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Review and Applications
of Basic Mathematics
Chapter 1
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After completing this chapter,
you will be able to:
> Perform arithmetic operations in their proper order
> Convert fractions to their percent and decimal equivalents
> Maintain the proper number of digits in calculations
> Solve for any one of percent rate, portion, or base, given
the other two quantities
> Calculate the gross earnings of salaried, hourly wage, or
commission employees
> Calculate the simple average or weighted average (as
appropriate) of a set of values
> Perform basic calculations of the Goods and Services
Tax,
Harmonized Sales Tax, provincial sales tax, and
real
property tax
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Order of Operations
BEDMAS
Brackets - Perform operations within brackets (in the
order of the following steps).
Exponents - Evaluate the powers.
Division & Multiplication - Perform multiplication and
division in order from left to right.
Addition, and Subtraction - Perform addition and
subtraction.
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Converting Decimals to Percents &
Percents to Decimals
.75
.35
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75%
35%
5
500%
2.5
250%
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Converting Fractions to
Percents
.10
1
10
.10 .
10%
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Rounding Percents
Correct to 2 decimal places
.384615
5
13
38.4615%
38.46%
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Bag of M&M’s
Color
Yellow
Red
Blue
Orange
Brown
Green
Total
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Fraction
18
55
10
55
9
55
7
55
6
55
5
55
55
55 = 1
Decimal
(hundredth)
Percent
(hundredth)
.33
32.73%
.18
18.18%
.16
16.36%
.13
12.73%
.11
10.91%
.09
_____
9.09%
_______
1.00
100.00%
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Rounding Decimals
Step 1. Identify the place
value of the digit you want
to round - here we want
two decimal places
Step 3. Drop all digits to the right
of the identified digit
.3272727
.337272
Step 2. Identify the digit to the right.
If 5 or more, increase by 1. If less than 5
do not change
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.33
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Converting Decimals to Decimal Fractions
Step 1
Step 2
24
1
Places
2
.24
Step 3
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24
24
100
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Percentage Formula
Portion (P) = Rate (R) * Base (B)
Portion “is”
P
R
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Rate “%” Base “of”
B
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Solving for Portion
Sales of McDonalds drive-thru customers are 60% of
total sales. Total McDonald sales are $1,600,000.
What are the drive-thru sales?
Portion== Rate
Rate**Base
Base
Portion
= .60 * $1,600,000
P
= $960,000
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R
B
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Solving for Rate
Sales of McDonalds drive-thru customers are $960,000. Total
McDonald sales are $1,600,000. What Percent of customers eat
in the restaurant?
Rate==Portion
Portion
Rate
Base
Base
P
R
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B
$640,000
000
==$640,
$1,600,000
$1,600,000
= 40%
$1,600,000
- 960,000
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Solving for Base
Sales of McDonalds drive-thru customers are 60% of
total sales. Sales of eat-in customers are $640,000.
What are McDonald’s total sales?
Base = Portion
Rate
P
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R
B
= $640,000
.40
= $1,600,000
$640,000 is
40% of base
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Rate of Percent Increase
Old
New
% change = Difference
Base
% change = $1,500
$1,000
= 1.5 or
$1,000
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$2,500
= 150%
Increase
Difference
between
old and
new sales
Old
sales
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Payroll Cycles
$40 000 per year
Find gross amount per pay
Salary Paid
Period
Weekly
52 times (once a week)
Biweekly
26 times (every two weeks)
Earning per period
$769.23 ($40,000/52)
$1,538.46 ($40,000/26)
Semimonthly 24 times (twice a month)
$1,666.67 ($40,000/24)
Monthly
$3,333.33 ($40,000/12)
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12 times (once a month)
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Hourly Rate of Pay;
Calculation of Overtime
Gross pay = Hours worked * Rate per hour
Hourly overtime pay rate = Regular hourly pay rate * 1.5
Gross pay = Earnings for 40 hours + Earnings at time-and-a-half rate
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Straight Commission with Draw
Commission
Commission is
is aa certain
certain
percentage
percentage of
of the
the amount
amount aa
salesperson
salesperson sells.
sells.
Draw
Draw is
is an
an advance
advance on
on the
the
salesperson’s
salesperson’s commission
commission
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Larry is paid a straight
commission of 8%. His
computer net sales were
$100,000. Larry’s draw was
$750. What is his gross pay?
$100,000 * .08 = $8,000
-750
$7 250
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Variable Commission Scale
Up to $25,000
5%
$25,001 - $40,000
7%
Over $40,001
8%
Juanita’s car net sales were
$120,000. What is her gross
pay based on the schedule?
Different commission rates for different levels of net sales
($25,000 * .05) + ($15,000 * .07) + ($80,000 * .08)
= $8 700
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Salary Plus Commission
Chung receives a salary of $2,500 per month. He also
receives a 5% commission for sales over $15,000. Last
month’s sales were $75,000. Calculate Chung’s gross pay.
Gross Pay = Salary + Commission
= $2,500 + ($60,000 * .05)
= $5 500.
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Calculating the Actual Sales Amount
before Tax
Register sales including 15% tax totals $5000. Find the
actual sales total before the tax was included
Sales Amount = Amount including tax
1 + tax rate
= $5000
1+ 0.15
= $4347.83
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Property Tax
Property taxes pay for local
fire and police protection,
schools, etc . They are based
on assessed value.
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Assessed value - The value of
property for the purposes of
computing property taxes
Assessed value =
Assessment rate * Market value
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Calculating Property Tax
Mill rate = amount of tax
per $1000 of assessed value
Property tax = Mill rate * assessed value
1000
= 26.923 * 240 000
1000
= $6 461.52
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If you live in a house with an
assessed value of $240 000, and
the current mill rate is $26.923,
find the amount of your property
tax for the year.
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Expressing Tax Rate
By percent
7.69%
Per $100 of
Per $1,000 of
assessed value
$7.69
assessed value
$76.90
Per $100 of
By percent
assessed value
$40,000 x 7.69% $40,000 = 400
$100
400 x $7.69
$3,076
$3,076
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In mills
76.90
Per $1,000 of
assessed value
In mills
$40,000 = 40
$1,000
40 x $76.90
$3,076
76.90 x .001x
$40,000
$3,076
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