Finding the quantity in percentage

 In this lesson we're going to learn finding the quantity in percentage. Previously I said percentages uses in our life every day. Sometimes you need to find part of the quantity from the total quantity which is in percentage.

 There are 3 methods to find the quantity.
Method 1 is convert percentages to fraction with the denominator of 100 then multiply.
Method 2 is convert the percentage to simplified fraction then multiply.
Method 3 is convert the percentage to decimal then multiply.

 1. Our first example is "Find 25% of $500."
 There are three methods to find the quantity. It doesn't matter which method you choose the answers are same.

Method 1: 25% = 25/100
i.e 25/100 x 500/1.
= $125.

Method 25% = 1/4 when is simplified.
1/4 x 500/1 = $125

Method 3: 25% = 0.25.

                                   500             500 x 0.05 = 25
                               x 0.25             500 x 0.20 = 100
                                    
                                     25
                             +    100
                                  
                                   125

Second example is " Find 35% of 50 laptops."

  35/100 x 50/1 = 1750/100 = 17.5 = 17 laptops.
OR 0.35 x 50 = 17.5 = 17 laptops.

 Third example is 10% of $850."
10/100 x 850 =$85
i.e  $85.

  Forth example is "Find 33 1/2% of 240."
In this case method 2 much more easier this time.

33 1/2% = 67/200

67/200 x 240 = 402/5 = 80.4.
i.e 80.4.

Conversions you must remember in percentage

 The table below is the conversion of percentages to decimal or fraction. This conversions are basic conversions that you must remember.

Percentage	Decimal	Fraction	Simplified fraction
25% 50% 75% 100%	0.25 0.50 0.75 1.00	25/100 50/100 75/100 100/100	¼ ½ ¾ 1
20% 40% 60% 80%	0.2 0.4 0.6 0.8	20/100 40/100 60/100 80/100	1/5 2/5 3/5 4/5
33 1/3% 66 2/3%	0.3333333333… 0.6666666666…	33 1/3/100 66 2/3/100	1/3 2/3
12 ½% 37 ½% 62 ½% 87 ½%	0.125 0.375 0.625 0.875	125/1000 375/1000 625/1000 875/1000	1/8 3/8 5/8 7/8

Changing percentages to decimals, changing decimals to percentage

 In this lesson we're going to do another converting lesson. This time is converting percentages to decimal and converting decimals tom percentages.

  Converting decimals to percentages or converting percentages to decimals is quite easy to do it.
Firstly to change percentages to decimals:
1. you need to divide the numerator from the denominator. 
2. Then move the decimal point to the left twice.

  Second is to change decimals to percentage, there are two methods you can choose.
1. Multiply decimal from 100.
2. Move the decimal point to the right, twice.


1. Our first example is "Convert 32% to a decimal."
32% = 32/100.
= 0.32

2. Second example is "Convert 253% as decimal."
253% = 253/100 = 2.53.

3. Third and last example is " Convert 78 1/5% to a decimal."
78 1/5% = 78.20/100 = 0.782.


1. Our first example in converting decimals to percentage is " Convert 0.34 as a percentage."
We move the decimal point to the right, or you do 0.34 multiplied by 100.
0.34 = 34%, 0.34 x 100 = 34%.

2. Second example is "Convert 7.52 to percentage."
Same as this, you move the decimal point to the right or do the multiplication.

  7.52 = 752% or 7.52 x 100 = 752%.

3. Third and example is "Convert 0.875 to percentage."
0.875 = 87.5% or 87 1/2% or
0.875 x 100 = 87.5% or 87 1/2%.

4. Forth and last example is "Convert 0.0525 to percentage."
0.0525 = 5.25% or 5 1/4% or
0.0525 x 100 = 5.25% or 5 1/4%. 

Converting fractions to percentage

 In this lesson we're going to learn further on converting fractions to percentage.
This lesson will show you where you have to convert fractions into percentage.

Just to keep in mind there are 2 methods to convert fractions into percentages.

1. Multiply with 100/1.
2. Make the denominator 100 by multiplying the number that it can be divided by 100.

1. Our first example is "If a chipmunk scores 6/20 in spelling test, what percentage is this?
You can use one of the methods above.

6 x 5 = 30/20 x 5 = 100
Therefore 30/100 = 3/10 and equals to 30%.

2. Second example is "There are 50 books from overseas. 10 books are from Untied States, 16 books from Germany, and the remainders are from Russia. Change these to percentages.

 10 of 50 are from Untied States,
therefore is 20%,
16 of 50 are from Germany,
therefore is 32%.

Lastly we need to find the remainder. To find the remainder you add all the percentages you found then subtract from 100%.

i.e 20% + 32% = 52%
100% - 52% = 48%.
Therefore 48% of the books are from Russia.

4. Forth and last example is " convert 56/200 into percentage."
Firstly we simplify and the equals 7/25,
secondly we times 4 on the numerator and denominator,

therefore the answer is 28/100 or 28%.

Changing fractions to percentages

 In this lesson we're going to learn converting fractions to percentages.
Converting fractions to percentages are important as converting percentages to fractions.

 There's an simple way to convert fractions to percentage.
to convert any fractions into percentage, multiply the fractions by 100% / 1.

 1. Our first example is " Convert 12/20 to a percentage."
  12/20 x 100/1.                    We multiply 12/20 by 100% /1.
                                                              
  12/20 x 100/1                                        Before we multiply,
 = 12/1 x 5/1                                         we find is there any number that it can be simplified.
 = 60/1                                                  we found 20 and 100.
 i.e 60%.                                               100 can be divided by 20 therefore 100 divided by 20 is 5.

2. Second example is " Express 4/5 as a percentage."
In this example I'm going to show you another method to convert fractions to percentages.

We know that 5 times 20 equals 100 so we times 20 on numerator and denominator.
4 x 20 / 5 x 20 = 80/100 = 80%.
Therefore the answer is 80%.

3. Third and last example is " Express 5 2/3 as a percentage."

We multiply with 100% /1 this time.

5 /2/3 x 100/1 = 17/3 x 100/1 = 1700/3 = 566%.
Therefore the answer is 566%.

*If you're doing the same method on example 2, make sure that the denominator must be 100.

Converting percentages as fractions,

 In this lesson we're going to learn converting percentages to fractions. I assume you guys are now confident with the converting so this lesson will be an easy one.

  Converting percentages to fraction is easy. reason we learned that the meaning of the percentage is hundredth or out of 100.  Also when you changed to fractions, some of the fractions can be simplified.

 1. Our first example is "Convert 60% to fractions."
 To review our work, percentage is one of special fraction,
which it has a denominator of 100.
So 60% can be written in 60/100 and we simplify and the answer is 3/5.

  2. Second example is "Convert 25% to a fraction."
25% can be written in 25/100, then simplify therefore our answer is 1/4.

  3. third example is 4 1/5% to a fraction."
   4 1/5% =  4 1/5 / 100                The numerator and denominator of a fraction must be whole numbers.
   = 4 1/5 x 5 / 100 x 5                 To make 4 1/5 a whole number, we change it to the improper fraction
   = 21/500                                    then multiply it by 5, same as the denominator, we multiply 100 by 5.
   i.e 21/500.

One whole of percentage

 In this lesson we're going to look at some particular questions that is about percentages.
Keep in mind when you're doing a question about percentage, it must be add up to 100%.

Previously I told you in percentage, percentage means hundredth or out of 100. Unfortunately I have to say the best solution to understand is working through these examples below.

 1. First example is "I scored 88% in maths test. What percentage have I got wrong?"
 We know that 88% is correct, we subtract 88% from 100%.
Therefore the answer is 12%.

 2. Second example is "A company consist 60% of females. What percentages are male?"
We know that 60% is female, so we subtract 60% from 100%.
Therefore the answer is 40%.

3. Third example is A class has 3 choice of sport in this term: tennis, swimming or shooting.
32% of the student choose to play swimming and 47% to do shooting. What percentage of the student will be playing tennis?

 Swimming + shooting = 32% + 47% = 79%
Total percentages must add up to 100%.
So, we subtract 79% from 100%.
Therefore the answer is 21%.

4. Forth and last example is "Jon got 56%, 23% and 98% in 3 separate history exams. What was his average marks?"

 When you're finding average you have to add all the scores and divide by the number of the scores.

Average = 56% + 23%+ 98% / 3.
Therefore the answer is 177/3 = 59
  i.e 59%.

* Another way to say the average is mean.

Percentage introduction

 In this lesson we're starting a new chapter percentage. Percentage uses in our life daily and is another special fraction which has denominator of 100. 

 Percentage occurs everyday in our life. For example your exam mark comes out in percentages, your school report comes out in percentages and statistics on population.

 Percent can be written as %.
It means hundredth, or out of 100 or per hundred and % is made by the two zeroes,
therefore that's why the percentage means hundredth or out of 100, or per hundred.

 For example if there are 100 squares and 34 of them are shaded, find the percentage of the squares that has been shaded.

We write the total in denominator and in numerator, write the number of the square which are shaded.

 Therefore the answer is 34/100 or 34% or 34 out of 100 or 34 hundredth.

Rounding off decimals

 In this lesson we're going learn rounding off decimals. Rounding off decimal is same as rounding off whole number, only the difference is we have to round of the tenth, hundredth and thousandth etc.

 When you're rounding off the decimal, always check the next decimal place because it depends on the number at the next decimal place whether it rounds off or round down.

 Just for revision, we round off a number when the number is 5 or higher (i.e add 1),
 if the number is less than 5 we round down.

 1. Round off 85.3176 to 2 decimal places.

 Check the third decimal place (7). now this is higher than 5, we must round up which it means add 1 to the number 1.

  Therefore the answer is 85.32.

* Another way to say is "Round off to the nearest hundredth."

2. Round off 102.537 to 1 decimal place.

  Look at the second decimal place, which is 3 and this is smaller than 5, it must be rounded down.
Therefore the answer is 102.5.

* Another way to say is "Round off to the nearest tenth."

Decimals in money 2

 In this lesson we're going to some more further work in decimals in money.
In most of the exam, like school certificate or major exams, there are 4 operation all the time and the 4 operation decimal is one of them. So what I would like to talk about is not a simple question, a short answer questions.

  1. Our first example is "Poppy went to the store and bought toothpaste for $5.32, liquid soap for $3.48, hair shampoo for $4 and razor for 97 cents. How much change will Poppy get from $30?

  We add all of the stuffs that Poppy bought and we subtract from the $30.
$5.32 + $3.48 + $4 + $0.97 = $13.77.
$30 - $13.77 = $16.23.

  Therefore the answer is $16.23.

  2. If a kilo of beef costs $9.57, ho much would 5 kilograms cost?
                                        
       $9.57                                 This question's structure is finding the quantity, so is multiplication.
     x       5                                 after the calculation is finished, you need to put the decimal point
                                                 2 figures to the right.
     $47.85 


  3.  A reward money of $ 6325.90 has to be shared equally between 5 people.
     How much does each person receive?

           1265.18
      5   6325.90                                  Shared equally means divide $6325.90 by 5.
           60
             32                                      
             30
               25
               25
                   9
                   5
                   40

  Therefore the answer is $1265.18.

Decimals in money

 In this lesson we're going to learn about decimals in money. The reason why I'm calling this lesson "Decimals in money is because when you're writing the currency (money), you write the cents in tenth and hundredth place.

  Also the 4 operations are applying to the decimals because it applies in exactly the same way to money problems that we're dealing everyday.

  Before I show you examples, I want to tell you how to write the currencies in numbers.
For example twenty three dollars and thirty seven cents.
                                                                                  
              $23.37        We write $23 in the whole number column and we write thirty cents in tenths and we just write 3 in there and 7 cents in hundredth.


     1.  Our first example is $539 + $78.26.
             1
         $539.00                       0 + 6 = 6, we just write 6 under, 0 + 2 = 2 we just write 2 under,
      +   $78.26                      9 + 8 = 17 we write 7 and write 1 above 3, 3 + 7 = 10 and we add 1
     =  $617.26                      that makes 11, so we write 1 and write another 1 above 5.
                                            Lastly we add 1 to 5 and that makes 6 therefore the answer is $617.26.
    
     2.  Second example is 183.74 - 54.26.

           $183.74                   We can't do 4 - 6 so we borrow 1 from 7 and that makes us 14 - 6 = 8,
        -   $54.26                   7 becomes 6. 6 - 2 = 4, we borrow 1 from 8, 13 - 4 = 9,
                                          8 becomes 7, 7 - 5 = 2, there's nothing do with 1 so we just write 1.
       = $129.48                  

  Therefore the answer is $129.48.

    3. Third example is $4.73 x 8.
                                   2
                              $4.73        Firstly, 3 x 8 = 24, we write 4 under 8 and write 2 above 7,
                           x        8       7 x 8 =56 56 + 2 = 58 we write 8 behind 4, write 5 above the 4.
                                              Lastly, 4 x 8 = 32, 32 + 5 = 37.
                           $37.84
  Therefore our answer is $37.84.

  4. Forth and last example is $76.82/2.
        38.41                                 
    2  76.82                   6 is close to 7 and is smaller so 2 x 3 = 6, 7 - 6 = 1,1 comes down so as 6,
        6                         it makes 16, 2 x 8 = 16, 16 -16 = 0, then 2 x 4 =8 equals to 8, 8 - 8 =0,
        16                       2 x 1 = 2 therefore we subtract 2 - 2 equals 2
        16
              8
              8
                2
                2
                0

 Therefore the answer is $38.41.

Multiplying and dividing decimals by powers of 10.

 In this lesson we're going to learn about multiplying and dividing decimals by powers of 10.
Sometimes when you're multiplying or dividing decimals, you have to multiply or divide by 10, 100, or 1000 etc,
so today we're going to learn how to multiply or divide the decimals just using the decimal point.

When multiplying a decimal by 10, 100 or 1000, move the decimal point 1,2 or 3 places to the right.
When dividing decimal by 10, 100 or 1000, move the decimal point 1,2 or 3 places to the right.


 Our first example is 76.23 x 10.
We need to move the decimal point to the right just once.
Reason is we're moving the decimal point by the number of the zeroes.
Therefore our answer is 762.3.


  Second example is 8.745 x 100.
Now we do the same but the position of the decimal point.
There are two zeroes at this time, so we move the decimal point to the right twice.
Therefore 8.745 x 100 = 874.5.

  Third example is "Convert 2.7 meters to centimeters.
1m = 100cm, the working out should be like this, 2.7 x 100.
Then we move the decimal point to the right twice.
Therefore our answer is 270cm.

  Forth and last example on multiplication is 2.967 x 1000.
This time there are 3 zeroes so we move the decimal point to the right three times.
Therefore the answer is 2967.

  In dividing decimals, you move the decimal point to the left.

  First example is 76.7/10.
There's only one zero so we move the decimal point to the left once.
Therefore the answer is 7.67.

  Second example is 984.5/100.
 There are two zeroes so we move the decimal point to left twice.

Therefore the answer is 9.845.


  Third and last example is 85.9/1000.
There are three zeroes so we move the decimal point to the left three times.
Therefore the answer is 0.0859.

Multiplying and dividing decimals.

  In this lesson we're going to learn multiplying and dividing decimals.  Difficulty of multiplying and dividing decimals are same as adding and subtracting decimals. Also the steps are similar as multiplying and dividing the whole number.

 When you're multiplying decimal, if you're confused with the decimal point,
erase the decimal point for a while then put the decimal point when the calculation is done.
After you finished your calculation of multiplying decimals, add how many places did decimal point moved on each decimal and add all the positions.

  Our first example is "Find 1.63 x 4.2."
Like we did on adding and subtracting decimals, we do it in easy way.
a
                                                 163                  
                                              x   42
                                               
                                                326                      
                                         +   652
                                         
                                              6846


 After the calculation is over, we put the decimal points.
When you're putting the decimal point, you  need to make sure that the answer has the same number of decimal places as the question.

Therefore, 2 in 1.63 and 1 in 4.2, the total is 3 therefore our answer is 6.846.


 Second example is " Find 0.4 of $5.60."
There are two way s to work out this question. You either go directly 0.4 times 5.60, or change the unit of $5.60 into 560 cents. The answer is same on which method you use.

Method 1 is  0.4
                x  5.60

  Therefore our answer is $2.24.

Method 2 is $5.60 is 560 cents, so 0.4 equals to 4/10
4/10 x 560 equals to 224, in dollar, is $2.24.

 
 In Dividing decimal, we do the same thing as we did it in multiplying decimal but the working out is different.

Example 1 is " Evaluate 6.47/5."

                                   1.294
                               5  6.47
                                   5
                                   1.4
                                   1.0
                                       47
                                       45
                                         20

Therefore our answer is 1.294.

  Second example is "Find 52.16/0.4."
 Firstly, we need to make 0.4 to whole number, and is 4.
Also we need to make sure that 52.16 turns into 521.6.
Reason is 0.4 moved to right to make a whole number, therefore the other decimal point must be moved to right.

                        130.4
                    4  521.6
                        4
                        12
                        12
                             1.6
                             1.6
                                0

Therefore our answer is 130.4.

Addition and subtraction in decimals.

  In this lesson we're going learn adding and subtracting decimals. Adding and subtracting decimals are different from adding and subtracting the whole number.
Reason is there's a decimal point and we need to put the decimal point in the right position.

On adding decimals,  you have to make the decimal point directly under each other.
On subtracting decimals you make the decimal point directly under each other, and borrow 1 if necessary.



  Our first example is 3.42 + 23.56 + 5.09 + 34.23.
Now we do it in the easy way.

                                                     3.42     All you need to remember is the order of operation and
                                                   23.56   and make all the decimal point directly under each other.
                                                     5.09
                                            +     34.23
                                                   
                                                    66.3                  
                                           
 Second example is 89.76 - 34.23.
                                               
                           89.76
                        - 34.23
                           55.53

  Therefore our answer is 55.53.


Third and last example is," On Monday I spend $25.45 on entertainment, $12.56 for transport, and $4.00 on drink. How much have I left over from $60.00?

  This question want s you to find the amount spend then subtract from $60.00
The total is $25.45 + $12.56 + $4.00 = $42.01
Then we subtract from $60.00.
Therefore $60.00 - $42.01 = $17.99,
and the answer would be $17.99 left.

* Don't forget to place all the decimal points directly under each other.

Converting difficult fractions to decimals.

 In this lesson, we're going learn more on converting fractions to decimals.
Now, previously, we understand the special fraction and what special fraction is, but sometimes when you have a fraction that's not an equivalent, the special fractions won't work.

  It happens most of the time wen you're converting fractions into decimals.
This is what you have to do. The method is very simple, only thing you have to do is divide the denominator from the numerator.

  Our first example is "Convert 7/9 into decimal."
Like I said, we need to divide the denominator from the numerator.
So 7 divide from 9 and the answer is 0.777777778.

  Second example is " Convert 5/21 into decimal."
Same as this, 5 divided by 21, and the answer is 0.238095238.

* In some of the fraction, you will notice that numbers tenths and hundredths are repeating.
In this case, you put a dot above the number on tenths and hundredth, it depends which number on which place is repeating and if the number on tenth is repeating, you put the dot above the number on tenth.

Fractions to decimals

 Previously, we learned converting decimal to fraction. In this lesson, we're going to learn converting fraction to decimal. Changing fraction to decimal is easy, if you know the special fraction.

  Now, to change the fraction to decimal, you need to make the denominator into 10, 100 or 1000 or etc depends on the denominator which it has tens, hundreds or thousands. Also if you're converting fraction to decimal, first thing you have to do is, figure out which number is going to make the product of 10, 100, 1000, etc.

Our first example is " Convert 1/5 into decimal.
To convert fraction into decimal, we need to multiply something with 5 to make the denominator 10.
Reason is 5 is close to 10, so we're going to times 2 to make the denominator 10.
Therefore, 5 got times by 2 and the answer is 10, and don't forget to times 2 to 1 because it needs to be equal.
Then our answer is 2/10 and in decimal is 0.2.


 Our second example is "Convert 7/25 into decimal."
In this example, you need to figure out which number needs to be multiply and make the product 100.
Now, 100 divided by 4 is 25 so then we need to do 7 times by 4, then our answer is 28.
Therefore our answer is 28/100 and in decimal, is 0.28.

Third and last example is " Convert 5/8 into decimal."
Now, 8 multiplied by 125 is 1000, and we do the same thing to the numerator.
5 multiplied by 125 is 625, therefore our answer is 625/1000
and in decimal is 0.625.

Decimal to fraction

 In this lesson, we're going to learn changing decimals to fraction. Changing decimal to fraction is quite easy because I shown the special fraction 1/10, 1/100, 1/1000 etc so it's easy when you're using these special fractions. 

  For example,  "Change the following decimals to fractions, simplify if is necessary."
  (a) 0.5  (b) 0.47  (c) 0.234  (d) 6.7 (e) 0.089

 In question (a), 0.5 has only one decimal point, so 0.5 equals to 5/10.
Then we simplify and the answer is 1/2.

 Question (b) has two decimal point, so we place 47 over 100 and it's 47/100.
This time we don't need to simplify it because there's no same number to divide by.


 Question (c) has three decimal points, so we place 234 over 1000.
Then we simplify by the same number which is 2,
therefore the answer is 117/500.

  Question (d) has one decimal point but there is 1 figure after the decimal point.
Therefore is 6 7/10.

Lastly, question (e), it has 3 decimal point, therefore we write 89 over 1000.
Therefore our answer is 89/1000.


* When there's 1 figure in front of the decimal point, place the number over 10.
When there's 2 figure in front of the decimal point, place the number over 100.
When there's 3 figure in front of the decimal point, place the number over 1000.

Placing the decimal orders

In this lesson we're going to learn placing the each decimal ascending order or descending order. Placing the decimals into descending order or ascending order shows us which decimal is bigger or smaller.

  Example 1 is "Order the following numbers in descending order."
                       77.4  77.04   77    77.44
 Now, 77.4. 77.4 equals to 77 + 4/10,
77.04 equals to 77 +  4/100,
there's no decimal on 77,
and lastly 77.44 equals to 77 + 44/100.

Therefore the answer is 77.44, 77.4, 77.04, 77.

 Second example is "Five hamsters ran in the 1m hamster marathon and recorded their time of finish in seconds. Order the following times in ascending order.
              31.07, 34.67, 31.37, 21.79, 56.45

 Now we do the same thing as we did it in the example 1.
31.07 equals to 31 + 7/100,
34.67 = 34 + 67/100,
31.37 = 31 + 37/100,
21.79 = 21 + 79/100,
56.45 = 56 + 45/100.

  Therefore the answer is: 21.79, 31.07, 31.37, 34.67, 56.45.

Decimal introduction and place value

 In this lesson, we're doing a new topic. The new topic is decimal. Previously we learned about the fraction, now we're going to change the fractions into decimals and decimals into fraction, then we're going to learn about place value in decimal.

 Firstly, changing decimal into fraction. Changing decimal into fraction is like this. Decimals are different from the the fraction but they're special fraction which the denominators are 10, 100, 1000, etc.

So for example, 1 and 59/100 is 1.59.

  Secondly I want to talk about is place value in decimal.
Decimal place value is similar as the whole number place value.
The only difference is there is a tenth, hundredth, thousandth, etc.
Tenth is 1/10 in fraction, hundredth is 1/100 in fraction and in goes on 1000, 10000, 100000 etc.

  For example 345.123.
We all know now that 3 is 300, 4 is 40, 5 just 5, and now,
1 is 1/10 because 1 is in tenth place, 
2 is 1/100 because 2 is in hundredth place, 
and 3 is 1/3000 because 3 is in thousandth place.

Second example is "write  34.56 in expanded form."
Expanded form is another way to show how much number are in each digits
that represents.

Therefore (3 x 10) + ( 4 x 1) + (5 x 1/10) + (6 x 1/100).


Third and last example is "What is the place value of 5 in 123.475?"
The answer is thousandth. Reason is 5 in the thousandth place,
the place value of 5 is 5 x 1/1000 = 5/1000.

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.