Web 2.0 Project

Semester 2

Divisibility Rules

Divisibility Rules

2- The last digit is even. (0, 2, 4, 6, 8)

3- The sum of the digits is divisible by three.

4- The last two numbers are divisible by four.

5- The last digit is 0 or 5.

6- The number is divisible by both 2 and 3.

7- If you double the last number. Then subtract that from the rest of the remaining number. Divide by 7 and if the number doesn't have decimals then it's divisible my 7.

8- The last three digits are divisible by three.

9- The sum of the numbers is divisible by 9.

10- The number ends in 0.

11- If you add every second number. Then add the remaining numbers together. Take the second set of numbers and subtract that from the first set. If the answer is 0 or 11 it can be divided by 11. EX-3729 ((7+9) - (3+2) = 11 YES

12- The number is divisible ny both 3 and 4.

http://www.mathsisfun.com/divisibility-rules.html

Factorization

Prime Numbers- A number that can only be divided by 1 and itself.

Composite Numbers- A number that can be divided by other numbers besides 1 and itself.

How to Factorize...

1) Factor Trees- Factor trees begin with one number. In this case 42, since 42 is even you can split it in half. Half of 42 is 21. You take 42 and write it below it draw an arrow pointing towards 42. On either side of that arrow put 2 and 21. Next you take 21 and figure out what it can be divided by. It's 3 and 7. Repeat this process until all of the bottom numbers are prime.

42

^

2 21

^ ^

1 2 3 7

2) Another way is to make a list like below. You take 1 and 42 first. Then think of other numbers that multiply to equal 42.

1, 2, 3, 7, 21, 42

Adding, Subtracting, Multiplying, and Dividing Fractions

ADDING

-When adding fractions you need to have common denominators. To get a common denominator you multiply both the numerator and denominator to match the other fraction. In some cases you will need to multiply both fraction to find common factors.

-To add a fraction you add to top normally but the bottom will always stay the same. After you've added the numbers you might be able to simplify depending on your answer.

-Lastly if your numerator becomes a higher number than the denominator you have two options. The first on you can leave it as an improper fraction. The second option is to make it a mixed number.

SUBTRACTING

-Subtracting fractions is the exactly the same as adding them except your subtracting not adding

MULTIPLYING

-When multiplying fractions you denominators do NOT have to be the same.

-The multiplication is straight across. You multiply the numerators, then the denominators.

-Once you've multiplied if you can simplify the number feel free to. The other option is to turn your fraction into a mixed number if the numerator is bigger than the denominator.

DIVIDING

-Dividing fractions is the same as multiplying fractions except dividing. You will still do your operation straight across.

Rational and Irrational Numbers

Rational Numbers- integer, whole numbers, ratio, it either ends or it repeats (4, 6/10, .3, 2/11)

Irrational Numbers- a number that never repeats (3.14 (pi), any number that doesn't repeat)


Square Roots

Finding Square Roots...

-To find a square root you can use a calculator if you have one, or you multiply the two numbers together (9 * 9) to get a square root

-Perfect Squares: are when two of the same whole numbers are multiplied (9 * 9 = 81)

-Not all numbers have perfect squares some will be irrational


1=1 * 1

4=2 * 2

9=3 * 3

16=4 * 4

25=5 * 5

36=6 * 6

49=7 * 7

64=8 * 8

81=9 * 9

100=10 * 10

121=11 * 11

144=12 * 12

169=13 * 13

196=14 * 14

225=15 * 15

http://www.mathwarehouse.com/arithmetic/numbers/list-of-perfect-squares.php


March 14

Happy Pi Day!!!

3.14

Multiplying and Dividing Fractions in Word Problems

Example: At Pia's Restaurant, 1/4 of the dished on the menu are vegetarian. Of the vegetarian dished, 1/2 are pasts dished. What fraction of the dishes on the menu are vegetarian pasta dishes?


Click this link for a Great Video on Multiplying and Dividing Fractions in Word Problems!!

https://www.khanacademy.org/math/arithmetic/fractions/multiplying_and_dividing_frac/v/multiplying-fractions-word-problem

Fraction Recipe Project

Dimensional Analysis

Example Questions

1.) How many miles will a person run during a 10 kilometer race?

2.) The moon is 250,000 miles away. How many feet is it from earth?

3.) A family pool holds 10,000 gallons of water. How many cubic meters is this?

4.) The average American student is in class 330 minutes/day. How many hours/day is this?

How many seconds is this?

5) How many seconds are there in 1 year?

https://static.squarespace.com/static/500b33e2e4b0d820d6a28cc3/t/516e1631e4b0be930df46694/1366169137639/Homework-Dimensional%20Analysis.pdf

Converting Percents to Decimals

To convert Percents to Decimals you take the percent and put it over 100. (90/100) So if you had 34% you would put it over 100 like this 34/100. Then you could simplify it.

Pythagorean Theorem

( a * a ) + ( b * b ) = ( c * c )

Scale Factor Drawings

For the Scale Factor Drawings we took an image then dilated them to be bigger. We ended up with much bigger drawings. To make this easier we would look at one square then draw just what we saw in that square. Once we finished all of the squares we connected the lines and made it look smoother.