Chapter 1 – Slide 1 Chapter 1 Whole Numbers Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 1 – Slide 2 Section 1.1 Introduction to Whole Numbers

Chapter 1 – Slide 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.

Chapter 1 – Slide Reading and Writing Whole Numbers 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.

Chapter 1 – Slide Example Identify the place value of the 8. a. 508 b. 8,430,999 c. 6,800,000,002

Chapter 1 – Slide 6 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. Reading and Writing Whole Numbers

Chapter 1 – Slide Example How do you read the number 521,000,072?

Chapter 1 – Slide 8 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. Reading and Writing Whole Numbers

Chapter 1 – Slide 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? BILLIONSMILLIONSTHOUSANDSONES OHTOHTOHTO

Chapter 1 – Slide 10 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 = BILLIO NS MILLIONSTHOUSANDSONES OHTOHTOHTO 5293

Chapter 1 – Slide Example Write 803 in expanded form. Write 8,407,800 in expanded form:

Chapter 1 – Slide Rounding Whole Numbers

Chapter 1 – Slide Rounding Whole Numbers

Chapter 1 – Slide 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?

Chapter 1 – Slide 15 Example 1-15 Write in words the amount of money taken in by The Lord of the Rings: The Two Towers

Chapter 1 – Slide 16 Example Round to the nearest ten million dollars the world total for The Lord of the Rings: The Two Towers.

Chapter 1 – Slide 17 Section 1.2 Adding and Subtracting Whole Numbers

Chapter 1 – Slide Identities and Properties The Identity Property of Addition The sum of a number and zero is the original number = 3or0 + 5 = 5 The Commutative Property of Addition Changing the order in which two numbers are added does not affect their sum = = 5

Chapter 1 – Slide Identities and Properties 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) = = 13

Chapter 1 – Slide 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.

Chapter 1 – Slide Example 1. Add 56 and Add: 8, , What is the perimeter of the region marked off for the construction of a brick patio? 18 feet 27 feet

Chapter 1 – Slide 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

Chapter 1 – Slide Subtracting Whole Numbers

Chapter 1 – Slide Example 1. Subtract: 219 – Find the difference between 400 and 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?

Chapter 1 – Slide Example Which park had the greatest number of visitors?

Chapter 1 – Slide Example How many visitors were there at Fort Sumter and Kings Mountain?

Chapter 1 – Slide Estimating Sums and Differences An estimation can be used to check an answer and see if your answer is “close” to the exact answer.

Chapter 1 – Slide Example 1. Compute the sum 8, ,825. Check by estimation. 2. Subtract 2,387 from 7,329. Check by estimating.

Chapter 1 – Slide Section 1.3 Multiplying Whole Numbers

Chapter 1 – Slide 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 crayons  5 = 30 The parts of a product, that is the 6 and 5, are called factors.

Chapter 1 – Slide Identities and Properties The Identity Property of Multiplication The product of any number and 1 is that number. 3  1 = 3or12  1 = 12 The Multiplication Property of 0 The product of any number and 0 is 0. 3  0 = 0or12  0 = 0

Chapter 1 – Slide Identities and Properties The Commutative Property of Multiplication Changing the order in which two numbers are multiplied does not affect their product. 3  2 = 2  3 6 = 6 The Associative Property of Multiplication When multiplying three numbers, regrouping the factors gives the same product. (4  7)  2 = 4  (7  2) 28  2 = 4  = 56

Chapter 1 – Slide Multiplying Whole Numbers To multiply whole numbers with reasonable speed, you must commit to memory the products of all single-digit whole numbers.

Chapter 1 – Slide Example 1. Multiply: 76 · 6 2. Multiply: 400  Calculate the area of the home office. 4. Multiply: (17)(4)(3) 8 ft 5 ft 9 ft 14 ft

Chapter 1 – Slide Estimating Sums and Differences An estimation can be used to check an answer and see if your answer is “close” to the exact answer. Examples 1. 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

Chapter 1 – Slide Section 1.4 Dividing Whole Numbers

Chapter 1 – Slide 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.

Chapter 1 – Slide Example Divide and check: 3024 ÷ 6. Compute Then check your answer.

Chapter 1 – Slide 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 R, such as 25 R3.

Chapter 1 – Slide 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.

Chapter 1 – Slide 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.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Section 1.5 Exponents, Order of Operations, and Averages

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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 5 Exponents

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example 1. Rewrite 4 ∙ 4 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 in exponential form. 2. Compute: a. 1 7 b Write 8 3 ∙ 4 2 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.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Example 1. Evaluate: 34 – 9 ∙ Find the value of ∙ (4 ∙ 6 2 ). 3. Find the value of ∙ (4 ∙ 6 2 ). 4. Simplify:

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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?

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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.FriSat High Temp. 42°F49°F53°F39°F30°F41°F54°F

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Calculator Examples 1. Evaluate 27 3 using your calculator. 2. Evaluate ÷ 3 × 2 by hand and check using your calculator.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Section 1.6 More on Solving Word Problems

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Four Basic Operations OperationMeaning +Combining −Taking away ×Adding repeatedly ÷Splitting up

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Clue Words

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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 FreshmenSophomoreJuniorSeniorTotal

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Breaking Up the Question Another effective problem-solving strategy is to break up the given question into a chain of simpler questions.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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?

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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.

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 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?

Chapter 1 – Slide Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Making A Table - Continued After Hour Remaining Miles 11,372 – 65 = 1,307 21,307 – 65 = 1,242 31,242 – 65 = 1, ,112 – 65 = 1,047 61,047 – 65 =