Summary Chapter 11

USING MENTAL METHOD: 11.1

Some percentages are easy to find because they are simple fraction.

*if you know 10%, you can find any multiple of 10%

EXAMPLE:

1. a) 35% of 84               b) 49% of 230

       35% = 25% + 10%       50% - 1%

       25% = 21                    50% = 115

       10% = 8,4                   1% = 2,3

       35% = 21 + 8,4            49 % = 155 – 2,3

       = 29,4                        =112,7

    C) 77% of 4400                        d) 99% of 7900          e) 45% of  56 000

        77% = 100% - 25% + 2%      99%= 100% - 1%      45% = 50% - 5%

        100% = 4400                           100% = 7900             50% = 28 000

        25% = 1100                              1% = 79                     5% = 280

        2% = 44                                  99% = 7900 - 79       45% = 28000 - 280

        77% = 4400 – 1100 + 44         = 7821                         =27720

        =3344

2. A. look at alicia's method for finding 85%.

        Answer = 50% + 25% + 10% 

    B. work out 85 % of:

        i) 7200g                                   ii) $64                         iii) 3.6m/ 360cm           iv) 1800ml

          50% = 3600                             50% = 32                     50% = 180                   50% = 900

          25% = 1800                             25 % = 16                    25% = 90                      25% = 450 

          10% = 720                               10% = 6,4                    10% = 36                      10 % = 180

          85 % = 3600 + 1800 + 720    85% = 32+16+6,4        85% = 180+90+36         85% =                                                                                                                                                        900+450+ 180

         = 6120g                                    = $272/$5                     = 306cm/3,06m            = 1530ml

        v) 85 second

            50% = 42.5

            25% = 21.25

            10% = 85

            85% = 42.5+21.25.85

            = 72,25

3. Use this fact ( 26% OF $78 = 20.28 ) to find:

    a) 52% of $78         b) 13% of 78kg        C) 65% of 78        d) 104% of 78 milion

        20.28 x 2  = 41        20.28 / 2 = 11                                     20.28 x 4 = 82

COMPARING DIFFERENT QUANTITIES: 11.2

You will need to compare groups that are different size.

 EXAMPLE:

1. There were 270 people in cinema.There were 168 women and 102 men.

    There were 152 people in a theatre . There were 78 women and 74 men.

    a) work out the percentage of women in each value

        cinema: 168/270 x 100 = 62%

        theatre: 78/152 x 100 =  52%

    b) work out the percentage of men in each value

        cinema: 102/270 x 100 =38%

        theatre: 74/152 x 100 = 48%

2. There are 425 girls & 381 boys in a school. 31 girls & 48 boys are overweight.

    a) work out the percentage  of the girls are overweight

        31/425 x 100 = 7%

    b) work out the percentage of the boys are overweight

         48/381 x 100 = 12%

    c) work out the percentage of all the students that are over weight

        79/860 x 100 = 9%

3. This table shows the result of survey in factory

     

                 smoker     non-smoker   total  

    men          12               64             76

    women      9                32             41

a) What percentage of men are smoker

     12/76 x 100 = 15%

b) Compare the percentage of men and women who are non-smoker

    men: 64/76 x 100 = 84%

    women: 32/41 x 100 = 78%

    

PERCENTAGE CHANGES: 11.3

 You can use percentages to describe a changes in a quantity. it could be increase or decrease.

 A percentage change is always calculated as a percentage of the initial value.

The initial value is 100%. it is important to choose the correct value to be 100%.

EXAMPLE:

 1. Here are the prices of three items in Alain,s shop.

     Game 40%     Phone $120     Computer $500

Alain increase all the prices by $10. Find the percentage increase for each items.

Game: 10/40 x 100 = 25%     Phone: 10/120 x100 = 8.3%   Computer: 10/500 x 100 = 2%

2. These are the masses of three children one April.

     Luke 6 kg   Bridget 14 kg     Tomas 25 kg

Over year, the mass of each of them increased by 10%.  Work out the new mass of each child.

    

 Luke: 10/100 x 6 =0.6kg      Bridget: 10/100 x 14 = 1,4kg    Tomas: 10/100 x 25 = 2,5kg

3. The price of a car was $20 000. In ta sale, the price decreased by 4%.
    After the sale it increased 4%.
a) What mistakes has Ahmad made?
    estimating the sales price

b)What is the correct price after the sales?
   4% =>  4/100 x $20 000 = 800
         = 20 000 - 800 = 19.200

   price after sale = 4/100 x 19 200 = 768
                          = 19 200 + 768


PRACTICAL EXAMPLES: 11.4

Profit: sell for more than you buy.
Loss: sell for less than you buy.
Discount: reduction in the price, it is usually given as a percentage
Interest: bank charges
Tax: if you buy something the price may include a additional price.
EXAMPLES:
 1. A woman bought an old chair for $240. She sold it for $300.
     Work out the percentage profit.

  $300 - $240 = 60
  60/240 x 100% = 25%

2. A man bought a car for $15 900. He sold      it for $9500
    Work out the percentage loss.

15 900 - 9500 = 6400
6400/15900 x 100% = 40,25%

3.A bottle of juice costs $6.50.
  If you buy six bottle you can get 10% discount.
  Work out how much he sells them for.

6 x 6.5 = 39
Discount = 10/100 x 39 =3,9
after discount = 39 - 3,9 = 35,1
39-35,1 = 3.9