Showing posts with label percentage. Show all posts
Showing posts with label percentage. Show all posts

Sunday, 4 November 2018

P1 : Percentage Practice


(Part 1) TEACHING(15-20 mins)       


(Part2) Core PRACTICE (35-50mins)
Tutor: Please observe and ensure that the student follows the method/step. 
Start Time:                    End Time:              
(I) Percent (10-15 mins)                                                    Working
Express each fraction as a percentage.
1.   13 /20 =                          2.  ¾ =

Express each decimal as a percentage
3.   0.026 =                            4.  0.107 =  

Express each percentage as a fraction in its simplest form.
5.  45% =                               6.  8% =          

Express each percentage as a decimal
7.  25% =                               8.  0.7% =  

(II) Word Problems (25- 40 mins)
9.    The figure below is made up of 5 identical squares.
What percentage of the figure is shaded? (9/p1/f)
(1) 10%
(2) 20%
(3) 25%
   (4) 80%

For question 10 and 11.
The pie chart below shows the Colour Houses of 40 pupils in a class. Study it carefully and answer questions 10 and 11. (10-11/p1/f)          
10. What percentage of the pupils are in the Green House?
(1) 10%
(2) 25%
(3) 35%
(4) 75% 

11. How many pupils are in the Yellow House?
(1) 10%
(2) 25%
(3) 35%
(4) 75%   

12.  Kim bought a smartphone at a sale. She has to pay an additional 7% for GST. How much did she pay in all? (25/p1/f)
For question 13 and 14
Study the advertisement below. (16/p2/18f)
Aunt Liz ordered a chicken, a box of banana fritters and a cake.
13.  How much was the total cost of ordering the food with the delivery charge?

14.  How much change did she receive if she paid the delivery man $150?

15.  Daniel spends 20% of his monthly salary on food and 15% on transport. He then saves the rest of his money. If he saves $2275, how much is his monthly salary? (5/p2/f)

16.  Karen gave away 80% of her dresses and threw away 30 spoiled dresses. She had 10 dresses left. How many dresses did Karen have at first? (30/p1/f)

17.  The usual price of a television is $1625. John bought the television at a discount of 20%. He had to pay a 7% GST on the discounted price. How much did he pay for the television in total?

18.  The graph below shows the number of visitors at Kidz Club from Monday to Friday. The bar that shows the number of visitors on Thursday has not been drawn. 
  
If the percentage of visitors decreased by 36% from Thursday to Friday, what is the number of visitors on Thursday? (28/p1/s)

19.  Simon earns $4600 per month. He gives his children $1500, his wife 20% of his remaining salary and saves the rest. How much will his wife get if Simon gets a 10% pay raise? (6/p2/s)

Extra
1.  Amy bought 7 kg of flour. She used 4.7 kg to bake cakes. What percentage of the flour was not used? Express your answer correct to 1 decimal place.

2. Patrick had $400. He bought a pair of glasses for $78 and spent $48 on a pair shoe. What percentage of his money was left?

3.* A youth club has 50 male and 70 female members. 16% of the male members and 10% of the female members are students. What percentage of the members are students?

4.*  After a discount of 25%, the price of a concert ticket is $60. Senior citizens are given a further discount of $12. What is the total percentage discount given to senior citizens for the ticket?

5.*       Ticket at $15 each. $10 discount for every 4 tickets
Mr. Tan paid $315 for tickets to the puppet show. Hoe many tickets did he get?

6.*            1st book at 10% discount,
                2nd book at 20% discount.
      Price of 2nd book should be equal to or lower than price of 1st book.
Joan and Jose each bought two books at the sale.
(a) Joan’s books were priced at $8 and $10. How much did she pay for them?
(b) Jose paid a total of $24.80 for his two books. He paid $4 more for the 1st book than the 2nd book. What was the price of the 2nd book before discount?

7.*  Hazel was given a fixed amount of pocket money each month. In July he spent $50 and saved the rest. In August he spend 10% less and her savings increased by 25%. How much was Hazel’s pocket money for each month?

8.* Linda bought a rice cooker for $126 after a discount of 30%.
(a) What was the price of the rice cooker before discount?
(b) She paid $40 for a toaster. The total discount for the rice cooker and the toaster was $64. What was the percentage discount given for the toaster?

TheMathbooklets Content Page 
Practice Content Page 

Percentage Answer Keys
1.         65%
2.         75%
3.         2.6%
4.         10.7%
5.         9/20
6.         2/25
7.         0.25
8.         0.07
9.         2
10.      1
11.      3
12.      $51.36
13.      $124.50
14.      25.50
15.      3500
16.      40 
17.      $1391
18.      2500
19.      712

Monday, 1 October 2018

P1 Percentage

PERCENT
"Percent % " means
"per 100"   or  'out of 100'  or  ‘per 100 of the total value’.
         -> the first quantity usually represents a part of, or a change in, the second quantity.

Defining Percent
Percent means “per 100” =>
            60% = 60 / 100
            25% = 25 / 100

Example:
What is 1 per 100 as a percent?
    1 per 100 means ‘1 out of 100  -> 1 is 1% out of a total value of 100 -> 1%  

Relating to Fractions:
  => Part/Whole x 100 = % 

Diagram illustration:


Examples
 (a) What is the 25 per 100 in percent?

       25 per 100 -> 25%
       Diagram illustration:
             
 (b)  What is the percent of 100 out of 100?
       100 per 100 -> 100%
               

Using Percentage
We can use percentage to help us:

(1) Compare 1 quantity with another.
            
     Duracell battery last 35% longer as compared to the next competing batteries
  (2) Express how large or small one quantity to the total quantity

               25% out of the full battery (out of 100%) is left

(3) Express change(increase or decrease) of quantity in relative to its original quantity.


Calculating Percentage
Common sentence construct in Percent:
            P as a percentage of Q -> OF VALUE.

   The OF ‘VALUE’ is the Total Value -> it has a percent of 100% (or as stated)
     
Formula
                           Percent =  Given Value   x 100%
                                             Total Value

                                 Value = Given percent  x Total value

                                                      100%

Example

Express 20 cm as a percentage of 250cm.


20cm as %, total= 250                   Step1: Write numbers

       Percent = Given Value x 100  Step2: Use/link, formula

                        Total Value

                     =   20 x 100

                         250

                    = 8%                          Step3: Calculate/Solve   

Example

a. What is 40% of 80. 

b. What is 150% of 80?

a. 40% , total = 80                 Step1: Write numbers

     = 40 x 80.                         Step2: Use/write formula

        100

     =  32                                Step3: Solve

 b. 150%, 80.                        Step1: Write 150% of number, 80

    =  150 x 80                       Step2: Use/write formula

        100

    =  120                              Step3: Solve
One-percent Method
This method is to compute the value of 1%, and then multiply it with the required value. It is similar to the cross-multiply method. It provides a more detailed breakdown for easy understanding.
Example: 

Express 50 cm as a percentage of 250cm

100% -> 250cm                          Step 1:  Write numbers

             100 % - > 250                Step 2: Use/link [ value of 1% ]

                  1% - > 250 / 100

                   1% -> 2.5cm

50cm -> 50 / 2.5 (per 2.5 -> divide). Step3: Solve

           = 20%


Converting Percent to Fractions
Percent can be expressed as #/100
            29% is 29/100 (29/100 is a fraction)
Example
Convert 15% to fraction.
Method
Step1: Express percent as  #/100
15% = 15/100
Step2: Simplify fraction to lowest term
        = 15 3 /100 20
               = 3 / 20
Example:
 (1) 0% = 0/100
             = 0
(2) 100% = 100/100
                = 1
(3) 120% = 100/100 + 20 1 /100 5
            = 1 + 1/5
            = 1 1/5

Converting Fractions to Percent
Example:
Express 1/2 as percentage

Step 1: Multiply by 100
            ½ x 100 = 50
Step 2: Express the fraction as percent
             1/2 as percent is  50%

Example:
Express 3/4 as a percentage
Step 1: Multiply by 100
            ¾ x 100 = 75
Step 2: Express the fraction as percent

            ¾ as percent is 75%

Converting Percent to Decimal
Example
Express 26% as a decimal.
Method:
Step1: Change % to    #/100
            26% - > 26/100
Step2: Change    2/100 to 0.#
            26/100 = 0.26
Example
  Express 37% as a decimal.
Method:
Step1: Insert decimal point (if required)
            37% = 37.0%
Step2: Shift decimal 2 places to the left
            37.0% = 0.37

Converting Decimals to Percent
Example
 Convert 0.345 to percent
Method
Step: Move Decimal point 2 places to the right
            0.345 = 0.0345 x 100% = 34.5%

SUMMARY
Expressing Percentages as Fractions and Decimals
Percentage
÷ 100
Fractions
Decimals
8%
8 ÷100 = 8 / 100
 2/25
0.08
25%
25 ÷ 100 = 25 / 100
 1/4
0.25
30%
30 ÷ 100 = 30 / 100
 3/10
0.3
50%
50÷ 100 = 30 / 100
 1/2
0.5
62.5%
62.5 ÷ 100 = 625 / 1000
 5/8
0.625
75%
75 ÷100 = 75 / 100
 3/4
0.75
80%
80 ÷ 100 = 80 / 100
 4/5
0.8
97.5%
97.5 ÷ 100 = 975 / 1000
 39/40
0.975
                      ~~~~ END ~~~~ :)

VIDEOS
Solving Percentage Question : using the 1% method

Solving Percentage Question : Using Model