Changing one quantity as a fraction of another amount

In this lesson, we're going learn rates in fraction. Rates in fraction is like this, finding a part in the whole part.
Also each fractions needs to be expressed in the same units and it needs to be tat the smaller part goes the above.

  First example is "What fraction is 30 minutes in 2 hours?"
Now we need to make the unit same so 1 hour equals 60 minutes, 2 hours equals 120 minutes.
Therefore 30 minutes/120 minutes equals 1/4.
This cancels down to 1/4.

Second example is "What example is 40 cents of $5?"
In this example 1 dollar is 100 cent,m so$5 is 500 cent.
Therefore, 40/500 equals 2/25.

  Third and last example is "What fraction is 24cm of 1m?"
Same as the other examples, we need to make the units same so 1m equals to 100cm,
so 24/100 equals to 6/25.

Finding a fraction of amount.

 In this lesson we're going to learn find an amount when multiplying the fraction. On  few of the previous lesson, we had a calculation like this fraction times by the whole number. So we're going to learn further this time on this.

 Now for example if the whole number is the quantity and the fraction is the amount that we need to find from the total amount we just multiply it.

The example 1 is "Find 5/6 of 85 ipods."
Now we do it like I showed you on previous lessons. In fraction any whole number is whole number over 1, so 85 is 85/1 in fraction, and the working out is 5 x 85 = 425 and 6 x 1 = 6.
Therefore the answer is 425/6, and if we simplify it, is 70.83333333... and we're going to round it off to the nearest rounds and is 71 ipods.

  Second example is "Find 8/9 of $72."
We do the same as the previous example.72 is 72/1 and 72 x 8 = 576 and 9 x 1 = 9.
Therefore 576/9 is 64, therefore is $64.

  Third and last example is "Find 8/40 of 100 Meters."
So as the last one, we do the same thing.
First is 100 is 100/1,
second is 8 x 100 = 800, 40 x 1 = 40.
Therefore our answer is 800/40 and if we simplify, the exact answer is 20, therefore is 20 meters.

* If you finished your calculation and doing the next question, double check later.
Reason is most of the questions have metric systems such as kilometers, meters, centimeters, etc.
Don't forget to write them!

Dividing fractions

In this lesson, we're going learn dividing fractions. Dividing fraction is bit difficult to understand in the starter but if you find the way to solve it, it will be easy.

 Now if you're dividing fractions, leave the first and make the second fraction a reciprocal, a reciprocal is flipping over, for example 3/4, if we do reciprocal, 3/4 turns into 4/3.

Example 1 is 6/8/ 4/5.
Now, we leave 6/8 and make 4/5, 5/4.
Then the working out is 6/8 x 5/4, 6 x 5 = 30 , 8 x 4 = 32.
Therefore the answer is 30/32 and we simplify by the common number that it can be divided equally, and is 15/16.

Second example is 6 / 3/6.
This time we make 6, 6 over 1 and flip 3/6.
Therefore 6/1 x 6/3 = 36/3.
Then we simplify by 3 because 3 can only divided by 3 or 1 in this case 36 needs to be divided by 3 because 36 and 3's common number is 3 so therefore the answer is 12.

  Third and last example is Divide 9 1/3 by 4/7.
Now the easiest way to do it is change 9 1/3 to improper fraction and is 28/3.
Then we flip 4/7 and is 7/4.
Therefore is 28/3 x 7/4.
Finally our answer is 196/12, but we forgot the one last thing to do, we simplify by the same number.
Then our answer is 16.333333333... but we're going to round it off to the nearest whole number.

* If there's a question which it has a mixed fraction, the easiest to it is change the mixed fraction to the improper fraction.

Multiplying fractions

In this lesson, we're learning multiplying fractions. Multiplying fraction is different to the adding and subtracting the fractions. When you're multiplying fractions you multiply numerators with numerators, denominators with denominators. Also when you're multiplying the whole number, write whole number over 1.
  
  Our first example is 3/5 x 1/5.
We multiply out numerator times numerator, denominator times denominator.
Therefore, 3 x 1 = 3, 5 x 5 = 25, and the answer is 3/25.

  Second example is 4/5 x 3/6.
We multiply numerator by numerator, denominator by denominator. That equals 4 x 3 = 12, 5 x 6 = 30.
Therefore our answer is 12/30, and if we simplify by 2,3 or 6, the answer will be 2/5.


  Third example is 15 x 2/3.
Like I said numerator by numerator, denominator by denominator. 
In this case, there's a whole number so we write 15 like this, 15/1.
Then we do the normal step, multiplying. 15 x 2 = 30, 1 x 3 = 3.
Therefore the answer is 30/3 but if we simplify, the exact answer is 10.

 Forth and last example is 8 1/4 x 2 4/8.
Now this time, we have to change it to the mixed fractions so 8 1/4 turns into 33/4, 2 4/8 turns into 20/8.
33 x 20 = 660, 4 x 8 =32.
660/32 = 165/8.
then we change it to the mixed fraction, is 20 5/8.
Therefore our answer is 20 5/8.

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.

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.