Overview
How does math play a role in everyday life? You can use
math in many ways: to find an address, make change, or
count calories. You can also use it to balance your
checkbook, measure ingredients, or take medication.
Clearly, math skills are important. In particular, this course
teaches you how to add, subtract, multiply, and divide
whole numbers and fractions. Moreover, throughout the
course, you will apply these topics to real-life situations.
Therefore, the goal of this course is to help you develop
basic math skills you need for daily living and further
studies.
This course includes twelve lessons. Lesson 1 introduces
whole numbers. Lessons 2 through 5 explain how to add,
subtract, multiply, and divide whole numbers. Lesson 6
describes certain relationships among whole numbers.
Lessons 7 and 8 introduce fractions and mixed numbers.
Lessons 9 and 10 explain how to multiply and divide
fractions. Finally, Lessons 11 and 12 describe how to add
and subtract fractions.
Overview
v
This course also includes some special features. “Math
Tips” supplement key information in each lesson. “Math in
Real Life” sections apply math skills to everyday activities.
For clarity, the lessons are written from the point of view of
a student using either print or a braillewriter. Keep this in
mind if you are using a slate and stylus to complete your
work for this course. For example, the lessons tell you to
write numbers from left to right. Slate and stylus users,
however, will write numbers in reverse, from right to left.
The practice exercises in each lesson are for your
personal development only. Do not send your responses
to your Hadley instructor. Rather, check your
comprehension by comparing your answers with those
provided. You can always contact your instructor,
however, to clarify concepts. You are also required to
submit twelve assignments, one at the end of each lesson.
These assignments enable your instructor to measure
your understanding of the material presented in the
course.
If you are ready to explore practical math, begin Lesson 1:
What Are Whole Numbers?
vi
Practical Math 1
Overview
vii
Lesson 1: What Are Whole Numbers?
Which one comes first? Which one comes last? Many
things form an order: calendar days, check numbers, and
street addresses, to name a few. You can also compare
items: Which soap brand has the lowest price? Which
player scored the most points? Lesson 1 introduces some
characteristics and basic uses of whole numbers.
Understanding these numbers helps you develop the math
skills you need for daily living and further studies.
Objectives
After completing this lesson, you will be able to
a.
b.
c.
d.
e.
f.
define whole numbers
indicate place value
change whole numbers from words to digits and vice
versa
tell if a whole number is greater than, less than, or
equal to another whole number
put whole numbers in order from least to greatest and
vice versa
round a whole number to the nearest ten, hundred, or
thousand
Lesson 1: What Are Whole Numbers?
1–1
Key Terms
The following terms appear in this lesson. Familiarize
yourself with their meanings so you can use them in your
course work.
digits: symbols that represent numbers: 0, 1, 2, 3, 4, 5, 6,
7, 8, and 9
equal sign (=): the symbol that means “equivalent to,” or
“having the same value”
even numbers: whole numbers that have 0, 2, 4, 6,
or 8 as the last digit
greater-than sign (>): the symbol that means “greater
than,” or “having larger value”
less-than sign (<): the symbol that means “less than,” or
“having smaller value”
odd numbers: whole numbers that have 1, 3, 5, 7, or 9 as
the last digit
place value: the value of a digit, which varies depending
on the digit's place in a number
rename: to indicate the place value of each digit in a
number
round: to change a number to the nearest place value, as
specified (i.e., to the nearest ten, hundred, thousand,
or so on)
1–2
Practical Math 1
whole numbers: digits starting with zero and going on
indefinitely, with each one being one more than the
previous one; used to count or tell how many
About Whole Numbers
This section defines whole numbers. It also identifies the
difference between even and odd numbers.
People use whole numbers to count, or to tell how many.
To write whole numbers, you use digits, which are the
numeric symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Whole
numbers start with 0 and continue into the millions,
billions, and beyond. The following is a list of whole
numbers from 0 to 50:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42, 43, 44, 45, 46, 47, 48, 49, 50
A single- or one-digit number has only one digit in it. Some
examples are 1, 3, and 8. Double- or two-digit numbers
have two digits in them. For example, 12, 25, and 78 are
all two-digit numbers.
Lesson 1: What Are Whole Numbers?
1–3
The whole numbers that end in 0, 2, 4, 6, or 8 are called
even numbers. For example, the number 72 is even
because it ends in 2. The whole numbers that end in 1, 3,
5, 7, or 9 are called odd numbers. For example, the
number 83 is odd because it ends in 3. In order, whole
numbers form a pattern: an odd number follows each even
number and vice versa.
You also can tell whether larger numbers are odd or even.
For example, 795 is odd number because it ends in 5. The
number 824 is even because it ends in 4.
Math Tip
The last digit on the right helps you determine if a
number is odd or even.
Example 1
How would you write the whole numbers from 10 to 20?
Remember, each whole number is one more than the
previous number. So the whole numbers from 10 to 20 are
10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.
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Practical Math 1
Example 2
Suppose you have the following list of numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15. Which of
these numbers are odd numbers?
Odd numbers end in 1, 3, 5, 7, or 9. The odd numbers in
this list are 1, 3, 5, 7, 9, 11, 13, and 15.
Example 3
Consider this list of whole numbers:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39, and 40. Which are
the even numbers?
Even numbers end in 0, 2, 4, 6, and 8. The even numbers
in this list are 30, 32, 34, 36, 38, and 40.
Math in Real Life
You use whole numbers in your everyday life. For
example, you probably write or tell people your address.
Most street addresses have a number and a street name,
such as 421 Elm Street.
In many cities, addresses with odd numbers are on one
side of the street, and addresses with even numbers are
on the other side. For example, the number 701 is odd,
Lesson 1: What Are Whole Numbers?
1–5
and the number 728 is even. So 701 Pine Street and 728
Pine Street usually would be on opposite sides of the
street.
Consider the following real-life example:
Jeffrey is on his summer vacation, and this is his first time
visiting relatives in another city. He’s planning how to
travel to different homes. In this city, odd-numbered
addresses are on the east side of the street, and even
ones are on the west.
What side of the street is each of the following addresses
on?
 Uncle Ralph and Aunt Clothilde
510 Central Street
Their house is on the west side: 510 is an even number.
 Cousin Tiffany
201 Skokie Boulevard
Their house is on the east side: 201 is an odd number.
Practice Exercise 1–1
1. Write the whole numbers from 20 to 30.
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Practical Math 1
2. Write the even numbers from 30 to 40.
3. Write the odd numbers from 40 to 50.
The following addresses are in a city where evennumbered addresses are on one side of the street, and
odd-numbered addresses are on the other. For each pair,
tell whether or not the addresses are on the same side of
the street and explain your answer.
4. 910 Avenue A and 916 Avenue A
5. 566 Ohio Street and 567 Ohio Street
6. Li moves from 129 Oak Street to 144 Oak Street. Is
she still on the same side of the street?
7. Tony lives at 801 Ocean Drive. Tina lives at 710
Ocean Drive. Do they live on the same side of the
street?
Answers 1–1
1. The whole numbers from 20 to 30 are 20, 21, 22, 23,
24, 25, 26, 27, 28, 29, and 30.
2. The even numbers from 30 to 40 are 30, 32, 34, 36,
38, and 40.
Lesson 1: What Are Whole Numbers?
1–7
3. The odd numbers from 40 to 50 are 41, 43, 45, 47,
and 49.
4. They are on the same side of the street. The numbers
910 and 916 are both even.
5. They are on opposite sides of the street. The number
566 is even and 567 is odd.
6. No, Li moved across the street. The number 129 is
odd and 144 is even.
7. No, Tony and Tina live on different sides of Ocean
Drive. The number 801 is odd, and the number 710 is
even.
This section defined whole numbers. It also discussed the
difference between even and odd numbers. Why not use
this information when you try to locate addresses?
Place Value
Numbers consist of digits. Place value refers to the value
of a digit, which varies depending on its place in a number.
You may find place-value charts helpful. When solving
math problems, use place-value columns.
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Practical Math 1
Place-Value Charts
When determining the place value of digits in a number,
work from right to left. The places in a number from right to
left are ones, tens, hundreds, thousands, ten thousands,
hundred thousands, millions, ten millions, hundred
millions, and so on. Starting from the right, a comma
comes after every third digit in a number.
Math Tip
To find the place value of a number, start with the ones
place and work toward the left.
Consider the following numbers. In each of them, the
6 stands for a different value, as noted:
 67
The 6 means 6 tens.
 605
The 6 means 6 hundreds.
 26
The 6 means 6 ones.
A simple chart can help illustrate the place value of each
digit in these numbers. A place-value chart is made up of
Lesson 1: What Are Whole Numbers?
1–9
columns, each for a specific place value. Going from right
to left, the chart has a column for ones, tens, hundreds,
and so forth.
Hundreds
6
Tens
Ones
6
7
0
5
2
6
If asked the value of a particular digit, you can use a
place-value chart to find the answer. For example, what is
the value of the digit 2 in the number 26? In this case, the
digit 2 is in the tens column, or the second column from
the right. Therefore, the digit 2 means 2 tens.
You can also use this chart to rename an entire number.
When you rename a number, you are saying the same
number but in a different way by showing the place value
of each digit:
 67 = 6 tens + 7 ones
 605 = 6 hundreds + 5 ones
(Note that you can skip, or not mention, a zero when
renaming a number.)
1–10
Practical Math 1
 26 = 2 tens + 6 ones
Math Tip
Think of the word rename. The prefix re- means
“again.” For example, the words redo, rebuild, and refill
mean “do again,” “build again,” and “fill again.” When
you rename a number, you’re naming it again in a way
that makes the number easier to use. Whether you call
the number 67 or 6 tens plus 7 ones, you are talking
about the same number!
Example
Consider this number:
4,328,765
You can use a place-value chart to show the value of its
digits:
Hundred
Ten
Million
Thousand
Thousand
Thousand
Hundred
Ten
One
s
s
s
s
s
s
s
4,
3
2
8,
7
6
5
Lesson 1: What Are Whole Numbers?
1–11
If someone asks you the value of a particular digit of this
number, you can use the chart to find the answer. For
example, what is the value of the digit 8 in the number
4,328,765? The digit 8 is in the thousands column, or the
fourth column from the right; therefore, it means 8
thousands.
Using this chart, you can also rename the entire number to
show the place value of each digit, as follows:
4,328,765 = 4 millions + 3 hundred thousands + 2 ten
thousands + 8 thousands + 7 hundreds + 6 tens + 5 ones
When solving place-value problems, you may want to
make charts like the ones shown here. Some people
prefer to memorize the order of the place values (ones,
tens, hundreds, thousands, etc.). Use the method that you
feel most comfortable with.
Math Tip
Starting from the right, a comma comes after every
third digit in a number.
1–12
Practical Math 1
Place-Value Columns
When you solve math problems, consider the place value
of the numbers you use. Often, you need to put numbers
in columns according to place value. To do so, vertically
line up the ones with the ones, the tens with the tens, and
so forth. Consider how you line up these three numbers
vertically:
67
605
26
All the ones digits are lined up one on top of the other, and
the same is true for the other place-value digits.
Remember place-value columns when you solve problems
later in this course.
Example
Consider how you line up these numbers vertically:
10,245
5,627
831
Lesson 1: What Are Whole Numbers?
1–13
All the ones digits are lined up one on top of the other, and
the same is true for the tens, hundreds, thousands, and
ten thousands. In this case, the 5 of 10,245 and the 7 of
5,627 and the 1 of 831 all are in the ones place. So they
all line up, one on top of the other, in the ones column.
Math in Real Life
You may encounter place values on the job, at school, at
the store, and elsewhere. Consider the following
examples:
 Tia needs a new washing machine. A machine costs
435 British pounds. How many hundreds are in the
cost?
Rename the amount: 435 equals 4 hundreds plus 3 tens
and 5 ones. So 4 hundreds are in the cost.
 The Carlson Corporation has an annual budget of
$3,270,500. How many millions are in the budget?
Rename the amount: 3,270,500 equals 3 millions +
2 hundred thousands + 7 ten thousands + 5 hundreds.
Therefore, 3 millions are in the budget.
1–14
Practical Math 1
 A school is collecting canned food for hurricane victims.
So far, the school has 1,324 cans. How many
thousands of cans have they collected?
Rename the number to show the place value of each
digit: 1 thousand + 3 hundreds + 2 tens + 4 ones. So the
school has collected over 1 thousand cans.
 Rashid was taking inventory at a home improvement
store. He counted 2,985 nails. He needs to fill out a form
that shows the place value of each digit. How would he
fill out the form?
Rename the number as follows: 2 thousands +
9 hundreds + 8 tens + 5 ones
Practice Exercise 1–2
Find the value of the digit 5 in each number.
1. 657
2. 59,672
3. 215,389
Lesson 1: What Are Whole Numbers?
1–15
Rename the following numbers to show the place value of
each digit:
4. 47
5. 9,944
6. 35,276
Line up the following numbers in place-value columns.
7. 1,853 and 175 and 14
8. 55,238 and 870 and 25
Solve the following real-life problems.
9. Sonia wants to buy a new sofa. The one she likes
costs $720. How many hundreds are in the cost?
10. In an election, the winning candidate received
3,226,905 votes. Rename the number to show the
place value of each digit.
Answers 1–2
1. 657 = 6 hundreds + 5 tens + 7 ones
The value of the digit 5 in the number 657 is 5 tens.
1–16
Practical Math 1
2. 59,672 = 5 ten thousands + 9 thousands +
6 hundreds + 7 tens + 2 ones
The value of the digit 5 in the number 59,672 is 5 ten
thousands.
3. 215,389 = 2 hundred thousands + 1 ten thousand + 5
thousands + 3 hundreds + 8 tens + 9 ones
The value of the digit 5 in the number 215,389 is 5
thousands.
4. 47 = 4 tens + 7 ones
5. 9,944 = 9 thousands + 9 hundreds + 4 tens +
4 ones
6. 35,276 = 3 ten thousands + 5 thousands +
2 hundreds + 7 tens + 6 ones
7. 1,853
175
14
8. 55,238
870
25
Lesson 1: What Are Whole Numbers?
1–17
9. 720 = 7 hundreds + 2 tens + 0 ones
7 hundreds are in the cost.
10. 3,226,905= 3 millions + 2 hundred thousands + 2 ten
thousands + 6 thousands + 9 hundreds + 5 ones
This section explained place value. It described how to
rename a number to show the place value of each digit. It
also described how to write numbers using place-value
columns. Remember these steps the next time you’re
considering the cost of a purchase.
Words and Digits
This section explains how to read and write whole
numbers by using words and by using digits. Read and
write numbers from left to right. Starting from the right, a
comma comes after every third digit in a number.
Changing a Number from Digits to Words
When changing a number from digits to words, follow
these steps:
 Work from left to right.
1–18
Practical Math 1
 Think in “threes.” Remember, a comma marks every
three digits of a number, counting from the right. Write
or say the number to the left of the first comma. For
example, consider the number 536,123. Begin by saying
“five hundred thirty-six.”
 When you reach the comma, write or say the place
name of the last digit of the “three numbers” but drop
the s. Again, consider 536,123. The place value of the
last digit before the comma is thousand. Say or write
“five hundred thirty-six thousand.”
 When you reach the ones place value, just say the
number, not the place value. Just say “five hundred
thirty-six thousand, one hundred twenty-three.” You
wouldn’t say “ones.”
Example
Consider how you would write or say the number
4,328,765 in words. If you prefer, make a place-value
chart such as the following to help you:
Lesson 1: What Are Whole Numbers?
1–19
Hundred
Ten
Million
Thousand
Thousand
Thousand
Hundred
Ten
One
s
s
s
s
s
s
s
4,
3
2
8,
7
6
5
 Start from the left; write the number that precedes the
first comma: four.
 Write or say the place-value name that immediately
precedes that comma, leaving off the s: million.
 So far you have “four million.”
 Write or say the number that precedes the next comma:
three hundred twenty-eight.
 Write or say the place-value name that immediately
precedes that comma, leaving off the s: thousand.
 You now have “three hundred twenty-eight thousand.”
 Write or say the next “three numbers,” but don’t say
“ones” for that place value: seven hundred sixty-five.
1–20
Practical Math 1
 The number 4,328,765 can be written as “four million,
three hundred twenty-eight thousand, seven hundred
sixty-five.”
Changing a Number from Words to Digits
When changing a number from words to digits, follow
these steps:
 Write each number you hear or read, using digits
instead of words.
 Write zeros for missing places.
 Write a comma every three places from the right.
Example
Consider the number five million, four hundred eighty-four.
To change it to digits, follow these steps:
 Write the number, using digits.
5 million, 484
 Fill in zeros for any missing place values. In this case,
the missing place values are hundred thousands, ten
thousands, and thousands. Write a comma every
three places from the right. The number is 5,000,484.
Lesson 1: What Are Whole Numbers?
1–21
 If you choose, make a place-value chart to check your
answer.
Hundred
Ten
Million
Thousand
Thousand
Thousand
Hundred
Ten
One
s
s
s
s
s
s
s
5,
0
0
0,
4
8
4
To summarize, five million, four hundred eighty-four can
be written as 5,000,484.
Math Tip
Commas help you group the parts of a number.
Math in Real Life
Writing large numbers with words or digits is useful in real
life, especially when discussing large groups of people.
For example, city populations are important: they are the
topic of newspaper articles, classroom discussions, and
government analysis. Moreover, in studying city
populations, you learn about the world around you.
Latasha is a journalist, and she is writing an article
comparing the populations of different cities around the
1–22
Practical Math 1
world. How would she use words to write the following city
populations?
 In 2006, Nairobi, Kenya, had a population of about
32,021,800.
Nairobi had a population of about thirty-two million,
twenty-one thousand, eight hundred.
 In 2006, Tokyo, Japan, had a population of about
34,200,000.
Tokyo had a population of about thirty-four million, two
hundred thousand.
Now examine how Latasha would use digits to write these
city populations:
 In 2006, Athens, Greece, had a population of about
three million, five hundred thousand.
Athens had a population of about 3,500,000.
 In 2006, Hong Kong, China, had a population of about
six million, eight hundred ninety-eight thousand, seven
hundred.
Hong Kong had a population of about 6,898,700.
Lesson 1: What Are Whole Numbers?
1–23
Practice Exercise 1–3
Write the following numbers in words.
1. 13,728
2. 200,914
3. 3,050,425
Write the following numbers in digits.
4. four hundred fourteen thousand, six hundred three
5. sixteen million, five hundred sixteen thousand, ninetyfive
Use words to write the following city populations.
6. In 2006, Paris, France, had a population of about
9,875,000.
7. In 2006, Mexico City, Mexico, had a population of
about 18,700,000.
Use digits to write the following city populations.
8. In 2002, Calcutta, India, had a population of about
four million, six hundred seventy thousand.
1–24
Practical Math 1
9. In 2002, Los Angeles, United States, had a population
of about three million, eight hundred five thousand,
four hundred.
Answers 1–3
1. 13,728 = thirteen thousand, seven hundred twentyeight
2. 200,914 = two hundred thousand, nine hundred
fourteen
3. 3,050,425 = three million, fifty thousand, four hundred
twenty-five
4. four hundred fourteen thousand, six hundred three =
414,603
5. sixteen million, five hundred sixteen thousand, ninetyfive = 16,516,095
6. 9,875,000 = nine million, eight hundred seventy-five
thousand
7. 18,700,000 = eighteen million, seven hundred
thousand
Lesson 1: What Are Whole Numbers?
1–25
8. four million, six hundred seventy thousand =
4,670,000
9. three million, eight hundred five thousand, four
hundred = 3,805,400
This section described how to read and write whole
numbers. Specifically, it showed how to use words or
digits. This may be helpful when you are using large
numbers to describe national populations or budgets.
Comparing Whole Numbers
This section explains how to compare whole numbers,
using certain symbols. The symbol > means “is greater
than.” The symbol < means “is less than.” The symbol =
means “is equal to.”
Now study how these symbols are used:
9 > 4 means “9 is greater than 4”
2 < 11 means “2 is less than 11”
7 = 7 means “7 is equal to 7”
1–26
Practical Math 1
When comparing two numbers, note how they may each
have a different number of digits. In such a case, the
number with more digits is greater than the other number.
Consider these numbers: 4,325 and 972. Which is
greater?
 4,325 has four digits.
 972 has three digits.
 Therefore, 4,325 > 972.
If you were asked, “Which number is less than the other?”
you would respond that 972 < 4,325.
Some numbers you compare will have an equal number of
digits. In this case, do the following:
 Line up the numbers vertically by place value.
 Compare the digits with the largest place value first. In
other words, start from the left.
 If the digits are the same, go to the next place value and
compare them. Continue until one digit is greater than
the other in the same place-value column.
Lesson 1: What Are Whole Numbers?
1–27
 If all the digits are the same, however, then the numbers
are equal.
Example 1
Consider these numbers: 7,345 and 7,281. Which is
greater?
 Line up the numbers vertically by place value:
7,345
7,281
 Compare the numbers starting from the left. The first
digit in both numbers is 7, so skip this digit.
 Compare the next digits, 3 and 2: 3 > 2.
 Therefore, 7,345 > 7,281
If you were asked, “Which number is less than the other?”
you would respond that 7,281 < 7,345.
Example 2
Now compare 67,500 and 67,500:
 Line up the numbers vertically by place value:
67,500
67,500
1–28
Practical Math 1
 They have the same digits in the same order.
 Therefore, 67,500 = 67,500.
Math Tip
Whether solving problems in real life or doing word
problems for an assignment, you can follow certain
steps to make it easier. First read the problem
carefully. Then plan what you need to do. Next do the
necessary steps to solve the problem. When you have
your answer, check if it makes sense.
Math in Real Life
You may find that you already compare whole numbers in
your daily life. For example, people often compare the
price of two products to find the best deal.
Jeannette wants to buy a coffeemaker. She notices that
the hardware store sells one for $99. At a grocery store,
the same coffeemaker costs $75. Which store has the
better price?
Lesson 1: What Are Whole Numbers?
1–29
Plan
What is the problem asking you to do? It is asking you to
compare two numbers, 99 and 75.
Solve
Line up the numbers vertically by place value. Then,
starting from the left, compare the digits.
99
75
9>7
99 > 75
Answer
The grocery store sells the coffeemaker for the lower price
of $75, so Jeannette decides to buy it there.
Practice Exercise 1–4
Indicate whether the following items are true or false. If
false, revise the item to make it true.
1. 15 > 19
2. 70 = 70
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Practical Math 1
3. 156 < 99
4. 708 = 1,200
5. 62,305 > 62,004
Solve the following real-life problems; explain each
answer.
6. Luke has saved $1,927 for a new computer. He finds
a computer that costs $1,650. Does Luke have
enough money to buy the computer?
7. Janice and Steve are playing the same video game.
Janice scored 675,486 points. Steve scored 625,486
points. Who scored the most points?
Answers 1–4
1. False. 15 < 19
2. True
3. False. 156 > 99
4. False. 708 < 1,200
5. True
Lesson 1: What Are Whole Numbers?
1–31
6. Luke has enough money to buy the computer
because 1,927 > 1,650.
7. Janice scored the most points because
675,486 > 625,486.
This section explained how to compare whole numbers. It
introduced specific symbols: >, <, and =. You may find this
helpful the next time you’re comparing prices or
populations.
Ordering Whole Numbers
What you have learned about comparing numbers can
help you put them in order. You can order numbers from
least to greatest or vice versa.
Ordering from Least to Greatest
When ordering numbers from least to greatest, first find
the smallest number. Then find the smallest of the
remaining numbers. Keep doing this until you have the
numbers in order from least to greatest.
How would you order the numbers 4,208; 496; and 4,501
from least to greatest?
 First find the smallest number.
1–32
Practical Math 1
 The number 496 has three digits, while the other
numbers have four digits. Therefore, the number 496 is
smallest.
 Compare 4,208 and 4,501; line them up vertically by
place value:
4,208
4,501
 Compare the digits in the largest place value. Here the
largest place value is the thousands place. But both
numbers have a 4 in the thousands place, so go to the
next place value. The number 4,208 has a 2 in the
hundreds place, and 4,501 has a 5 in the hundreds
place.
 You know that 2 < 5. Therefore, 4,208 < 4,501.
 The numbers from least to greatest are 496; 4,208; and
4,501.
Example
Examine how you would order these numbers from least
to greatest: 375; 924; and 2,873.
 First find the smallest number.
Lesson 1: What Are Whole Numbers?
1–33
 The numbers 375 and 924 have three digits, while the
other number has four digits. Therefore, the numbers
375 and 924 are smaller than 2,873.
 Compare 375 and 924. Line them up vertically by place
value.
375
924
 Compare the digits in the largest place value.
3<9
 Therefore, 375 < 924.
 The numbers from least to greatest are 375; 924; and
2,873.
Ordering from Greatest to Least
When you order numbers from greatest to least, first find
the largest number. Then work down from there.
How would you order the numbers 152, 178, and 165 from
greatest to least?
 First find the largest number. All three numbers have
three digits. Therefore, you cannot tell which number is
the greatest just by considering the number of digits.
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Practical Math 1
 So line up the numbers vertically by place value.
152
178
165
Consider the digits in the largest place value. All the
numbers have the digit 1 in the hundreds place;
therefore, go to the tens place.
 Compare the digits in the tens place: 7 > 6 > 5.
 The numbers from greatest to least are 178, 165, and
152.
Example
Consider how you would order these numbers from
greatest to least: 252; 371; and 4,325:
 Find the largest number.
 The number 4,325 has four digits, while the other
numbers have three digits. So 4,325 is the largest.
 Next compare the remaining numbers 252 and 371.
Since they have the same number of digits, line them up
by place value:
252
Lesson 1: What Are Whole Numbers?
1–35
371
 Compare the digits in the largest place value. Here, the
largest place value is the hundreds place. The number
371 has a 3 in the hundreds place, and 252 has a 2 in
the hundreds place.
 You know that 3 > 2. Therefore, 371 > 252.
 The numbers from greatest to least are 4,325; 371; and
252.
Math in Real Life
You can put many items in numerical order, such as
checks and invoices. Ordering these items helps you
perform certain tasks. For example, putting checks in
order makes balancing your checkbook easier. If you work
at an office, numbering invoices helps you track them.
For example, Jaya wants to balance her checkbook. She
wants to record checks with the following numbers: 362,
360, 364, 361, and 363. How would she write the check
numbers in order from least to greatest?
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Practical Math 1
Plan
Determine what the problem is asking you to do. It is
asking you to put these numbers in order from least to
greatest: 362, 360, 364, 361, and 363.
Solve
Line up the numbers by place value. Starting from the left,
compare the digits.
362
360
364
361
363
3=3
6=6
0<1<2<3<4
360 < 361 < 362 < 363 < 364
Answer
Jaya would write the check numbers in this order from
least to greatest: 360, 361, 362, 363, and 364.
Lesson 1: What Are Whole Numbers?
1–37
Practice Exercise 1–5
Order each of the following groups of numbers from least
to greatest.
1. 45, 86, 2
2. 698; 1,243; 742
3. 2,906; 1,381; 660
Order each of the following groups of numbers from
greatest to least.
4. 12, 47, 35
5. 1,375; 6,001; 1,075
6. 54,800; 62,961; 51,244
Solve the following real-life problems.
7. A store is selling three television sets with prices as
follows: $375, $380, and $350. To find the best price,
put them in order from least to greatest.
8. In 1790, Connecticut had a population of 238,000;
Massachusetts had a population of 379,000; and New
York had a population of 340,000. Your history
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Practical Math 1
teacher asks you to list the states by population from
greatest to least.
Answers 1–5
1. 2 < 45 < 86
2. 698 < 742 < 1,243
3. 660 < 1,381 < 2,906
4. 47 > 35 > 12
5. 6,001 > 1,375 > 1,075
6. 62,961 > 54,800 > 51,244
7. The prices in order from least to greatest are $350,
$375, and $380. (350 < 375 < 380)
8. In 1790, the states by population from greatest to
least were Massachusetts, New York, and
Connecticut. (379,000 > 340,000 > 238,000)
This section explained how to order whole numbers. You
can put numbers in order from least to greatest or vice
versa. Follow the steps shown in this lesson the next time
you’re in a store deciding which product to purchase.
Lesson 1: What Are Whole Numbers?
1–39
Rounding Whole Numbers
Sometimes, you do not need to know an exact number.
Instead, you need to know an approximate amount, or
about how many. You can find this information by
rounding, or changing, a number to the nearest ten,
hundred, thousand, ten thousand, hundred thousand,
million, or so on. This section, however, focuses on
rounding to the nearest ten, hundred, and thousand.
The tens numbers are 10, 20, 30, 40, 50, 60, 70, 80, and
90. The hundreds numbers are 100, 200, 300, 400, 500,
600, 700, 800, and 900. The thousands numbers are
1,000; 2,000; 3,000; 4,000; 5,000; 6,000; 7,000; 8,000;
and 9,000.
When rounding numbers, keep the following in mind:
 If the digit to the right of the rounding place is less than
5, then round down.
 If the digit to the right of the rounding place is 5 or
greater, then round up.
 When you finish rounding, the digit(s) to the right of the
rounding place will always be zero(s).
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Practical Math 1
 If the digit in the rounding place is a 9, you may need to
round up to the next higher place.
Math Tip
When rounding, consider the digit in the rounding place,
as well as the digit to the right of the rounding place.
Example 1
Consider how you would round 74 to the nearest ten:
 The digit in the tens, which is the rounding place, is 7.
 To the right of the digit 7 is the digit 4.
 Because 4 < 5, round 74 down to 70.
Example 2
Consider how to round 95 to the nearest ten:
 The digit in the tens, which is the rounding place, is 9.
 To the right of the digit 9 is the digit 5.
 Because 5 = 5, round 95 up to 100.
 Note that because the digit in the rounding place is 9,
you move up to the next higher place (i.e., from the tens
to the hundreds).
Lesson 1: What Are Whole Numbers?
1–41
Example 3
How would you round 986 to the nearest hundred?
 The digit in the hundreds, which is the rounding place, is
9.
 To the right of the digit 9 is the digit 8.
 Because 8 > 5, round 986 up to 1,000.
 Note that because the digit in the rounding place is 9,
you move up to the next higher place (i.e., from the
hundreds to the thousands).
Example 4
Study how you would round 2,631 to the nearest
thousand:
 The digit in the thousands, which is the rounding place,
is 2.
 To the right of the digit 2 is the digit 6.
 Because 6 > 5, round 2,631 up to 3,000.
Math in Real Life
Many everyday activities involve rounding whole numbers.
For example, people often round dollar amounts when
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Practical Math 1
filling out tax or financial aid forms. People also estimate
(i.e., round) when answering certain questions, such as
the following: About how far away is the park? About how
long does it take to get there?
Hidalgo has $1,274 in his savings account. He needs to
include an estimate of this amount on a credit-card
application. How would he round this amount to the
nearest thousand?
Plan
Round 1,274 to the nearest thousand.
Solve
The digit in the thousands place is 1. To its right is the digit
2. Because 2 < 5, round 1,274 down to $1,000.
Answer
If Hidalgo needs to round the amount in his savings
account to the nearest thousand, he would round $1,274
to $1,000.
Practice Exercise 1–6
Round each number to the nearest ten.
1. 84
Lesson 1: What Are Whole Numbers?
1–43
2. 37
Round each number to the nearest hundred.
3. 335
4. 453
Round each number to the nearest thousand.
5. 3,595
6. 9,817
Solve the following real-life problems.
7. You have $734 dollars in the bank. Is the amount you
have closer to $700 or $800?
8. 5,972 people attended a soccer game. You work for a
newspaper. Round the number of people to the
nearest thousand to include in a headline.
Answers 1–6
1. 84 rounded to the nearest ten is 80.
2. 37 rounded to the nearest ten is 40.
3. 335 rounded to the nearest hundred is 300.
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Practical Math 1
4. 453 rounded to the nearest hundred is 500.
5. 3,595 rounded to the nearest thousand is 4,000.
6. 9,817 rounded to the nearest thousand is 10,000.
7. $734 is closer to $700 (i.e., 734 rounded to the
nearest hundred is 700).
8. 5,972 rounded to the nearest thousand is 6,000.
This section explained how to round whole numbers. It
demonstrated how to round them to the nearest ten,
hundred, and thousand. Use this information the next time
you need to estimate an amount of money!
Summary
This lesson introduced whole numbers, including the
difference between even and odd numbers. It also
explained place value. Moreover, you learned how to read
and write whole numbers, both by using words and by
using digits. In addition, this lesson described how to
compare, order, and round whole numbers.
Lesson 1: What Are Whole Numbers?
1–45
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Practical Math 1
Assignment 1
For general instructions on completing assignments, refer
to the Welcome Letter. Start this assignment by giving
your full name, address, and telephone number. Also list
the course title, Assignment 1, your instructor’s name, and
the date. Be sure to include the question number along
with each answer. Where applicable, show each step you
take to find an answer. This way, your instructor may
assign partial credit even if your answer is wrong. This
assignment is worth 100 points.
Assignment questions have the following point values:
1 through 16: 2 points each
17 through 20: 5 points each
21 through 26: 4 points each
27 through 30: 6 points each
Choose the correct response for each of the following
questions.
1. Which of the following numbers is an odd number?
a. 3
b. 4
c. 6
Assignment 1
1–47
2. In the number 548, which digit is in the tens place?
a. 5
b. 4
c. 8
3. When you change a number to the nearest place
value, what are you doing?
a. renaming
b. counting
c. rounding
Identify each number as even or odd.
4. 56
5. 1,327
Find the value of the digit 4 in each number.
6. 941
7. 4,678,913
Rename each number to show the place value of each
digit.
8. 96
9. 2,475
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Practical Math 1
Write each number in words.
10. 15,212
11. 100,510
Write each number in digits.
12. six thousand, eight hundred, ninety-one
13. fifty-four thousand, six hundred seven
Indicate whether the following equations or inequalities are
true or false.
14. 24 < 24
15. 984 < 1,065
16. 98,245 = 97,856
Order the numbers from least to greatest.
17. 75, 72, 9
18. 6,725; 1,350; 5,461
Order the numbers from greatest to least.
19. 72, 94, 86
Assignment 1
1–49
20. 26,750; 32,825; 26,891
Round each number to the nearest ten.
21. 37
22. 81
Round each number to the nearest hundred.
23. 496
24. 250
Round each number to the nearest thousand.
25. 7,464
26. 9,530
Solve the following real-life problems.
27. Tamara lives at 890 Lake Shore Drive. Michael lives
at 875 Lake Shore Drive. In their city, odd-numbered
addresses are on one side of the street, and evennumbered ones are on the other. Also, addresses that
have the same digit in the hundreds place are on the
same block.
a. Do Tamara and Michael live on the same block?
How do you know?
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Practical Math 1
b. Do they live on the same side of the street? How
do you know?
28. Pat has saved $2,100 for a new computer. He finds
one that costs $2,325. Does Pat have enough money
to buy the computer? Explain your answer.
29. City A has a population of 394,017; City B has a
population of 368,383; and City C has a population of
358,548. List the cities by population from least to
greatest.
30. You have $2,100 in a savings account. Is the amount
you have closer to $2,000 or $3,000?
When you have completed this assignment, proceed to
Lesson 2: Addition with Whole Numbers.
Assignment 1
1–51