Adding and subtracting simple fractions,

 In this lesson, we're going to learn adding and subtracting simple fractions.
Adding and subtracting fraction is using 2 operations ( addition and subtraction) in fraction.
If the denominators are equal, we can just add or subtract the numerator, but if the denominators are different, we have to find the LCM (lowest common multiple), or use the equivalent fraction to make the other fraction's denominator to make common denominator.

 First example is 5/8 + 2/8.
Now if we look carefully, the denominators are equal. So the numerator can be added, 5 + 2 = 7.
Therefore the answer is 7/8.

  Second example is 8/9 - 6/9.
Same the denominators are same so we just subtract the numerator, 8 - 6 = 2.
Therefore our answer is 2/9.

  Third example is 5/6 + 4/12.
If we see it very carefully, the denominators aren't same, so we find the relationship between 6 and 12 and is times 2. Then 5/6 becomes 10/12 and 10/12 + 4/12 equals 14/12.

14/12 equals 7/6. 7/6 is 1⅙. Therefore the answer is 1⅙.

Forth example is 3/7 - 3/21.
same as the previous example, the denominators are different. The difference between 7 and 21 is times by 3 so 3/7 equals 9/21.
  9/21 - 3/21 = 6/21.
Then we simplify 6/21 and our answer is 2/7.


Fifth example is 2- 1/2
Now we need to subtract the fraction by whole number.
Therefore a whole number in fraction equals denominator by denominator, the denominator is 2 therefore is 2/2.
1 + 2/2 - 1/2 = 1.5 or 1 1/2.
Therefore our answer is  1 1/2.

Sixth and last example is 2 ⅛ + 3⅕. 

Now there are 2 steps to do this. First is add or subtract the whole number, then add or subtract the fractions. 

 2 + 3 =5 

⅛ + ⅕ = 13/40.
Therefore the answer is 5 13/40.



* if you finish your working out, don't forget to simplify.

Mixed Fractions to improper fractions.

  In this lesson, we're going to learn about mixed fraction into improper fraction, also we're going to learn changing the improper fraction into mixed fraction.

  Mixed fraction is like this, there's a whole number right next to the fraction.

  e.g: 3 ⅓.

 An improper fraction is the numerator is bigger than the denominator. 

 e.g: 8/4.

 When you have to change the mixed fraction into the improper fraction:

1) Multiply the whole number with denominator.

2) Add the numerator with the answer which you got from the 1).

3) Now place the answer over the denominator of the fraction part.

Our first example is change 4⅔ to an improper fraction.

1)  Multiply 4 and 3 together then add 2.

2) place this total above the denominator of 3.

 When you're changing the improper fraction to mixed fraction: 

1) Divide the numerator by the denominator to find the whole number part. 

2) Write the remainder over the denominator.

For example change 23/3 to a mixed fraction.

Divide the numerator 23 by 3 to find the whole number 7 and the remainder 2. 

Therefore, 23/3 = 7⅔.

Comparing fractions

 In this lesson, we're going to learn about comparing fractions. Comparing fractions are to find out which one is larger or smaller, depends on the fraction. Also it's easy to compare when the denominator is same.

  Our first example is 5/10 and 8/10.
 Now the denominator is same so we have to see the numerator. Now the denominator is same, so we have to compare the numerator. Therefore, 8 is more bigger than 5 so 8/10 is bigger.

  The second example is 4/5 and 5/10.
  Now the denominator is different so we have to make the denominator same. 5 multiplied by 2 equals 10 so the difference between 5 and 10 is 5 so times by 2. Therefore is 8/10. 8 is bigger than 5, then our answer is 4/5 is bigger than 5/10.

  Third and last example is place the following fractions in order from the ascending order.
3/4, 1/2, 5/8.
Now each denominator needs to be 8 to compare easily, so 3/4 = 6/8, 1/2 = 4/8, 5/8 = 5/8.
Therefore the answer is  1/2, 5/8, 3/4.

* Another one is if the question says descending order, it means biggest to smallest.

Simplifying fraction

 Last lesson we learned about equivalent fractions. Also I told you a bit of the simplifying fractions. This is the one that we're going learn today. Simplifying fraction is also know as canceling down or reducing the fraction. Another one is the denominator and numerator must be divided by the same number. 

  Our first example is 8/10.
4 x 2/5 x 2, we divide them by 2 and the answer is 4/5.

  Second example is 45/75.
This time there are few numbers to divide but the answer is same, but we'll do in a easy way. 15 x 3 = 45, 15 x 5 = 75. we divide 45 and 75 using 15. Then our answer is 3/5.

  Third and last example is 50/100. Now 50 is half of 100 so in common sense, 50/100 would be 1/2.



*When you have several numbers that can be divide, and the quotient is whole number, find the common number that can be divide the denominator and numerator equally. I don't mean like the answer should be same, I'm talking about the dividing number should be the same.

Equivalent fractions

In this lesson, we're going to learn about the equivalent fraction. Equivalent fraction is like this. The whole numbers on denominator and numerator is different but it must be acquired to multiply or divide by the same number.

 For example, 1/2 = 5/10 = 25/50.
They are equal or equivalent fractions even they have the different numerators and denominators.

  Our first example is 3/7 = x/35.
The denominator 7 got timed by 5 to get 35,
so we times 5 to 3 and we have 15. Therefore is 15/35.

 Second example is 40/80 = x/8.
Now this time, we have to find the x by using denomination. 80 became 8 because it is divided by 10.
So we divide 40 by 10 and we got 4 and lastly 4/8 can be divide into 4 so our final answer is 1/2.

 Our third and last example is 19/20 = x/100.
The working out is same as the working out in e.g.1. We find the relations between 20 and 100, and is 5 and we times 5 with 19 and we have 95 therefore our answer is 95/100.


* equivalent means equal amount value, weight, meaning, etc.

Fractions

 It would be easier and feels incredible when the measuring numbers are only in whole numbers like 1,2 and 3. The measuring number that we uses sometimes, we use the part of the whole number, we call fractions.

 In fraction the top part is called the numerator and bottom part is called the denominator.
For example, there are 10 box and 5 of them are colored and we do it like this.
we write like this. 5 is the numerator and 10 is the denominator.
Also don't forget to simplify. 

Second example. There are 100 equal squares and 45 of em are shaded.
We write like this 45 is the numerator and 100 is the denominator.


* When you're simplifying the fraction, see the whole numbers that can be divide into the same number.
For example, 5/15. Now 5 can be divided into 5 so 5 divided 5 is 1 and 15 divided by 5 is 3 therefore or i.e. 1/3.

The binary number system

Previously we we learned about place value. The one that made me interesting was each place value was increasing by the power of 10.


  For example, 456015 = (4 x 10 ⁵) + (5 x 10 ⁴) + (6 x 10^3) + (0 x 10^2) + (1 x 10^1) + ( 5 x 1)
                                    = 400000 + 50000 + 6000 + 0 + 10 + 5