Download Practice Problems

DEV 085
Unit 3 Notes
Decimals
Percents
Proportions
Decimal Place Value:
•Decimal points are read as the word
“and”
•Place values to the right of the decimal
point represent part of a whole
•Read the numbers in groups of three
then read the place value name
•Place values to the right of the decimal
point end with “ths”
•Place values to the right of the decimal
point “mirror” place values to the
left of the decimal point
Thousandths
Hundredths
___ , ___ ___ ___
Tenths
Ones
Tens
Hundreds
Thousands
Decimal Place Value:
___ ___ ___
Rounding Decimals:
Steps for Rounding:
Step 1: Identify the place value you are
rounding to and underline it
Step 2: Circle the number to the right
Step 3: Determine whether to “round up” or
to “round down”
• If the circled number is 0-4, the underlined number
stays the same and all the digits to the right of the
circled number fall off
• If the circled number is 5-9, the underlined number
goes up one and all the digits to the right of the
circled number fall off
Rounding Practice Problems:
Nearest
Tenth
Nearest
Hundredth
4.576
4.6
4.576
4.58
13.804
13.8
13.804
13.80
1 7 9.8 5 6
179.9
1 7 9.8 5 6 179.86
Comparing Decimals:
Steps for Comparing Decimals Values
Step 1: List the numbers vertically
“Stack” the decimal points
Add zeros as place holders as needed
Step 2: Compare the whole number part then
compare the decimal parts moving to
the right (as you would if you were
alphabetizing words)
Step 3: Put in the correct order (from least to
greatest or greatest to least)
Comparing Decimals Practice:
Practice Problems: Arrange each group of
numbers in order from least to greatest.
0.342
0.304
0.324
0.340
0.304
0.324
0.340
0.342
2.37
2.7
2.3
2.73
2.3
2.37
2.7
2.73
Comparing Decimals Practice:
Practice Problems: Arrange each group of
numbers in order from least to greatest.
5.23
5.023
5.203
5.032
5.023
5.032
5.203
5.23
1.010
1.101
1.011
1.110
1.010
1.011
1.101
1.110
Basic Operations with Decimals:
Addition and Subtraction
Step 1: Write the numbers vertically
“Stack” the decimal points
Add zeros as place holders
Step 2: Move the decimal point straight
down into your answer
Step 3: Add or subtract
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the sum or
difference for each.
2.3 + 3.71 + 27 = 33.01
3.14 + 2.073 + 8.9 = 14.113
4.023 + 24.311 = 28.334
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the sum or
difference for each.
31.73 – 12.07 = 19.66
9 – 8.185 = 0.815
23.5 – 17.097 = 8.593
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the sum or
difference for each.
2.45 – 4.66 = -2.21
3 + 5.76 + 0.11 = 8.87
25 – 0.14 + 2.36 = 27.22
Multiplying Decimals:
Steps for Multiplication
Step 1: Write the problem vertically (just as
you would a regular multiplication problem)
Step 2: Ignore the decimal point(s) and
multiply as if you were multiplying whole
numbers
Step 3: Determine where the decimal point
goes in the product
However many digits are to the right of the decimal
point(s) in the problem… that’s how many digits are to
be to the right of the decimal point in the product.
Multiplying Decimals Practice:
Practice Problems: Find the product of
each.
2 x 3.14 = 6.28
8.097 x .05 = 0.40485
1.042 • 2.3 = 2.3966
Multiplying Decimals Practice:
Practice Problems: Find the product of
each.
4.7 x 1000 = 4,700
3 x 0.567 =
1.701
0.27 • 15 =
4.05
Multiplying Decimals Practice:
Practice Problems: Find the product of
each.
(2.5)(1.02) = 2.55
(1.003)(0.42) = 0.42126
5.41 x 200 = 1,082
Dividing with Decimals:
There are 2 types of division problems
involving decimal points:
No decimal in the divisor
Decimal in the divisor
Division with Decimals:
NO decimal point in the divisor…
Step 1: Write the problem in the
traditional long division format
Step 2: Move the decimal point in the
dividend straight up into the quotient
Step 3: Divide as usual
Remember to divide out one more place
than you are rounding to…
Division with Decimals:
Yes…Decimal point in the divisor…
Step 1: Write the problem in the traditional
long division format
Step 2: Move the decimal point in the divisor to
the far right of the divisor
Step 3: Move the decimal point the SAME
number of places in the dividend
Step 4: Move the decimal point in the dividend
straight up into the quotient
Step 5: Divide as usual
Remember to divide out one more place than you are
rounding to…
Division Practice:
Practice Problems: Find the quotient for
each.
3.753  3 = 1.251
8.7  100 = 0.087
245.9 ÷ 1000 = 0.2459
0.65 ÷ 5 =
0.13
Division Practice:
Practice Problems: Find the quotient for
each.
428.6 ÷ 2 = 214.3
2.436 ÷ 0.12 = 20.3
4.563 ÷ 0.003 = 1,521
21.35 ÷ 0.7 = 30.5
Division Practice:
Practice Problems: Find the quotient for
each.
97.31 ÷ 5 = 19.462
0.8542 ÷ 0.2 = 4.271
67.337 ÷ 0.02 = 3,369.5
1500.4 ÷ 1000 = 1.5004
Problem Solving with Decimals:
Follow the correct Order of Operations only
remember to apply the rules that go with decimals.
P – Parenthesis
E – Exponents
P.E.M.D.A.S.
M- Multiplication
D – Division
A – Addition
S – Subtraction
Do whichever one
comes first working
from left to right
Order of Operations Practice:
Practice Problems: Solve each by
following the correct order of operations.
2.3 x 4  2 + 4 = 8.6
3.5  7 + 2.15 x 0.13 = 0.7795
2(7 – 2.49) + 0.3 = 9.32
14  0.2 + (3.1 – 2.56) x 2 = 71.08
Order of Operations Practice:
Practice Problems: Solve each by
following the correct order of operations.
5 + (7.8 – 5.5)2 – 14.3 = -4.01
(40 ÷ 0.5 • 7) + 5 – 14 = 551
-8 • 0.75 + 15.23 – 4 = 5.23
Percents:
Understanding Percent:
•A percent is one way to represent a
part of a whole.
•“Percent” means per 100
•Sometimes a percent can have a
decimal.
•A percent can be more than 100.
•A percent can be less than 1.
•When you write a fraction as a percent:
Change the fraction to a decimal
value then change it to a percent.
Percents, Decimals, and Fractions:
To change between formats…
Fractions
Decimals
Divide the
numerator
by the
denominator
Percents
Move the
decimal point
to the right
2 places and
add a % sign
Percents, Decimals, and Fractions:
To go the other direction…
Fractions
Decimals
Put the # (to the
right of the
decimal) on top.
The # on the
bottom will
represent the
appropriate place
value. Reduce to
lowest terms
Percents
Move the
decimal point
to the left
2 places and
add drop the
% sign
Practice Problems:
Fractions
Decimals
4
5
.8
80%
1
6
.166
16.6%
.52
52%
13
25
1
34
8
25
3
50
3.25
Percents
325%
.32
32%
.06
6%
Proportions:
A proportion shows that two ratios are
equal.
2 = 4
3
6
5 = 17.5
7 24.5
3 = 27
2
18
Ratio Equivalency:
To check the equivalency of two ratios,
you CROSS MULTIPLY. (If your products
are equal, your ratios are equal).
3 = 12
5
20
(3)(20) = (12)(5)
60 = 60
EQUAL
Ratio Equivalency:
To check the equivalency of two ratios,
you CROSS MULTIPLY. (If your products
are equal, your ratios are equal).
2.4 = 13
3
15
(2.4)(15) = (13)(3)
36 = 39
NOT EQUAL
Proportion Practice:
Check to see if the proportions are equal
or not.
3
7
=
Equal
9
21
2
5
=
5
14
Not Equal
1
12
=
6
Equal
2
8
Proportion Practice:
Check to see if the proportions are equal
or not.
3
8
=
4
9
Not Equal
2.5
5
=
6.5
13
Equal
5¾ = 11½
9
20
Not Equal
Solving Proportions:
When you know three of the four
parts of a proportion, you can CROSS
MULTIPLY then DIVIDE to find the
missing value.
Solving Proportions:
4
5
=
x
20
(4)(20) = (x)(5)
80
= 5x
80
5
= 5x
5
16
= x
Cross
Multiply
Show what you
are multiplying
in your first
line…in your
second line show
your products
Divide
(divide by
the number
with the
variable)
9 = 3
x
8
(9)(8) = (3)(x)
72 = 3x
72
3
24
= 3x
3
= x
Solving Proportions Practice:
Solve for the missing value.
3 = X
2 = 5
6
12
7
X
6 = X
X = 17.5
X =
24
2
3
X = 16
Solving Proportions Practice:
Solve for the missing value.
2.5 = X
10 = 5
5
18
11
X
9 = X
X =
5.5
4 = X
10
33
X = 13.2
Solving Proportions Practice Problems:
Practice: Solve each.
One person can move 120 barrels in one
hour. How many barrels can that
person move in 2.5 hours?
One person could
move 300 barrels
in 2.5 hours
Solving Proportions Practice Problems:
Practice: Solve each.
A baseball player hits 55 times in 165
at bats. At this rate, how many at
bats will he need to have to reach 70
hits?
The player would
need 210 at bats
to reach 70 hits
Solving Proportions Practice Problems:
Practice: Solve each.
In her garden, Maggie plans to plant 8
blue petunias for every 12 red
geraniums. If she buys a total of 70
plants, how many plants are petunias?
28 plants are petunias
Solving Proportions Practice Problems:
Practice: Solve each.
The sun is shining on two buildings
(short and tall) creating 30 ft and 45
ft shadows. The tall building is 60 ft
tall. What is the height of the shorter
building?
The shorter building
was 40 feet tall
Solving Percent Problems:
A proportion setup can be used to solve
percent problems. Set the problem up
as a proportion and solve for the missing
information.
When solving percent problems, think of
the proportion set-up as:
Partial %
100 %
=
“is”
“of”
Solving Percent Problems using a
Proportion Setup:
Step 1: Put your numbers in the
correct places
Step 2: Solve the proportion by crossmultiplying then dividing
Solving Percent Problems
Practice:
23 is 20% of what?
Find 80% of 40
24 is what % of 72?
40 is 50% of what?
115
33.3%
Find 6½ % of 24
1.56
32
80
5 is 5.5% of what?
90.90
Solving Percent Problems
Practice:
Find 8% of 150
108 is 72% of what?
12
3.75 is what % of 50
7.5%
150
Applications Using Percents:
TAX
Tax = (Purchase Price) x (Percent of Tax)
OR
% =
100
Amount of Tax
Purchase Price
TOTAL COST = Purchase Price + Tax
Tax Application Example:
You buy a television set for $289. The local tax rate is
7.5%. Find 1) the amount of tax and 2) the total cost of
your purchase.
$289
x 0.075
1445
+20230
21.675 (Tax)
$289.00 (orig amt)
+ 21.68 (tax)
$310.68 (total cost)
$21.675 becomes $21.68…must round because it is money
Applications Using Percents:
DISCOUNT
Discount = (Original Cost) (Percent of Discount)
OR
% = Amount of Discount
100
Original Cost
Original Cost
- Amount of Discount
DISCOUNTED PRICE
Discount Application Example:
You buy a microwave oven for $135. You can save 25%
if you shop at today’s sale. Find 1) the amount of
discount and 2) the discounted price of your purchase.
$135
x 0.20
$27.00 (discount)
$135.00 (orig amt)
- 27.00 (discount)
$108.00 (discounted
price)
Applications Using Percents:
MARK-UPS
Mark-ups = (Original Cost) (Percent of Mark-up)
OR
% = Amount of Mark-up
100
Original Cost
Original Cost
+ Amount of Mark-up
MARK-UP
Mark-Up Application Example:
I buy t-shirts for $3.00. I turn around and mark them
up 75% and sell them. Find 1) the amount of mark-up
and 2) the mark-up price.
$3.00
x 0.75
1500
+ 21000
$2.2500 (mark-up)
$3.00 (orig amt)
+ 2.25 (mark-up)
$5.25 (mark-up
price)
Applications Using Percents:
COMMISSION
Commission = (Total Sales) (Percent of Commission)
OR
% = Commission
100
Total Sales
Salary
+ Commission
TOTAL PAY
Commission Example:
Tony has a base salary of $22,000 a year. He makes 5%
commission on all of his sales. Over the course of a year, he
has a total sales amount of $135,000. Find 1) the amount of
his commission and 2) his total pay for the year.
$135,000 (base salary)
$135,000
(
commission)
+
6,750
x 0.05
$6,750 (commission) $141,750 (total pay)
Applications Using Percents:
In order to find Percent of Increase or
Percent of Decrease you must first find
the Amount of Increase or Amount of
Decrease.
To find the amount of increase or the
amount of decrease, find the difference
between the original amount and the
second amount.
Applications Using Percents:
PERCENT OF INCREASE
Percent of Increase = Amount of Increase
Original Amount
OR
% = Amount of Increase
100
Original Amount
Percent of Increase Example:
I buy a box of pencils for $4.00 and sell it for
$5.00. what is my percent of increase?
$5.00 - $4.00
$4.00
$1.00
=
$4.00
Find the difference between
the two amounts… divide by the
original amount
.25
=
25% increase
Convert to a percent
Applications Using Percents:
PERCENT OF DECREASE
Percent of Decrease = Amount of Decrease
Original Amount
OR
% = Amount of Decrease
100
Original Amount
Percent of Decrease Example:
I buy a box of books for $10.00 and sell it for
$8.00. What is my percent of decrease?
$10.00 - $8.00
$10.00
$2.00
=
$10.00
Find the difference between
the two amounts… divide by the
original amount
.20
=
20% decrease
Convert to a percent
Applications Using Percents:
SIMPLE INTEREST
I = P  R  T
I = Interest
P = Principal
R = Percentage Rate
T = Time (in years)
Total Amount = Principal + Interest
Simple Interest Application Example:
I had to borrow $15,000 to buy a new car. My interest rate
was 5%. My loan was for 5 years. Find 1) how much interest
will I pay for borrowing $15,000 and 2) the total amount of
my loan.
I=
P

R  T
I = ($15,000) (0.05) (5)
I = $3,750
$15,000 - Principal
+ 3,750 - Interest
$18,500 - Total amt of loan
Applications Using Percents:
MONTHLY PAYMENT OF A LOAN
principal + interest
Monthly payment = Total # of payments
Monthly Payment of a Loan Example:
If my total loan for the purchase of a new car is $18,750 and
I’m going to pay it over the course of 5 years, what is my
monthly payment?
$18,750
60 mo
(Loan amount)
= $312.50/mo
(Number of payments)
Monthly
payment
Review the things that you need
to review.
Study the things that you need
to spend more time on.
Ask questions about things you
don’t understand.
PRACTICE…PRACTICE…PRACTICE