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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

Overview v

fractions. Finally, Lessons 11 and 12 describe how to add and subtract fractions.

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

vi Practical Math 1

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?

Overview vii

viii Practical Math 1

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.

ObjectivesAfter completing this lesson, you will be able toa. define whole numbersb. indicate place valuec. change whole numbers from words to digits

and vice versad. tell if a whole number is greater than, less

than, or equal to another whole numbere. put whole numbers in order from least to

greatest and vice versa

Lesson 1: What Are Whole Numbers? 1–1

f. round a whole number to the nearest ten, hundred, or thousand

Key TermsThe 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 9equal 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

1–2 Practical Math 1

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)

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 NumbersThis 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.

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.

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, 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 Tiffany201 Skokie Boulevard

Their house is on the east side: 201 is an odd number.

Practice Exercise 1–11. Write the whole numbers from 20 to 30.

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 even-numbered 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.

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 ValueNumbers 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.


Place-Value ChartsWhen 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 TipTo 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 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 Tens Ones6 7

6 0 52 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.)

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:


Millions

HundredThousan

ds

TenThousan

dsThousan

dsHundre

dsTen

sOne

s4, 3 2 8, 7 6 5

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.

Place-Value ColumnsWhen 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:

67605 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

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 LifeYou 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.

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 1–2Find the value of the digit 5 in each number.1. 657

2. 59,672

3. 215,389

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.

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

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 DigitsThis 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.

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:

Millions

HundredThousan

ds

TenThousan

dsThousan

dsHundre

dsTen

sOne

s4, 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.

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 DigitsWhen 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.

If you choose, make a place-value chart to check your answer.


Millions

HundredThousan

ds

TenThousan

dsThousan

dsHundre

dsTen

sOne

s5, 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 LifeWriting 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 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.

Practice Exercise 1–3Write 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, ninety-five

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.


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 twenty-eight

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, ninety-five = 16,516,095

6. 9,875,000 = nine million, eight hundred seventy-five thousand

7. 18,700,000 = eighteen million, seven hundred thousand


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 NumbersThis 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”


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.

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:

7,3457,281

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:

67,50067,500

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 LifeYou 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?

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.

9975

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 1–4Indicate whether the following items are true or false. If false, revise the item to make it true.1. 15 > 19

2. 70 = 70

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

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 NumbersWhat 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 GreatestWhen 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.

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:4,2084,501


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.

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.

So line up the numbers vertically by place value.152178165


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:252371

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 LifeYou 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?


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.

362360364361363

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.

Practice Exercise 1–5Order 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 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.

Rounding Whole NumbersSometimes, 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).

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.


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).

Example 3

How would you round 986 to the nearest hundred? The digit in the hundreds, which is the rounding

place, is 9.



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.


Because 6 > 5, round 2,631 up to 3,000.

Math in Real LifeMany everyday activities involve rounding whole numbers. For example, people often round dollar amounts when 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 1–6Round each number to the nearest ten.1. 84

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.

4. 453 rounded to the nearest hundred is 500.


5. 3,595 rounded to the nearest thousand is 4,000.


7. $734 is closer to $700 (i.e., 734 rounded to the nearest hundred is 700).


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!

SummaryThis 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.


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 each17 through 20: 5 points each21 through 26: 4 points each27 through 30: 6 points each

Choose the correct response for each of the following questions.

Assignment 1 1–53

1. Which of the following numbers is an odd number? a. 3b. 4c. 6

2. In the number 548, which digit is in the tens place?a. 5b. 4c. 8

3. When you change a number to the nearest place value, what are you doing? a. renamingb. countingc. 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

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

Assignment 1 1–55

18. 6,725; 1,350; 5,461

Order the numbers from greatest to least. 19. 72, 94, 86

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 even-numbered 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?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 1–57

practical math 1 - hadley€¦ · web viewwhich one comes first? ... math tip. think of the word...

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