Download How to Round Numbers - NelsonEssentialMath - home

Essentials of Math 11
Booklet #1 – Review
Instructor – Paula Nelson
ACC Adult Collegiate
Fall 2012
1
Table of Contents
1. Course Outline…………………………………….
2. Skills Review PRETEST………………………….
3. Adding/Subtracting Review and Practice………....
4. Multiplying/Division Review and Practice………..
5. Basic Fraction Review…………………………….
6. Decimal and Percentage Review…………………..
7. Order of Operations Review………………………
8. Rounding…………………………………………..
9. Skills Review POSTTEST………………………...
10. Review (with answers)……………………………
11.Websites for Extra Practice………………………..
2
Pages 3-4
Pages 5-6
Pages 7-16
Pages 17-27
Pages 28-33
Pages 34-40
Pages 41-42
Page 43
Pages 44-45
Page 46
Page 47
Essential Mathematics 11 – Course Outline
SLOT: Tuesdays and Thursdays, 5pm-7pm INSTRUCTOR: Paula Nelson
E-MAIL: [email protected]
COURSE SCHEDULE:
TOPIC
# OF WEEKS
Review
Financial Services
Personal Budgets
Slope and Rate of Change
Midterm
Graphical Representations
Surface Area, Volume and Capacity
Trigonometry of Right Angles
Scale Representations
Final
1
2
2
2
2
2.5
1.5
1
EVALUATION:
Tests/Projects
60%
Midterm Exam
20%
Final Exam
20%
TEXTBOOKS:
 MathWorks 11
Pacific Educational Press, University of British Columbia
REQUIRED SUPPLIES:
scientific calculator, ruler, protractor, pencils, graph paper, binder, looseleaf paper
POLICIES:
Overdue Assignments and Missed Tests
Students are expected to attend all classes, complete assignments by the scheduled due
date, and write tests during scheduled times. Under reasonable circumstances, a make-up
test or assignment extension may be negotiated if the student initiates the request for an
extension. If an extension has not been negotiated, missed tests and late assignments will
receive a mark of zero.
COURSE WEBPAGE/WIKI:
https://nelsonessentialmath.wikispaces.com/
3
Please ensure that you know your username and password to access the computers at
ACC Adult Collegiate.
LEARNING OUTCOMES:
Financial Services:
It is expected that students will be able to:
 Demonstrate an understanding of compound interest
 Demonstrate of credit options, including credit cards and loans
 Solve problems that require the manipulation and application of formulas related
to simple interest and finance charges.
Personal Budgets:
It is expected that students will be able to:
 Solve problems that involve personal budgets
 Demonstrate an understanding of financial institutions services used to access and
manage finances.
Slope and Rate of Change:
It is expected that students will be able to:
 Demonstrate an understanding of slope as rise over run and as a rate of change by
solving problems
 Solve problems by applying proportional reasoning and unit analysis
 Solve problems that require the manipulation and application of formulas related
to slope and rate of change
 Solve problems that involve scale
 Demonstrate an understanding of linear relations by recognizing patterns and
trends, graphing, creating table of values, writing equations, interpolating and
extrapolating solving problems
Graphical Representations:
It is expected that students will be able to:
 Solve problems that involve creating and interpreting graphs, including bar
graphs, histograms, line graphs and circle graphs
Surface Area, Volume and Capacity:
It is expected that students will be able to:
 Solve problems that involve SI and imperial units in surface area measurements
 Solve problems that involve SI and imperial units in volume and capacity
measurements
 Solve problems that require the manipulations and application of formulas related
to volume and capacity and surface area
Trigonometry of Right Triangles:
It is expected that students will be able to:
 Solve problems that involve two and three right triangles
Scale Representations:
It is expected that students will be able to:
 Model and draw 3-D objects and their views
 Draw and describe exploded views, component parts, and scale diagrams of
simple 3-D objects
4
Skills Review PRE TEST
5
Skills Review PRE TEST continued…
6
As adapted from http://www.gcflearnfree.org/math
Adding and Subtracting Review
Addition
Addition is the math function that lets you know how much you have when you combine
two or more numbers. Every time you put money into your bank account, you are adding
to your balance.
As you work with numbers, you will realize that each number has its own special
qualities. The place of a digit in a number determines its value. Some whole numbers,
such as 632, have 3 digits. Each digit represents a different value.
In the number 632:
the 2 is in the ones digit place 632
the 3 is in the tens digit place 632
the 6 is in the hundreds digit place 632
So there are two ones (2), three tens (30) and six
hundreds (600) in the number 632. Knowing the value
of the digits in a number is important as you learn about
addition.
Think of place values like this:
Practice Place Values:
http://www.aaamath.com/g4-21bplacevaluebutton.html#section2
Addition is the combining of two or more numbers to get a sum. For example, if you
have 3 lemons and you go to the store and buy 2 more, you have a sum of 5 lemons. You
might write 3 + 2 = 5 which means 3 plus 2 equals 5. The plus sign is used when you
add.
An easy way to add numbers is to stack them in their value places.
To stack numbers:
 Place the numbers you want to add on tope of each other in
their value places.
 Place the plus sign, +, on the left of the stack.
 Draw a line at the bottom.
7
As adapted from http://www.gcflearnfree.org/math
Suppose you want to add 12 and 3.
To add the numbers:
First, add the 3 and 2 in the ones place to get 5
Since there is nothing in the tens place to the left of 3, bring down the 1.
The sum is 15. Place is below the line in the addition problem.
Carrying Numbers
If you want to add 16 and 18, the steps are a little different because you’ll need to
carry a number to the next place value. You carry when the numbers in a place value
add up to more than 9. This is an important skill you’ll need to learn in order to do
some addition.
To add 16 and 18:
 First, add 6 and 8 in the ones place: 6 + 8 = 14
 The number 14 has a 4 in the ones place and a 1 in the tens place.
 Put the 4 in the ones places of your sum
 Next, place the remaining 1 over the ones in the tens place in your problem. This
is called carrying to the next place value.
 Add all the ones
 Place 3 in the tens place of your sum.
The sum of 16 plus 18 is 34.
**TRY IT**
You want to buy a portable stereo for $125 and two CDs for $28. Stack the
numbers and add them.
(If you added correctly, you’ll know
that the sum of 125 & 28 is 153.)
PRACTICE – please complete on a separate sheet of paper.
1. You want to buy a microwave oven for $205 and a casserole dish set for $39. Add
205 + 39 to find out much the microwave oven and the casserole dish set will
cost. Stack the numbers and don't forget to carry!
2. Stack and add 22 + 23.
3. Stack and add 88 + 24.
4. Stack and add 245 + 35.
8
As adapted from http://www.gcflearnfree.org/math
5. You have put together 35 information packets and your co-worker has done 29.
How many packets have you both completed altogether?
6. Donna needs to send letters to people on different mailing lists. One list contains
18 names and the other list contains 23 names. How many letters will she need to
produce?
7. Stack and add 42 + 104.
8. You're planning a small outdoor party. If you have 8 lawn chairs and your
neighbours say they will loan you 12 lawn chairs, how many chairs will you have
altogether?
9. Stack and add 123 + 8.
10. Stack and add 14 + 62.
Answers: (1) 244 (2) 45 (3)112 (4) 280 (5) 64 (6) 41 (7) 146 (8) 20 (9) 131 (10) 76.
Other tips to making ADDITION easier – especially if you don’t have a pen and
paper to write everything down on – grouping by tens, using an addition table, and
using a calculator!
Grouping 10s
It is important to learn how to add numbers mentally in order to do daily tasks. For
example, you may want to keep track of the cost of items in your grocery cart so you
don’t go over $30. There’s a quick way to add some numbers in your head – use groups
of 10.
Suppose you are in charge of collecting money from your co-workers to buy a gift for the
boss. You know that Aaron plans to give $10, Maria will give $12, David will contribute
$5 and you will give $11. Find out how much money you will have to spend, by making
groups of 10. Think about the numbers 10, 12, 5 and 11, like this:
Three 10s plus 8 ones equals 38.
9
As adapted from http://www.gcflearnfree.org/math
Try It!
How would you group 25 + 12 into groups of 10 in order to add them? How about
grouping 34 + 15 into 10s?
Of course, you can also group into 10s, 20s and 30s to add. For example, you might
group 25 plus 12 into: 20 + 5 + 10 + 2 becomes 30 + 7 becomes 37!
Calculating Numbers
A calculator is a tool you can use to add numbers and do other math. You can use a
hand-held one or one that comes on your computer. For this class you will need a
SCIENTIFIC CALCULATOR.
Try It!
An office supply warehouse has 528
notepads in stock. A truck delivers a
box containing 1,550 notepads and
another box containing 775 notepads.
Use a calculator to add up all of the
notepads and figure out how many are
now in the warehouse.
If you added 528 + 1550 + 775 and got
2,853 as the answer then you are
correct.
10
As adapted from http://www.gcflearnfree.org/math
Addition Table
Practice adding small numbers using this
addition table. To find out the sum of two
numbers select the numbers in the left and
top columns. Your answer is the
intersection of the two columns.
Example – to find the sum of 8+ 5, find
the 8 in the top or left column and the 5 in
the remaining column. Where they
intersect will be the answer, which is 13 in
this case.
PRACTICE – please complete on a separate sheet of paper.
1. Group 32 into 10s.
2. Group 28 into 10s.
3. Tonya plans to buy three pizzas: a small one for $12, a medium for $15 and a
large for $20. Think in groups of 10 to figure out how much she will spend for
each pizza.
4. Add these numbers in your head: 10 + 10 + 6 + 1.
5. Add these numbers in your head: 10 + 10 + 10 + 8 + 2
6. Using a calculator, add 134 + 286 + 304.
7. Using a calculator, add 1,450 + 355.
8. You have to pay four bills: $32, $45, $186 and $205. Use a calculator to figure
out how much money will you spend on these bills.
9. Janet and the staff are decorating a ballroom for a party. They need 2,450 white
balloons, 1,250 gold balloons and 1,250 black balloons. Use a calculator to figure
out how many balloons they need altogether.
10. Use a calculator to add 3,528 + 1,245.
Answers: (1) 10 + 10 + 10 + 2 (2) 10 + 10 + 8 (3)10 + 2; 10 + 5; 10 + 10 (4) 27 (5) 40
(6) 724 (7) 1805 (8) 468 (9) 4950 (10) 4773
11
As adapted from http://www.gcflearnfree.org/math
Subtraction
In math, subtraction is the method used to find the difference between two numbers. It is
the OPPOSITE of addition. When you take an item off the shelf in the grocery store, you
are subtracting it from the stores inventory. When you withdraw money from your bank
account, the bank subtracts the amount from your balance. We will again use the “stack
and subtract” method and we will review how to “borrow” when you are subtracting
numbers.
What's the Difference?
Subtraction is the method used to find the difference between two numbers. It is the
opposite of addition (this will become very important to know later when we review
Order of Operations). For example, the difference between 9 and 4 is 5. Suppose you
have nine lemons and you give four away. Think of four lemons taken away from a
group of nine lemons and five lemons remain.
When you subtract one number from another number, it is a good idea to stack them
based on their place values. To stack the numbers for subtraction:
Stack the numbers, placing the number you want to take away on the bottom.
Stack the numbers according to their place values
Place a minus sign, -, on the left side of the stack.
To subtract 6 from 18:
First, subtract 6 from 8 in the ones places to get 2.
Since there is nothing in the tens place to the left of the 6, bring down the one.
The answer is 12. Place it below the line.
Borrowing
When you subtract numbers, you sometimes borrow. You borrow from the tens place
when you can’t subtract from a digit in the ones place.
To subtract 5 from 24:

Since you can’t take 5 from 4, you must borrow to
make it 14.

When you borrow 1 from the tens places, you are
actually taking 10 and adding it to the 4 in the ones
place to get 14.

Fourteen minus five equals nine. (14-5=9)
12
As adapted from http://www.gcflearnfree.org/math

Since there is nothing to subtract from the 1 remaining in the tens place, you bring
down the 1 to get the answer 19.

Now you know the difference: 24 – 5 = 19
Subtracting Larger Numbers
When borrowing, keep tract of what is left in the digit place that you borrow from.


To subtract 14 from 32:
 Since you can’t take 4 from 2, borrow 1
from the 3 in the tens place to make it 2.
 (when you borrow 1 from the tens place,
you are actually taking 10 and adding it to
the 2 to get 12).
 Twelve minus four equals eight (12 – 4 = 8)
 Since you borrowed 1 from the tens place
in the top number, a 2 is left. Two minus one equals one (2 – 1 = 1)
The answer is 18.
Now you know the difference: 32 – 14 = 18
Checking Subtraction
Since the opposite of subtraction is
addition, you can check your subtraction
by adding.
Try It!
Borrow to answer the following question: You and some friends go out to eat. You
have $22 and you spend $6 for lunch. How much money do you have left?
If you figured out that you will have $16 left, then you
figured correctly.
13
As adapted from http://www.gcflearnfree.org/math
Practice
1. Sharon had 8 decorative plants in her yard. She gave her neighbour 3 of them.
How many plants does she have left?
2. Wesley has $52. If he spends $25 on groceries how much money will he have
left?
3. Carol has delivered 4 of the 12 packages in her truck. How many more packages
does she have to deliver?
4. Subtract 12 from 44
5. What's the answer to 125 - 16?
6. What's the answer to 220 - 10?
7. Joe loaded 12 bales of hay onto his truck but 3 fell off when he hit a bump. How
many bales did he have when he arrived home?
8. Denise brought 24 hotdogs to the picnic. The guests ate 18. How many hotdogs
were left?
9. Subtract 4 from 62.
10. What's the answer to 122 - 8?
Answers: (1) 5 (2) 27 (3) 8 (4) 32 (5) 109 (6) 210 (7) 9 (8) 6 (9) 58 (10)114
Other tips to making SUBTRACTION easier – especially if you don’t have a pen
and paper to write everything down on – breaking numbers in to parts and using a
calculator!
Subtracting in Parts
Subtracting numbers in parts is a subtraction shortcut. For example, your boss tells you
to take $80 in cash to buy a paper shredder. You find one on sale for $63. To find out
how much money will be leftover, subtract 80 – 63, using subtract in parts method.
To subtract 63 from 80 in parts:
Break 60 into 60 + 3
It’s easy to subtract 60 from 80. You get 20.
Next, subtract 3 from 20 to get 17.
By breaking the numbers into parts, you quickly figure out that 80 – 63 i= 17.
14
As adapted from http://www.gcflearnfree.org/math
Try It!
Robert is helping his daughter sell candy as a school fundraiser.
Anyone who sells 50 boxes is deemed a top seller and earns a
prize. His daughter has already sold 38 boxes. How many more
boxes must she sell to be a top seller?
Do some mental subtraction using the subtracting in parts method.
What's the answer to 50 - 38?
Did you subtract in parts to get the correct answer? To become a top seller, Robert's
daughter must sell 12 more boxes of candy.
Using a Calculator to Subtract
Sometimes you may not want to subtract in your head or on a paper, especially if dealing
with large numbers.
For example, suppose you earn $27,500 a year and you plan to apply for a job that pays
$34,000. How much more money would you earn if you get the job? Use a calculator.
Try It!
Using a calculator, find out the difference in
pay between a job that pays $29,500 per year
and one that pays $32,300.
32,300 - 29,500 =
If you used the calculator correctly, you found
out that the difference in pay is $2,800.
Practice – please complete on a separate sheet of paper.
1. Break 30 - 21 into parts and subtract.
2. Break 20 - 12 into parts and subtract.
3. Break 70 - 62 into parts and subtract.
4. Lewis spent $2,143 of the $3,000 he budgeted for a new computer and software.
Use a calculator to find out how much money does he have left?
5. Last year, 3,283 people attended the festival. This year, 3,188 attended. Use a
calculator to find out the difference in attendance.
15
As adapted from http://www.gcflearnfree.org/math
6. The computer learning center served 1,428 students last year and this year it
served 2,083. Use a calculator to determine the difference in the number of people
served.
7. Using a calculator, subtract 5,496 - 4,450.
8. Using a calculator, subtract 9,500 - 4,655.
9. Dan reserved an auditorium that seats 2,000 people. By the time the program
started, 1,587 people had been seated. How many empty seats were in the
auditorium?
10. Julia plans to travel 1,220 miles by the time her trip is over. So, far she has
traveled 884 miles. How many more miles does she have to travel?
Answers: (1) 30 - 1 = 29, 29 - 20 = 9 or 30 - 20 = 10. 10 - 1 = 9 (2) 20 - 10 =10, 10 - 2
= 8 (3) 70 - 60 = 10, 10 - 2 = 8 (4) $857 (5) 95 people (6) 655 people (7) 1046 (8) 4845
(9) 413 seats (10) 336 miles
16
As adapted from http://www.gcflearnfree.org/math
Multiplying and Dividing Review
Multiplication is a quick way of adding the dame number many times. For example, a
lemonade recipe calls for the same number of lemons each time you make one pitcher. If
you need to make several pitchers of lemonade, how will you know how many lemons to
buy at the store? By multiplying numbers!
One of the easiest ways to learn multiplication is to use the times table – but you may not
always have it when you need it. This lesson will explain how to easily multiply
numbers and specifically shows you: how to read a multiplication table, how easy it is
multiplying numbers by zero or one, that skip counting by twos, threes, fours, fives and
tens can make multiplication easy.
What is Multiplication?
Multiplication is related to addition. It’s a quick way of adding the same number many
times. If you have four numbers that are the same, such as 3 + 3 + 3 + 3, you can
multiply them.
SO, 4 multiplied by 3 means 4 times 3. You are adding 3 4 times.
Setting Numbers Up to Multiply
When you multiply, you can write the numbers a couple of ways
using the times sign x.
When multiplying small numbers you can write them on the same
line with the X in the middle: 6 X 4
However, you’ll want to stack them when multiplying with larger
numbers:
Factors and Product
The two numbers that
you are multiplying are
called factors.
The result is the product 
17
As adapted from http://www.gcflearnfree.org/math
Multiplication Table
A multiplication table is a tool used to
determine the product of two numbers.
Use the table below to find the
product of 8 X 2 by finding where the
numbers intersect.
Start at the top of the table. Move
downward until you arrive on the
same row as the 2 on the left. The
intersection point is 16.
So, 8 X 2 = 16
Tips for Learning Times Tables
The easiest way to learn multiplication
is to memorize the multiplication
table.
First, memorize the 0’s and then the
1’s.

Multiplying by 0 is easy
because any number times
zero is ZERO.

Multiplying by 1 is also easy because any number multiplied by one equals
itself.

Now that you know the 0’s and 1’s of the multiplication table, a good way to
remember the 2s to count by 2s:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
If you can count by 2’s, it’s easier to remember than 2 x 1 = 2, 2 x 2 = 4, etc

You can get to know the threes in a similar way – count by 3s:
18, 21, 24, 27, 30, 33, 36
3, 6, 9, 12, 15,
This makes it easier to remember than 3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, etc
More Tips for Learning the Times Tables

Learn to count by 5 for the 5s times tables: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…

Learn the 10s by counting by 10: 10, 20, 30, 40, 50, 60, 70, 80…

Learn the times that rhyme: 6 x 6 = 36, 6 x 4 = 24, 6 x 8 = 48
Try saying them out loud to remember them better.
18
As adapted from http://www.gcflearnfree.org/math
Practice
1. Using the multiplication table in this lesson, find the answer to 8 X 9.
2. Use the table in this lesson to figure out 7 X 12.
3. Barbara bought 3 cartons of eggs to cook breakfast for some guests. Each carton
contains 12 eggs. How many eggs does she have? Use the table to find out.
4. Barbara also plans to bake 2 pans of blueberry muffins. Each pan will hold 9
muffins. How many muffins will she bake? Use the table to find out.
5. Think about this in your head and answer, what's 2 X 4?
6. Think about this in your hand and answer, what's 2 X 5?
7. Count by twos up to the number 12
8. Count by threes up to the number 15
9. Count by fives up to the number 30
10. Count by tens up to the number 70
Answers: (1) 72 (2) 84 (3) 36 eggs (4) 18 blueberry muffins (5) 8 (6)10 (7)2, 4, 6, 8, 10,
12 (8)3, 6, 9 , 12 , 15 (9) 5, 10 , 15, 20 , 25, 30 (10) 10, 20, 30, 40, 50 , 60, 70
Multiplying Larger Numbers
Most times tables only go up to the 12s. So this lesson will help you learn multiplication
rules that apply to all numbers – big or small and practice multiplying larger numbers.
Memorizing the multiplication table makes small numbers easy.
When you are multiplying larger numbers, make sure you stack the
numbers in their places (value places).
Multiplying with larger numbers takes a little more time since you
are working with more numbers.
Let's multiply 5 X 43:
First, multiply 5 x 3
You get the partial product: 15.
Place 5 in the ones place of the product and carry the 1.
Now, multiply 5 x 4 to get 20:
Add 20 and the 1 that you carried to get the final product: 215.
19
As adapted from http://www.gcflearnfree.org/math
Try It!
Martin's wife and three teenage daughters are taking a train trip
and he's buying the tickets. The tickets are $40 each. How much
will Martin spend for the four tickets?
Stack the numbers and multiply 4 X 40.
Martin will end up paying $160 for four train tickets.
Multiplying with Larger Numbers
When you multiply larger numbers, be sure to carry and, then add the appropriate
numbers.
For example:
TO MULTIPLY 143 X 5:

First, multiply 5 x 3.

You get the partial product: 15.

Place 5 in the ones place of the product and
carry the 1.

Now, multiply 5 X 4 to get 20.

Add 20 and the 1 that you carried to get 21.

Place the 1 in the tens place and carry the 2.

Next, multiply 5 X 1 to get 5.

Add 5 and the 2 that you carried to get 7.

Place the 7 in the hundreds place to get the final product: 715.
More Multiplication
When you multiply even larger number, you need to do some more addition to get your
product. As you multiply, stack and add the partial products to get your product.
Remember to keep the partial products in the correct value places.
For example:
TO MULTIPLY 15 X 143:

First, multiply 5 x 143 to get 715.

Be sure that the 5 in 715 occupies the one place
on the line below the problem.
20
As adapted from http://www.gcflearnfree.org/math

Next, multiply 1 x 143 to get 143.

Since the 1 occupied the tens place in the problem—place the 3 in the 143 in the
tens place.

The final step is to add the partial products (715 and 143 together) to get your
final answer.
Try It!
You need to order 12 first aid kits for your organization at a cost
of $129 each. How much will they cost?
The total cost of 12 first aid kits will be $1,548.
Practice
1. Multiply 5 X 82
2. Multiply 6 X 48
3. Multiply 12 X 185
4. Robert wants to buy 3 pairs of pants at a cost of $23. How much will he spend?
5. Anna buys 6 boxes of printer paper at a cost of $25 per box. How much does she
spend?
6. Multiply 14 X 32
7. Multiply 15 X 102
8. Ed leases storage space for $90 per month. How much does he pay to lease it for
12 months?
9. Multiply 16 X 180
10. Multiply 9 X 104
Answers: (1) 410 (2) 288 (3) 2220 (4) $69 (5) $150 (6) 448 (7) 1,530 (8) $1,080 (9)
2,880 (10) 936
Sometimes it is helpful to use a calculator to multiply large numbers – that will be
the focus in this class.
21
As adapted from http://www.gcflearnfree.org/math
Division is the opposite of multiplication. Instead of combining groups many times (like
you do when you multiply), when you divide numbers, you are splitting them into
smaller, equal groups. You won’t always have equal groups when you are dividing
numbers or items, sometimes, you may have items leftover – what do you do then? In
this lesson we will figure that out by: explaining the concept of dividing numbers, giving
division practice, helping you divide numbers that have remainders and showing you how
to check your division.
What is Division?
Division is the opposite of multiplication. It’s a method of making equal groups.
Suppose you have 12 flowers and you want to divide them among 4 family members. If
you divide the flowers equally, how many flowers will each person get?
You could write the problem like this: 12/4 = ____. The
slash, /, means “divided by.”
Or you could write the problem with the division
symbol, ÷. So 12 ÷ 4
Either way you write it, each person gets three roses. Since 3 X 4 = 12, you can see the
connection between multiplication and division. Know the multiplication table can help
you with division
Remember factors from the multiplication lesson? A good rule to remember is that a
number (for example 12) is always divisible by its factors (1, 2, 3, 4, 6 and 12). That
means that you can divide 12 equally by 1, 2, 3, 4, 6, and 12.
Quotient, Dividend and Divisor
When you divide a
number, the answer you get
is the quotient.
The number that you’re
dividing is the dividend. 
The number that you’re dividing by is the divisor. 
22
As adapted from http://www.gcflearnfree.org/math
Dividing Numbers
When dividing numbers you can set them up in threes ways:
To divide a two-digit number:



Work on one digit at a time, beginning on the left. In this case,
divide 2 by the 2 in the tens place of 24. (2/2 = 1).
 Place a 1 in the ten’s place of the quotient. It’s
important to place the numbers in the correct digit places
of your quotient.
 Next, subtract (in this case subtract 2 – 2)
Bring down the remaining number 4.
Next divide 4 by 2. (Place your answer, 2, on top in your quotient and
subtract 4 below).
Once you get a 0 at the bottom and there are no more numbers to divide,
stop. Look at the top to get your answer, or quotient. (In this case, 12)
If you’ve practices your times tables, you probably know that 24 divided by 2 is 12
because 12 x 2 = 24!
Try It!
You need divide 46 brochures equally to distribute at two
different meetings. How many brochures will you take to each
meeting?
23
As adapted from http://www.gcflearnfree.org/math
Remainder
While division is a process of making equal groups, not all numbers divide equally. The
remainder is the number after you divide.
Suppose you want to divide 38 notepads equally among 12 people: 38/12 = ?

Since you may recall from the times tables 3 X 12 = 36, put a
3 in the one’s place of the quotient.

Next, subtract. In this case, subtract 38-36)

You get a remainder of 2. So, if you have 38 file notepads
that you need to divide among 12 people, each person would
get 3 and you’d have 2 leftover.
The remainder is always less than the divisor. If you get a remainder that is greater
than the divisor, check your division.
Checking Your Division
For 38/12, you got a quotient of 3 and a remainder of 2. Remember
38 is the dividend and 12 is the divisor.
Check you division by multiplying. Be sure to put the numbers in
their correct digit places.

Since you may recall from the times tables that 3 X 12 = 36,
put a 3 in the one’s place of the quotient.

Next, subtract. (In this case, subtract 38-36)

You get a remainder of 2. So, if you have 38 file notepads that you need to divide
among 12 people, each person would get 3 and you would have 2 left over.
24
As adapted from http://www.gcflearnfree.org/math
Try It!
Fourteen children have completed a summer reading program.
Thirty-two books need to be divided among them as a reward.
How many books will each child get and how many will be
left over?
If you figured out that each child will get two books and four
will remain, you're right.
Practice
1. Doug and three friends earned 184 doing yardwork. Divide 184 by 4 to find out
what each person earned
2. Jason and Greg have to make 34 deliveries. If they divide by 2, how many
deliveries will each person do?
3. 84 / 5 =
4. 256 /12 =
5. 44 / 20 =
6. Divide 52 by 7
7. Divide 336 by 3
8. 456 / 8 =
9. If you have 240 boxes of books to divide among 10 schools. How many boxes
does each school get?
10. The company has 275 accounts which 5 representatives handle equally. How
many accounts does each representative handle?
Answers: (1) 46 (2) 17 (3) 16 r 4 (4) 21 r 4 (5) 2 r 4 (6) 7 r 3 (7) 112 (8) 57 (9) 24 (10) 55
accounts
Division Made Easy
Sometimes you need to divide numbers quickly. If you are at dinner and splitting the bill
with some friends, you need to know your portion of the bill. You probably won’t want
to write it out on the napkin, even if you did you have a pen.
Next, are some tricks to making dividing numbers easier for you, including: checking to
see if the number is evenly divisible and using a calculator.
25
As adapted from http://www.gcflearnfree.org/math
Is it Divisible?
How can you tell if a number is divisible by another (equally)? Here are some tips for
dividing by 3, 4, 5 and 10.
Dividing by 3:
Add up the digits. If you can divide the sum by three, the number is divisible by three.
For example, you want to divide 75 by 3:
Check by adding 7 +5
You get 12
Is 12 divisible by 3? YES
So, now you know you can get equal groups of 3 out of 75. In fact, if you divide
75 by 3, you get 25.
Dividing by 4:
Look at the last two digits. If they are divisible by 4, the number is as well.
144 is divisible by 4 and so it 39312.
Dividing by 5:
If the last digit is a five or a zero, then the number is divisible by 5.
40, 100, 945, and 1,235 are all divisible by 5.
Dividing by 10:
If the number ends in a 0, then it’s divisible by 10.
40, 190, and 1,330 are all divisible by 10.
Using a Calculator to Divide
Sometimes you may not want to divide in your head or on a paper, especially if dealing
with large numbers.
Suppose you need to divide 2,112 cartons of supplies equally among 32 schools. How
many cartons will each school get?
Type in 2112 into the keypad, hit the division sign ÷, and then enter the next number (32
in this case) and press the = sign. The answer is 66.
26
As adapted from http://www.gcflearnfree.org/math
Try It!
You decide to put half of your $1,384
pay cheque into your chequing account
and half into your savings account.
Using a calculator, divide $1,384 by 2
to figure out the amount you'll put in
each account.
If you calculated and got $692 as the
answer, you are right. That's half of a
$1,384 pay cheque.
Practice
1. Is 45 equally divisible by 3?
2. Is 64 equally divisible by 4?
3. Is 220 equally divisible by 4?
4. Is 95 equally divisible by 5?
5. Is 1,937 equally divisible by 5?
6. Is 2,440 equally divisible by 10?
7. Is 3,432 equaly divisible by 10?
8. Using a calculator divide 4,432 by 8.
9. Using a calculator divide 1,872 by 12
10. Using a calculator divide 12,192 by 48
Answers: (1)Yes (2)Yes (3)Yes (4) Yes (5)No (6) Yes (7)No (8)554 (9) 156 (10) 254
27
As adapted from http://www.gcflearnfree.org/math
Basic Fraction Review
What is a FRACTION? In math, fractions are a way to represent parts of a whole
number. Imagine you have a pizza for dinner. That pizza can be cut into any number of
pieces so that everyone at dinner can have a piece. Since each slice is a part, or fraction,
of the whole pizza.
You can add fractions – if your friend had two slices of pizza and then has another. You
can subtract them, too – if there are two slices left and you take one.
But adding and subtracting fractions can be challenging. There are certain steps you have
to do to make sure you get the correct answer.
Anyone can read and write fractions.
Adding fraction is easy if they have common denominators.
Subtracting fractions with common denominators is a snap.
Working with improper fractions and mixed numbers doesn’t have to be scary.
A fraction is a number that is part of a whole.
Suppose you cut an apple pie into 8 slices.
You and your friends eat 7 slices. The 1 slice
that remains is a fraction of the whole pie: 1/8
A fraction can refer to a certain part of a group of items. For example, one of your
neighbours has 3 pets: 1 dog and 2 cats.
1/3 of the pets (group) are dogs.
2/3 of the pets (group) are cats.
Try It!
What fraction describes the following statement?
Four of the five staff members prefer to meet in the morning.
If you figured out that 4/5 of the staff likes to meet in the morning, you're correct.
28
As adapted from http://www.gcflearnfree.org/math
Numerators and Denominators
A fraction has 2 parts: a numerator and a denominator
The denominator is the number of equal parts into
which a whole is divided. It’s written at the bottom
(below the line of the fraction).
The numerator names a certain number of those parts.
It’s written on top (above the line in a fraction).
Reading and Writing Fractions
When you read or write fractions, you use regular number words for the numerator.
However, you use special words for the denominator.

For example, 1/3 is read “one third”
However, if the numerator is more than 1, then the denominator is plural.

For example, 2/3 is read “two thirds”
Here is a short list of some of the words used to describe denominators:

2 – half

3 – third

4 – fourth

5 – fifth

6 – sixth

7 – seventh

8 – eighth

9 – ninth

10 – tenth

11 – eleventh

12 – twelfth
For more numbers, a good rule to remember is to add a “th” as in 13 thirteenth to 100
hundredth.
29
As adapted from http://www.gcflearnfree.org/math
Reducing a Fraction to its Simplest Form
Reducing a fraction to its simplest form means changing it to a fraction that has the same
value as the original but uses smaller numbers.
For example, if you have a pizza with 4 pieces and you eat 2 pieces of that pizza, you
have eaten ½ of the pizza. So 2/4 reduced to its simplest form is ½.
To reduce a fraction to its simplest form you need to be able to
divide the same number into both the top number (numerator) and
the bottom number (denominator) of the fraction.
Reduce a Fraction:
In the case of the pizza, 2 and 4 can both be divided by 2.
The simplest form of 2/4 is ½.
Now reduce 9/12 to its simplest form.
Divide the numerator and the denominator by 3.
The simplest form of 9/12 is ¾.
You can do this more than once and you can divide by any number as long as you can
divide evenly by the same number on the top as you do on the bottom. Dividing evenly
means there will be no remainder.
For example, to reduce 48/60 to its simplest form, do it in steps.
 Divide the numerator and the denominator by 6 to get 8/10.
 Then divide both numbers by 2 to get 4/5.
The simplest form of 48/60 is 4/5.
30
As adapted from http://www.gcflearnfree.org/math
Let’s do one more example. Reduce 24/64 to its simplest form.
You can reduce 24/64 down by dividing by 2 multiple times.
The simplest form of 24/64 is 3/8.
We found that by dividing by the same number (2)
several times.
When there are no more common factors (numbers that can be divided evenly into both
the numerator and the denominator) you have found the simplest form of that fraction.
Because some fractions are already in simplest form you will not always need to reduce.
Example: ½ is in its lowest form so you would not need to reduce.
Adding or Subtracting Fractions with Common Denominators
To add of subtract fractions, you need common denominators – denominators that
are the same. Add or subtract the numerators and place the result over the common
denominator.
To add 1/5 and 2/5:




First, add the numerators: 1 plus 2 to get 3.
Bring over the common denominator of 5.
Place the 3 over the common denominator.
The answer is 3/5.
If the denominators are not the same, you need to find the lowest common
denominator. This means finding the smallest multiple that the denominators have in
common.
31
As adapted from http://www.gcflearnfree.org/math
Improper Fractions and Mixed Numbers
Typically the numerator of a fraction is less than the denominator. However, sometimes
you may encounter improper fractions where the numerator is larger than the
denominator. In that case, you can divide the numerator by the denominator to get a
mixed number: a whole number and a fraction.
Suppose you combine 3/5 of a gallon of ginger ale with 4/5 of a gallon or
orange/pineapple juice to make punch. You would get an improper fraction of 7/5.
To get a mixed number out of 7/5:

Divide 7 by 5

Get the whole number 1 with a remainder of 2.

The 2 becomes the numerator in your fraction.

Place the 2 above the denominator to get 2/5.

Your answer is 1 2/5.
So, by combining the ginger ale and juice, you get 1 2/5 gallons of
punch.
Any fraction with the same number for its numerator and its
denominator is equal to 1 because a number divided by itself
equals 1.
Try It!
Change these improper fractions into mixed numbers.
4/3
11/8
If you changed 4/3 to 1 1/3 and 11/8
into 1 3/8, you've done it correctly.
32
As adapted from http://www.gcflearnfree.org/math
Practice
1. John shared his birthday cake with some friends. The birthday cake was sliced
into 10 pieces and 7 pieces were eaten. What fraction of the cake was eaten?
2. When Kenneth and family decided to go out to eat, 5 out of 7 family members
wanted Chinese food. What fraction wanted Chinese food?
3. Add 4/8 and 1/8.
4. Jessica adds 3/4 cup of water to 1/4 cup of water. How much water does she
have?
5. Change this improper fraction into a mixed number: 14/3.
6. Change this improper fraction into a mixed number: 13/9.
7. You would write the fraction 1/4 as ________.
8. You would write the fraction 4/5 as ________.
9. One sixth can be written as the fraction ________.
10. Seven tenths can be written as the fraction ________.
Answers: (1) 7/10 (2) 5/7 (3) 5/8 (4) 4/4 or 1 cup (5) 4 2/3 (6) 1 4/9 (7) one fourth (8)
four fifths (9) 1/6 (10) 7/10
33
As adapted from http://www.gcflearnfree.org/math
Decimal and Percentage Review
In math, decimals are just another way to show fractions. The decimal numbers you are
probably most familiar with are money. One dollar is sometimes written as $1.00. Four
quarters equal one dollar. A quarter is ¼ of a dollar and it is written as $0.25. 0.25 is the
written decimal for fraction ¼. It will get easier with practice  Practice will include:
reading and writing decimals, adding decimals, subtracting decimals, converting
decimals to fractions and using a calculator with decimals.
What is a Decimal?
A decimal is another way of describing a fraction. Decimals and fractions are names for
parts of a whole.
Decimals are commonly used when dealing with any type of money. For example, if you
have eight dollars and fifteen cents, it’s written as a decimal:
This means that you have eight whole dollars and 15 parts of a
dollar.
Decimals are written using a decimal point that looks like a period.
Reading and Writing Decimals
Decimals are fractions with special denominators. You write decimals as tenths,
hundredths and thousandths because the place value of decimals tells you the value of
each digit.
Decimals, unlike whole numbers, have place values to the right of the decimal point.
The illustration below shows the place values for
12.935
This number can be read or written as twelve and nine
hundred thirty-five thousandths. Notice that you
read the place value of the last digit.
34
As adapted from http://www.gcflearnfree.org/math
Fractions as Decimals
Remember, decimals are another way of showing fractions. Let’s look at how some
fractions convert into decimals: 8/10 is the same as 0.8 or 8 tenths.
If a fraction has a denominator of 10,
100 or 1000 you can easily find the
decimal equivalent by looking at the
numerator and counting over the
correct number of places.
For example, to convert 23/100 into a decimal:
 Start at the right of the 23 in the numerator and move two places to the left.
 Place a decimal point to the left of the 23 to show 0.23 or twenty three
hundredths.
For other fractions, you can divide to find the decimal equivalent. For example, if you
use a calculator to divide 1/8 (1 divided by 8) you get 0.125
Try It!
Quickly find the decimal equivalent of 3/10. Remember the decimal place values.
3/10 = 0._________
If you ended up with .3, then you got the right decimal.
Adding or Subtracting Decimals
Here are some tips to keep in mind when working with decimals:
Add or subtract in their place values.
You can estimate the sum or result when adding or subtracting decimals.
Suppose you decide to pay for a friend’s lunch. Your meal cost $6.54 while your friend’s
meal cost $5.95, how much will you spend for both meals?
To estimate the total bill, think of it this way:
0.95 (in 5.95) is close to whole number 1, so 5.95 is close to 6
0.54 (in 6.54) is close to 0.50, so 6.54 is close to 6.50
If you combine 6 and 6.50 you get an estimate of $12.50
35
As adapted from http://www.gcflearnfree.org/math
Using a Calculator to Add or Subtract Decimals
If you don’t want to add of series of decimal numbers such as 15.38 + 29.39 + 124.25 in
your head or on paper, use a calculator. You can also easily subtract decimals using this
tool.
Familiarize yourself with the location of the decimal point on your calculator since you
will use it a lot when working with decimals.
Try It!
Use a calculator to subtract 212.45 from 436.58:
If you calculated correctly, your answer is 224.13
Practice
1. At the store, you buy two sodas and a bag of chips for $2.14 and you give the
cashier $5.25 How much money should you get back in change?
2. Add 11.04 and 4.33
3. Subtract 2.14 from 16.23
4. Stacy's part-time catering business had $7,234.25 in sales last year. This year the
company had $8,225.50 in sales. Use a calculator to find out the different between
how much more money the business had in sales this year versus last year.
5. Using a calculator subtract 586.54 from 1,750.85.
6. Change 16/100 into a decimal.
7. Change 3/10 into a decimal.
8. Write the words for .34:__________________
9. Write the words for .9:____________________
10. Write the words for .124: __________________________________
Answers: (1)3.11 cents (2) 15.37 (3)14.09 (4) $991.25 (5) 1164.31 (6) .16 (7) .3 (8) thirty
four hundredths (9) nine tenths (10) one hundred twenty four thousandths
36
As adapted from http://www.gcflearnfree.org/math
Percents Made Easy
Every time you go shopping, you are dealing with decimals and percents. But what is
percentage?
You must have seen signs that say Sale Today – 25% off! 25% off tells you that you are
getting a good deal – you will save twenty-five percent or twenty-five cents for each
dollar that the item costs. The actual amount of money you don’t have to spend on the
item is the percentage you’ve saved.
This lesson will teach you more about how percents are related to decimals and fractions.
It will also give you the chance to practice changing percents to decimals, figuring
percentages using sale prices, dealing with percentages.
What is a Percent?
Fractions, decimals and percents are related. A percent is another way to identify part of
a whole. In fact, a percent is a fraction where the denominator is 100!
For example, 15 percent is equal to 15/100 or 0.15
The gold shaded areas in the
picture below represent 15
percent.
YOU WRITE PERCENT USING THE % SIGN as in 15%
Some situations in which you might deal with percents:
taxes, interest store sales and tips.
37
As adapted from http://www.gcflearnfree.org/math
Changing Percents to Decimals
Sometimes, you may need to change a percent to a decimal. The decimal point in a
percent doesn’t appear but it’s understood to be at the left of the number. For example,
in 75%, the “invisible” decimal point is to the left of the “7”: 0.75
75% and 0.75 are equal – they mean the exact same thing.
To change a percent to a decimal:
 Add a decimal point two places to the
left. (if the percent is one digit and
doesn’t have two places to the left, add a
zero to the left to create two decimal
places.)
 Drop the percent sign
 Remove any zeros in the hundredths
place of a decimal (see chart)
Try It!
Change 35 percent to a decimal.
If you moved the “invisible” decimal point and got 0.35 then
you got the correct answer!
38
As adapted from http://www.gcflearnfree.org/math
Changing Decimals to Percents
You’ve learned how to change percents to
decimals. Now, let’s learn how to change
decimals to percents.
To change a decimal to a percent:
 Move the decimal point two places to
the right
 Remove the decimal point
 Add a percent sign
Figuring Out Percentages and Sale Prices
How often have you seen items on sale in a store for 10% or 15% off? Learn about
percentages so you’ll be able to quickly figure out potential savings on merchandise.
A percentage is a given percent of another number. For example, 50 percent of 40 is 20.
The percentage is 20.
To calculate a percentage:
 Change the percent to a decimal. (since 50 percent equals .50 you can drop the
zero: .5)
 Multiply the decimal by the whole number you are dealing with (.5 X 40)
 Remember, when multiplying by a decimal count over the same number of
decimal places in your answer. (.5 X 40 = 20.0 or 20)
 So, 50% of $40 is $20
Knowing how to calculate percentages can be helpful when you are trying to determine
the sale price of an item. For example, Lynn found a suit on sale for 30% off. The suit
regularly costs $50. What is the sale price?
To find the sale price of an item:
 First, find out the percentage is by change the percent into a decimal and
multiplying: (.3 X 50 = 15)
 To find the sale price of an item, subtract the percentage: (50-15 = 35)
 To $50 suit, at a discount, is $35
39
As adapted from http://www.gcflearnfree.org/math
Try It!
Jason found a $30 jacket on sale for 15% off. What's the dollar amount off?
If you figured out that 15% off of $30 is $4.50 then you can
quickly figure out that the sales price of the jacket is $25.50.
Tips for Dealing with Percents
Occasionally you may need to change a fraction to a percent. Here is a quick way to do
it:

Multiple the fraction by 100/1

Simplify if possible and divide

Add the percent sign
For example, ¼ X 100/1 = 100/4. Divide 100 by 4 and you get 25. or 25%
Need to figure out 10% of a number? Move the “understood” decimal point one place
over to the left. For example, 10 percent of 20 is 2 and 10 percent of 85 is 8.5.
Practice
1. What is 15% of $25?
2. If you save 15% off of a $25 shirt, what is the sale price of the item?
3. What is 50% of 42?
4. 10% of 40 =
5. 20% of 40 =
6. If you purchased a TV for $100 and the sales tax is 6%, what is the total cost of
the TV?
7. You would like to leave a 15% tip for a lunch that cost $8.75, how much do you
leave?
8. If you have a coupon worth 25% off an item that normally costs $75, what is the
sale price of the item?
9. What is 50 percent of 60?
10. If 70 people out of 100 passed a test, what percentage of people passed the test?
Answers: (1) 3.75 (2) $21.25 (3) 21 (4) $4 (5) $8 (6) $106 (7) $1.31 (8) $56.25 (9) 30
(10) 70
40
As adapted from http://www.gcflearnfree.org/math
Order of Operations Review
When there is more than one operation involved in a mathematical problem (for example
multiplication and addition in the same question), it must be solved by using the correct
order of operations. A number of teachers use acronyms with their students to help them
to retain the order. Remember, calculators will perform operations in the order which you
enter them, therefore, you will need to enter the operations in the correct order for the
calculator to give you the right answer.
* In Mathematics, the order in which mathematical problems are solved is extremely
important.
Rules:
1. Calculations must be done from left to right.
2. Calculations in brackets (parenthesis) are done first. When you have more than one set
of brackets, do the inner brackets first.
3. Exponents (or radicals) must be done next.
4. Multiply and divide in the order the operations occur.
5. Add and subtract in the order the operations occur.
Remember to:




Simplify inside groupings of parentheses, brackets and braces first. Work with the
innermost pair, moving outward.
Simplify the exponents.
Do the multiplication and division in order from left to right.
Do the addition and subtraction in order from left to right.
BEDMAS (Brackets, Exponents, Divide,
Multiply, Add, Subtract)
41
As adapted from http://www.gcflearnfree.org/math
Examples
12 ÷ 4 + 32
12 ÷ 4 + 9
3+9
12
(42 + 5) - 3
21 - 3
18
20 ÷ (12 - 2) X
32 - 2
20 ÷ 10 X 32 - 2
20 ÷ 10 X 9 - 2
18 - 2
16
Rule 3: Exponent first
Rule 4: Multiply or Divide as
they appear
Rule 5: Add or Subtract as
they appear
Rule 2: Everything in the
brackets first
Rule 5: Add or Subtract as
they appear
Rule 2: Everything in the
brackets first
Rule 3: Exponents
Rule 4: Multiply and Divide
as they appear
Rule 5: Add or Subtract as
they appear
Does It Make a Difference? What If I Don't Use the Order of Operations?
Mathematicians were very careful when they developed the order of operations.
Without the correct order, watch what happens:
15 + 5 X 10 -- Without following the correct order, I know that 15+5=20 multiplied by
10 gives me the answer of 200.
15 + 5 X 10 -- Following the order of operations, I know that 5X10 = 50 plus 15 = 65.
This is the correct answer, the above is not!
You can see that it is absolutely critical to follow the order of operations. Some of the
most frequent errors students make occur when they do not follow the order of operations
when solving mathematical problems. Students can often be fluent in computational work
yet do not follow procedures. Use the handy acronyms to ensure that you never make this
mistake again.
42
As adapted from http://www.gcflearnfree.org/math
How to Round Numbers
When rounding whole numbers there are two rules to remember:
Rule One. Determine what your rounding digit is and look to the right side of it. If the
digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are on the right
hand side of the requested rounding digit will become 0.
Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is
5, 6, 7, 8, or 9, your rounding digit rounds up by one number. All digits that are on the
right hand side of the requested rounding digit will become 0.
Rounding with decimals: When rounding numbers involving decimals, there are 2 rules
to remember:
Rule One Determine what your rounding digit is and look to the right side of it. If that
digit is 4, 3, 2, or 1, simply drop all digits to the right of it.
Rule Two Determine what your rounding digit is and look to the right side of it. If that
digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.
An example:
765.3682 becomes:
1000 when asked to round to the nearest thousand (1000)
800 when asked to round to the nearest hundred (100)
770 when asked to round to the nearest ten (10)
765 when asked to round to the nearest one (1)
765.4 when asked to round to the nearest tenth (10th)
765.37 when asked to round to the nearest hundredth (100th.)
765.368 when asked to round to the nearest thousandth (1000th)
43
As adapted from http://www.gcflearnfree.org/math
Skills Review POST-TEST
44
As adapted from http://www.gcflearnfree.org/math
Skills Review POST-TEST Continued…
45
As adapted from http://www.gcflearnfree.org/math
BOOKLET #1 Review
Please answer the following questions on a separate sheet of paper. This will help you to
prepare for the test on this booklet. Answers have been provided and full solutions will
be available in class. A reminder you may also have a single-sided, hand-written
(printed) 8.5 x 11 CHEAT SHEET for the test. This must be completed ahead of time.
Please show all of your work – calculators can be used.
1. Do the following operations
a)
Add 1,204 + 620
b)
Subtract 5,789 – 385
c)
Multiply 59 X 42
d)
Divide 365 ÷ 73
2. Add or subtract the following fractions:
a)
4/5 + 2/5 = ? , now – convert it to a mixed fraction.
b)
½+¾=?
3. Calculate the following using the correct order of operations.
a)
(7 + 6 X 5)2 = ?
b)
10 + (34 – 6 ÷ 2) - 15 = ?
c)
3–1+5X6=?
2
4. Convert 56% to a reduced fraction.
5. Convert 8/9 to a decimal. Use your calculator. Round to 2 decimal places.
6. Solve the following:
a)
40/60 is what percent (round to 1 decimal place)?
b)
Write 0.3879 as a percent.
c)
Write 3.7 as a percent.
d)
9/10 is what percent?
7. Convert 43.5% to a decimal.
Answers:
(1 a) 1824 (b) 5405(c) 2478 (d) 5 (2 a) 6/5 = 1 1/5 (b) 5/4 or 1 ¼ (3 a) 1369 (b) 73 (c) 16
(4) 14/25 (5) 0.89 (6 a) 66.7% (b) 38.79% (c) 370% (d) 90% (7) 0.435
46
As adapted from http://www.gcflearnfree.org/math
Resources Used and Websites for Extra Practice
The majority of this booklet was adapted from was adapted from
http://www.gcflearnfree.org/math
Websites for Extra Practice:
Awesome Website for reviewing the basics of Addition and Subtraction
http://www.gcflearnfree.org/additionandsubtraction
Practice Place Values http://www.aaamath.com/g4-21b-placevaluebutton.html#section2
More information on multiplication and factors
http://www.math911.com/pwc/03Multiplication%20Whole%20Factors.pdf
Beginning fractions http://www.aaamath.com/B/fra16_x2.htm
Adding fractions http://www.aaamath.com/B/fra410x2.htm
Order of Operations
http://math.about.com/library/weekly/aa040502a.htm
http://www.mathgoodies.com/lessons/vol7/order_operations.html
http://glencoe.mcgraw-hill.com/sites/dl/free/0078740428/589238/m1_nat_wpwb.pdf
Rounding
http://math.about.com/od/arithmetic/a/Rounding.htm
47
As adapted from http://www.gcflearnfree.org/math