1. Algebra
Unit #1 --- 2-1
R&A
Algebra
Chapter 2
PowerPoint Presentation
Prepared by
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
C Quinn, Seneca College.

2. Algebra
Unit #1 --- 2-2
Algebra
R&A
Formula Manipulation
Both sides of the equation must be
treated in exactly the same way!
You can add the same number to both sides
You can subtract the same number from both sides
You can multiply or divide both sides
by the same number or variable
You can raise both sides to the same exponent
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

3. Algebra
Unit #1 --- 2-3
Algebra
R&A
LO 2.
Substitution
Equation 6.1
P = $100
principal
amount
Amount of interest
Evaluate I = Prt
r = 0.09 t = 7/12
7 Months
rate of
time in
interest
years
I = $100 * 0.09 * (7/12)
I = $100 * 0.0525
I = $5.25
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Think
5.25
Use Calculator
BEDM
AS

4. Algebra
Unit #1 --- 2-4
Algebra
R&A
LO 2.
Substitution
Equation 6.2
P = $100
Total Amount
r = 0.09
t = 7/12 7 Months
S = $100 [1 + 0.09*(7/12)]
S = $100[1.0525]
S = $105.25
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
S = P(1 + rt)
Think
105.25
Use Calculator
BEDMAS

5. Algebra
Unit #1 --- 2-5
Algebra
R&A
LO 2.
Formula Manipulation
Example
S = $105.25
Evaluate S = P(1 + rt)
P = $100 r = 0.09 t = ?
We must solve for t
OR
First substitute the
numerical values given,
and then manipulate the
equation to solve for t
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
First rearrange the
formula to isolate t, and
then substitute the given
numerical values give.

6. Algebra
Unit #1 --- 2-6
Algebra
R&A
Formula Manipulation
LO 2.
Example
Evaluate S = P(1 + rt)
First rearrange the formula to isolate t, and then
substitute the given numerical values give.
Multiply through by P
S = P(1 + rt)
S = P + Prt
Subtract P from both sides
S - P = Prt
(S – P) / Pr = Prt/Pr Divide both sides by Pr
(S – P) / Pr = t
Now substitute
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

7. Algebra
Unit #1 --- 2-7
Algebra
R&A
LO 2.
Formula Manipulation
Example continued….
t = (S-P) / Pr
S = $105.25
P = $100 r = 0.09
Now substitute
t = (105.25 -100) / 100*0.09
t = .5833 years
t = 7 months
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Multiply by 12 to
change years to months

8. Algebra
2-8
R&A
LO 5.
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

9. Algebra
Unit #1 --- 2-9
R&A
Base Method
Formula
% change = Final Value – Initial Value
Initial Value
c = Vf – Vi * 100%
Vi
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

10. Algebra
Unit #1 --- 2-10
Algebra
R&A
Monday’s Sales were $1000 and Tuesday’s were
$2500. Find the percent change.
$
%
(/100)
Initial Value 1000
100
1
250
Final Value
2500
2.5
Change 1500
150
1.5
x
100%
=
2500
150% Increase
1000
Cross - multiply
X = 2500*100% / 1000 =
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
250%
…Alternate solution

11. Algebra
Unit #1 --- 2-11
R&A
Monday’s Sales were $1000 and Tuesday’s
were $2500. Find the percent change.
This method is referred
to as
the Base Method
% change = Difference
Base
c = Vf – Vi * 100%
Vi
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
Initial(Base)Value
Final Value
$ 1000
2500
Difference $ 1500
$ 1500
% change =
$ 1000
= 1.5 or 150% Increase

12. Algebra
Unit #1 --- 2-12
R&A
In the making of dried fruit, 15kg. of fruit
shrinks to 3 kg. Find the percent change.
Initial(Base)Value
Final Value
15
3
% change = Difference
Difference
Base
12
c = Vf – Vi * 100% % change =
15
Vi
12
= .8 or 80% Decrease
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
…Alternate solution

13. Algebra
Unit #1 --- 2-13
R&A
In the making of dried fruit, 15kg. of fruit
shrinks to 3 kg. Find the percent change.
Kg.
Initial Value
Final Value
Difference
x
100%
=
3
%
15
3
12
100
20
80
(/100)
1
.2
.8
Cross - multiply
15
X = 3*100% / 15 = 20%
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
80%
Decrease

14. Algebra
Unit #1 --- 2-14
R&A
A chartered bank is lowering the interest rate
on its loans from 9% to 7%.
What will be the percent decrease in the interest
rate on a given balance?
% change = Difference
Base
= .07 - .09 = -.02
.09
.09
-
= .2222 or
22.22% Decrease
Increase in Interest Rate
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

15. Algebra
Unit #1 --- 2-15
R&A
A chartered bank is increasing the interest rate
on its loans from 7% to 9%
What will be the percent increase in the interest
rate on a given balance?
% change = Difference
Base
= .09 - .07 = .02
.07
.07
=.2857 or
28.57% Increase
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved

16. Algebra
Unit #1 --- 2-16
R&A
You paid $51.75 for a meal in Ontario which
includes the taxes of 14%.
What was the price of the meal prior
to the addition of the taxes?
Initial value = Final value
1 + % change
= 51.75 =
1+ .14
=$45.39
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
51.75
1.14

17. Algebra
Unit #1 --- 2-17
R&A
You paid $75 for a new coat
after a 20% discount.
What was the original price of the coat?
Initial value = Final value
1 - % change
Here the change is negative
= 75.00 =
1 - .20
=$93.75
©2008 McGraw-Hill Ryerson Ltd. All Rights Reserved
75.00
.80