sep 17:03 AM Practice Questions Sep 29:39 AM 12

13 Cheat Sheet Remember, winking men are all bad. ex. 8 + ( 4) Remember, kill the sleeping man. Not literally. It's a metaphor. A math metaphor. ex. 8 ( 4) Also uses the Superhero Blind Date Rule! + x + = + x = + + x = x + = Sep 29:39 AM Order of Operations Why do we use it? to mathematical notation Who can we curse as the inventor of it?. It just sort of evolved after we started using Hindu Arabic Numerals. Aaaand, it continues to evolve. When was it developed? Around the Oct 7:26 PM 13

14 Other Math History Facts: Hindu Arabic Numerals were developed around the 800s AD in India > Came to Europe (landed in Spain first) after going through the Middle East and North Africa > The Italian mathematician, Fibonnaci, made them famous in Europe in the 1200s AD He picked them up while studying in Spain Operational symbols developed later: +in the 1400s in the 1500s in the 1600s in the 1600s Oct 7:46 PM How it helps shorten mathematical notation: ex. 2x 2 + 3x + 4 would need to be written out like this: (2(x 2 )) + (3x) + 4, if we followed a left to right technique. Khan Academy Video (Introduction to Order of Operations video) Oct 7:40 PM 14

15 BEDMAS Steps Oct 8:06 AM ex x 2 ex x * You must start working DOWN the page. These questions should resemble upsidedown triangles. Oct 8:20 AM 15

16 ex. [() x () + 1] () 4 Oct 8:28 AM Studying for Math Tests I CAN study for a math test. Use your. 1. Find examples. 2. Copy the questions on piece of paper. 3. Try the question looking at your notes. 4. to see if you are right! 5. If you're right, move on to the question. 6. If not, find your, it, and then try. 7. If you don't understand what went wrong, even after checking for your error, then look over the in your notes, ask a who is confident about the topic, or the teacher. Sep 21:27 PM 16