chapter 1 – slide 1 chapter 1 whole numbers copyright © 2008 pearson addison-wesley. all rights...

Chapter 1 – Slide 1

Chapter 1Whole Numbers

Copyright © 2008 Pearson Addison-Wesley. All rights reserved.


Section 1.1

Introduction to Whole Numbers

Chapter 1 – Slide 31-3

Reading and Writing Whole Numbers

We read whole numbers in words, but we use the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 to write them.

We read the whole number fifty-one, but write it 51, which is called standard form.

Each of the digits in a whole number in standard form has a place value.



The place value chart is shown below.

When we write large numbers we insert commas to separate the digits into groups of three, called periods.


Example

Identify the place value of the 8.

a. 508

b. 8,430,999

c. 6,800,000,002


To Read a Whole Number

Working from left to right,

• read the number in each period and then

• name the period in place of the comma.



Example

How do you read the number 521,000,072?


To Read a Whole Number

Working from left to right,

• write the number named in each period and

• replace the period in place of the comma.



Example

1. Write the number six billion, twelve in standard form.

2. The treasurer of a company write a check in the amount of three hundred thousand, two hundred eight. Using digits, how would she write this number?

BILLIONS MILLIONS THOUSANDS ONES

O H T O H T O H T O


Writing Whole Numbers in Expanded Form

Expanded form of a number can be written using the number and its place value of its digits. The place value chart is shown below.

5,293 = 5 thousands + 2 hundreds + 9 tens + 3 ones

Expanded form = 5000 + 200 + 90 + 3

BILLIONS

MILLIONS THOUSANDS ONES

O H T O H T O H T O

5 2 9 3


Example

Write 803 in expanded form.

Write 8,407,800 in expanded form:


Rounding Whole Numbers


Example

Round 89,541 to:

a. the nearest thousand

b. the nearest hundred.

The Robinson’s are having new windows installed. The price is $12,870. How much is this to the nearest thousand dollars?


Example

1-15

Write in words the amount of money taken in by The Lord of the Rings: The Two Towers


Example

Round to the nearest ten million dollars the world total for The Lord of the Rings: The Two Towers.


Section 1.2

Adding and Subtracting Whole Numbers


Identities and Properties

The Identity Property of AdditionThe sum of a number and zero is the original number.

3 + 0 = 3 or 0 + 5 = 5 The Commutative Property of Addition

Changing the order in which two numbers are added does not affect their sum.

3 + 2 = 2 + 3

5 = 5



The Associative Property of Addition

When adding three numbers, regrouping addends gives the same sum. Note that the parentheses tell us which numbers to add first.

(4 + 7) + 2 = 4 + (7 + 2)

11 + 2 = 4 + 9

13 = 13


Adding Whole Numbers

We add whole numbers by arranging the numbers vertically, keeping the digits with the same place value in the same column. Then we add the digits in each column.

When the sum of the digits in a column is greater than 9, we must regroup and carry, because only a single digit can occupy a single space.


Example

1. Add 56 and 39.

2. Add: 8,935 + 478 + 2,825

3. What is the perimeter of the region marked off for the construction of a brick patio?

18 feet

27 feet


Subtracting Whole Numbers

We write the whole numbers underneath one another, lined up on the right, so each column contains digits with the same place value.

Keep the following properties of subtraction in mind.• When we subtract a number from itself, the result

is 0: 6 – 6 = 0 • When we subtract 0 from a number, the result is the

original number: 32 – 0 = 32


Subtracting Whole Numbers


Example

1. Subtract: 219 – 58

2. Find the difference between 400 and 174.

3. The junior class donated 365 cans of food to the food drive. The senior class donated 286 cans. How many more cans did the junior class donate?


Example

http://www.scprt.com/files/Research/National_and_State_Parks.htm

Which park had the greatest number of visitors?


Example

http://www.scprt.com/files/Research/National_and_State_Parks.htm

How many visitors were there at Fort Sumter and Kings Mountain?


Estimating Sums and Differences

An estimation can be used to check an answer and see if your answer is “close” to the exact answer.


Example

1. Compute the sum 8,935 + 478 + 2,825 . Check by estimation.

2. Subtract 2,387 from 7,329. Check by estimating.


Section 1.3Multiplying Whole Numbers


The Meaning and Properties of Multiplication

Multiplication is repeated addition.

For example, suppose you buy 5 packages of crayons for your child and each package has 6 crayons.

6 + 6 + 6 + 6 + 6

30 crayons

+ + + +

6 5 = 30

The parts of a product, that is the 6 and 5, are called factors.



The Identity Property of MultiplicationThe product of any number and 1 is that number.

3 1 = 3 or 12 1 = 12 The Multiplication Property of 0

The product of any number and 0 is 0.

3 0 = 0 or 12 0 = 0



The Commutative Property of MultiplicationChanging the order in which two numbers are multiplied does not affect their product.

3 2 = 2 3 6 = 6

The Associative Property of MultiplicationWhen multiplying three numbers, regrouping the factors gives the same product.

(4 7) 2 = 4 (7 2)28 2 = 4 14

56 = 56


Multiplying Whole Numbers

To multiply whole numbers with reasonable speed, you must commit to memory the products of all single-digit whole numbers.


Example

1. Multiply: 76 · 6

2. Multiply: 400 60

3. Calculate the area of the home office.

4. Multiply: (17)(4)(3)

8 ft

5 ft

9 ft

14 ft


Estimating Sums and Differences

An estimation can be used to check an answer and see if your answer is “close” to the exact answer.

Examples1. Multiply 412 by 198. Check the answer by estimating.

2. A class planning their class trip saved $3000 for theatre tickets. Each ticket costs $62, and a total of 28 tickets are needed. By estimating, decide if the class has set aside enough money for the tickets


Section 1.4Dividing Whole Numbers


The Meaning and Properties of Division

In a division problem, the number that is being used to divide another number is called the divisor. The number being divided is the dividend. The result is the quotient.

We can also think of division as the opposite (inverse) of multiplication.


Example

Divide and check: 3024 ÷ 6.

Compute Then check your answer.49,021

.7


Remainders

(Quotient × Divisor) + Remainder = Dividend

When a division problem results in a remainder as well as a quotient, we use this relationship for checking.

We will often write the results of a division problem as <Quotient> R <Remainder> , such as 25 R3.


Example

1. Find the quotient of 23,399 and 4. Then check.

2. Compute and check.

3. Find the quotient and remainder of 12,861 and 63. Then check.

4. Divide and check: 9,000 ÷ 30.

1,867

23


Checking by Estimating

As for other operations, estimating is an important skill for division. Checking a quotient by estimating is faster than checking it by multiplication, although less exact. And in some division problems, we only need an approximate answer.

Example An office building has an area of 329,479 square feet. If there are 9 floors in the building, estimate the square footage of each floor.


Writing an expression in exponential form provides a shorthand method for representing repeated multiplication of the same factor.

Definition

An exponent (or power) is a number that indicates how many times another number (called the base) is used as a factor.

3 • 3 • 3 • 3 • 3 = 35

Exponents


Example

1. Rewrite 4 ∙ 4 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 in exponential form.

2. Compute:a. 17

b. 132

3. Write 83 ∙ 42 in standard form and evaluate.

4. Approximately 10,000 seedlings were planted in a state forest. Express this number in terms of a power of 10.


Example

1. Evaluate: 34 – 9 ∙ 3.

2. Find the value of 7 + 3 ∙ (4 ∙ 62).

3. Find the value of 7 + 3 ∙ (4 ∙ 62).

4. Simplify:

27 4 8 2 6 .


Averages

Definition

The average (or mean) of a set of numbers is the sum of those numbers divided by however many numbers are in the set.

Example What is the average of 87, 95, and 88?


Example

The following shows the high temperatures in Virginia during one week in November.

a. What is the average temperature for the week?

b. Which day(s) has a temperature higher than the average temperature.

Sun. Mon. Tues. Wed. Thurs. Fri Sat

High Temp.

42°F 49°F 53°F 39°F 30°F 41°F 54°F


Calculator Examples

1. Evaluate 273 using your calculator.

2. Evaluate 5 + 9 ÷ 3 × 2 by hand and check using your calculator.


Section 1.6

More on Solving Word Problems


To Solve Word Problems

• Read the problem carefully

• Choose a strategy (such as drawing a picture, breaking up the question, substituting simpler numbers, or making a table).

• Decide which basic operation(s) are relevant and then translate the words into mathematical symbols.

• Perform the operations.

• Check the solution to see if the answer is reasonable. If it is not, start again by rereading the problem.

Solving Word Problems


Four Basic Operations

Operation Meaning

+ Combining

− Taking away

× Adding repeatedly

÷ Splitting up


Clue Words


Drawing a Picture

Sketching even a rough representation of a problem, can provide insight into its solution.

Example: At Greenfield High School, there are 292 freshmen, 213 sophomores, and 524 juniors. If there are 1,036 total students, how many seniors are there in the school?

Greenfield High School

Freshmen Sophomore Junior Senior Total

292 213 254 1036


Breaking Up the Question

Another effective problem-solving strategy is to break up the given question into a chain of simpler questions.


Example

On her way to work, Melinda must travel through 18 traffic lights. If she is stopped by 5, how many more traffic lights did she get a green light than a red light?

How many traffic lights were green? How many did she get stopped by? How many more traffic lights were green than red?


Substituting Simpler Numbers

A word problem involving large numbers often seems difficult just because of these numbers. A good problem-solving strategy is to consider first the identical problem but with simpler numbers.


Example

Dinner tickets for a benefit are sold at $12 each. How many dinner tickets must be sold before the benefit profits if the break even amount for the cost of food is $2,700?

To determine the operation, substitute a simpler number such as $24 for the break even amount. Because it is a “fit in” question, we must divide $24 by $12. Going back to the original problem, we see that we must

divide $2,700 by 12.


Making a Table

When a word problem involves many numbers, organizing the numbers in a table often leads to a solution.

Example A semi truck driver must travel 1,372 miles to its destination. If the driver travels 65 miles in an hour, how many miles are remaining after 8 hours?


Making A Table - Continued

After Hour

Remaining Miles

1 1,372 – 65 = 1,307

2 1,307 – 65 = 1,242

3 1,242 – 65 = 1,117

4

5 1,112 – 65 = 1,047

6 1,047 – 65 = 982

7

8

chapter 1 – slide 1 chapter 1 whole numbers copyright © 2008 pearson addison-wesley. all rights...

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