Transcript Percent Increase and Decrease

WEEK 4
1. Finding Percenatages
1. Percentage increase &
decrease
STARTER
On your notebook, write the following sets in
the ROSTER NOTATION.
1. {x : x is even and x ≤ 8}
1.
{x : x = 3n, n ∈ N, n ≤ 4}
1.
{x : x = n2, n ≤ 5, n ∈ N}
1.
{x : x is odd}
STARTER ANSWERS
1. A = {2, 4, 6, 8}
1. B = {3, 9, 27, 81}
1. C = {1, 4, 9, 16, 25}
1. D = {1, 3, 5, ......}
OBJECTIVES
1. Find percentages of quantities
2. Interpret percentage as an operator.
3. Use a multiplier to increase or decrease.
What is a percentage?
What is a percentage?
A percentage is a ratio of a number to 100.
The symbol % is used to indicate a percent.
The word percent means “per cent” , “per
hundred.” So 6% means “6 out of 100.”
Example
Notice the 10 x 10 square grid.
There are 100 total squares.
Seven of the squares are colored.
Seven red squares of 100 total
squares can be shown like this:
7
=7%
100
A
67
B
23%
Which of the following is an example
of a percent?
Example 1: Modeling Percentage
Write the percent modeled by each grid.
A.
shaded
_______
total
Steps
B.
32 = 32%
___
100
shaded
_______
total
75 = 75%
___
100
Example 2: Modeling Percentage
Write the percent modeled by each grid.
A.
shaded
_______
total
Steps
B.
44 = 44%
___
100
shaded
_______
total
66 = 66%
___
100
Additional Example 3: Writing Percentage as Decimals
Write 21% as a decimal.
Method 1
Use pencil and paper.
Write the percent as a fraction with a
21% = 21
100
denominator of 100.
= 0.21 Divide 21 by 100.
Method 2 Use mental math.
21% = 0.21 Move the decimal point two places
to the left.
I do: How did I calculate the percent to a decimal?
Finding Percentages of a number!
Example 1:
34% of 5
= (34/100) x 5
= 1.7
Example 2:
6% of 1.45
= (6/100) x 1.45
= 0.087
Finding Percentages of quantities?
Example 1:
21% of 650 AED
= (21/100) x 650
= 136.5 AED
Example 2:
85% of 38 KG
= (85/100) x 38
= 32.3 KG
Example 3:
Find 3½% of $80
First > Express (7/2)/100 as a fraction = 7/200 = 0.035
Second > (0.035) x (80) = 80/15 = $2.80
Increasing and Decreasing Quantities by a Percentage
When increasing or decreasing by a percentage, there are two
ways to do this:
1. Find the actual increase or decrease and add it to, subtract it
from the original amount.
2. Use a simple multiplication
For example, to increase by 20%, multiply by 1.2. We increase an
amount (b AED) by 20%.
The increase is b AED x (20/100) = 0.2 b
So the new price is b AED + 0.2b = (1 + 0.2)b = 1.2b
A 20% increase is the same as to multiply by 1.2 to get the new
price.
100% + 20% = 120% = 120/100 = 1.2
1.2 is the multiplier!
A 20% decrease of 20% is the same as:
100% - 20% = 80% = 80/100 = 0.8
0.8 is the multiplier!
What is a multiplier? How does it help to increase and
decrease the change in percentage?
Example question 1 - Increase AED130 by 20%.
An increase of 20% is an increase from 100% to 120%.
To do this you would multiply by 120/100, which is the same as
multiplying by 1.2.
In other words, multiplying an amount by 1.2 is the same as
increasing it by 20%.
So the number 1.2 is the multiplier needed to do the calculation,
which now looks like this:
AED 130 x 1.2 = AED156, which is the answer.
Teacher to go over Example 4.4 & 4.5
(Maths iBook page 72 & 73)
CLASSWORK 1
Pair Activity
On your notebook, show an organized
solution on the following:
G11 Mathematics Website
WK 4 – L1 CLASSWORK 1 IGCSE Past
Paper Questions on Percentage
CLASSWORK 2
Individul Activity
On your notebook, show an organized
solution on the following:
iBook G11 Maths, page 75 – 76
#’s 1, 2, 3 a, c, f, h, 4, 5, 6
HOMEWORK
On your notebook, show an organized
solution on the following:
1. iBook G11 Maths, page 76 #’s 7 & 8
2. Any classwork NOT finished
EXTENSION ACTIVITY
For advanced students:
On your notebook, show an organized
solution on the following:
G11 Mathematics Website
WK 4 – L1 Extension Activity 1 Percentage
PLENARY
Share one or two things you have learned
in today’s lesson
THANK YOU! 