Division with Decimals

To master division with decimals, you have to become very familiar with exponents and place values. The equation of a decimal being divided is the decimal being divided by the power of ten. Depending on the exponent is how many times you move the decimal place to the left to get your answer.
Example: 5.06 divided by 10 ^ 4 = .000506
No matter if the exponent is negative of positive the decimal still moves to the left.

9's TRICK:
If any number is over 9, 99, 999, 9999, etc. that number will be repeated in the decimal form. It just depends on the place value of the 9.
1/9 = 0.11111111....
8/9 = 0.8888888...
* The pattern changes when the place value of 9 changes:
7/99 = 0.0707070707...
        - the 0 represents the missing tens place value in the number 7
37/99 = 0.3737373737.....
        - Notice how the 0 was replaced but a 3, because 37 has a number in the tens place.
* The pattern changes once again when the place value of 9 gets larger:
49/999 = 0.049049049049...
       -Once again the 0 is representing how the number 49 does not have a number in the hundreds place
749/999 = 0.749749749749...
       - The 0 was replaced with 7 because that us the number in the hundreds place.

***The reason why this numbers constantly repeat is because the number .999999 is actually equal to 1.

Converting Decimals to Fractions:
Method #1:
0.27777....
= 0.2 + 0.7777...              ( separate the lonely number from the repeating number)
= 2/10 + 0.777...   
= 2/10 + 0.777... / 10
= 2/10 + 7/9 * 1/10         (just found out any repeating number is over a 9 number)
= 2/10 + 7/90
= 18/90 + 7/90                (common denominator multiply 2/10 by 9)
= 25/90

Method #2:
0.4191919...
10n = 4.191919...
100n = 41.91919...
1000n = 419.191919...
* you want to get two answers that have the same repeating decimal. (in this case 10n and 1000n do)
1000      =     419.191919...
- 100      =         4.191919...
   990             415
The answer then comes to 415/990

Fractions

When learning how to use fractions there is one thing you must know from the beginning. That is that the top number (a) is called the numerator, and the bottom number (b) is called the denominator. The denominator can NOT be zero. There are a few different ways to look at a fraction:
1. Part-to-Whole, which is when the numerator equally goes into the denominator and the fraction is just representing a part to the whole unit.
2. Division Concept, which is just converting the fraction into a division problem. For example, 1/4 now becomes 1 divided by 4.

3. Ratio Concept, which is when you compare one amount to another.
I had also learned the Fundamental Law of Fractions: let a/b be a fraction. Then for any number k can NOT equal 0. (a/b = ka/kb) Also, Equivilent Fractions can be formed by multiplying or dividing the numerator and denominator by a number.
You can find the answer to the addition of two fractions by adding the top two numbers across and the two bottom numbers across leaving you with a fraction answer still.

Intergers

 Today in class we went over Integers, and different ways to understand them or solving simple math equations. When using Integers i learned you use a debt (-) for a negative number, and a credit (+) for a positive number. First, we practiced multiplication, and how to set up a array with the equation. For example, we used 5 x -3 so we made five columns and 3 rows of debts. This can also be said as 5 debts of size 3. After we mastered that we covered division. There are a few different ways of showing division by using debts and credits. One way is the sharing method, this is used when the divisor is positive and the dividend is negative. The other method is measurement, this is used when the divisor and dividend are both negative. When solving a multiplication or division problem, there are a few key tricks to understand.



Integers are a very fun thing to learn I believe, and I really enjoyed learning new and different methods to solving multiplication and division problems using debts and credits. There were a few more methods we went over to help us understand. I learned the number line model when dealing with temperature vs. time. That is simply just creating a number line and depending on your equation and moving up or down the number ling till you reach your correct answer. For example, The temperature is now 0 degrees, the temperature goes down 4 degrees every 3 hours, what is the temperature in 6 hours. (You would start at 0, and go down by five 6 times, leaving your answer to be -30 degrees)


Start Practicing Now:
practicing multiplication with Intergers