Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.2 Place Value and Names for Numbers

Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Place Value The digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 can be used to write numbers. The whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, … The position of each digit in a number determines its place value.

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples a. 48,761 b. 249 c. 524,007,656 Find the place value of the digit 4 in each whole number. ten-thousands tens millions

Martin-Gay, Basic Mathematics, 4e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Whole Numbers in Words and Standard Form The whole number 1,083,664,500 is written in standard form. Each group of three digits is called a period.

Martin-Gay, Basic Mathematics, 4e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write each number in words. a. 36 b. 487 c. 32,984 thirty-six four hundred eighty-seven thirty-two thousand, nine hundred eighty-four

Martin-Gay, Basic Mathematics, 4e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Whole Numbers in Words and Standard Form

Martin-Gay, Basic Mathematics, 4e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write each number in standard form. a. seventy-two b. nine hundred six c. eight thousand, six hundred fifty-four ,654

Martin-Gay, Basic Mathematics, 4e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Writing a Whole Number in Expanded Form The expanded form of a number shows each digit of the number with its place value.

Martin-Gay, Basic Mathematics, 4e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Write 804,557 in expanded form. 800,

Martin-Gay, Basic Mathematics, 4e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Reading Tables Tables are often used to organize and display facts that involve numbers.

Martin-Gay, Basic Mathematics, 4e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example

Martin-Gay, Basic Mathematics, 4e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example a. How many total Nobel Prize winners are from France? b. Which countries have more Nobel Prize winners than Germany? Germany has 82, The United Kingdom has 110 and the United States has

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.3 Adding Whole Numbers and Perimeter

Martin-Gay, Basic Mathematics, 4e 14 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers, p 16 When the sum of digits in corresponding place values is more than 9, carrying is necessary. Example: ones + 9 ones = 14 ones or 1 ten + 4 ones Write the 4 in the ones place and carry the 1 ten to the tens place. 1 ten + 6 tens + 8 tens = 15 tens or 1 hundred + 5 tens Write the 5 tens in the tens place and carry the 1 hundred to the hundreds place. Add the hundreds-place digits.

Martin-Gay, Basic Mathematics, 4e 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example, p 17 Add: 32, ,761 Practice Problem 2 Add: 27, , ,341

Martin-Gay, Basic Mathematics, 4e 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers, p 17 Addition Property of 0 The sum of 0 and any number is that number. For example, = = 7

Martin-Gay, Basic Mathematics, 4e 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers, p 17 Commutative Property of Addition Changing the order of two addends does not change their sum. For example, = 5 and = 5.

Martin-Gay, Basic Mathematics, 4e 18 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers, p 18 Associative Property of Addition Changing the grouping of addends does not change their sum. For example, 3 + (5 + 7) = = 15 and (3 + 5) + 7 = = 15. Apply Practice 3 to the Commutative and Associative Properties

Martin-Gay, Basic Mathematics, 4e 19 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding the Perimeter of a Polygon A polygon can be described as a flat figure formed by line segments connected at their ends. The perimeter of a polygon is the distance around the polygon. This means that the perimeter of a polygon is the sum of the lengths of its sides. P 18

Martin-Gay, Basic Mathematics, 4e 20 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the perimeter of the polygon. 5 in 8 in 4 in 3 in 6 in To find the perimeter (distance around), we add the lengths of the sides. 5 in. + 8 in. + 6 in. + 3 in. + 4 in. = 26 in. P 19

Martin-Gay, Basic Mathematics, 4e 21 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Adding, p 19 Key Words or Phrases ExampleSymbols added to 2 added to plus 5 plus increased by 13 increased by more than 9 more than total the total of 3 and sum the sum of 391 and P 19

Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Adding Example The state of Hawaii has 1851 miles of urban highways and 2291 miles of rural highways. Find the total highway mileage in Hawaii. (Source: U.S. Federal Highway Administration) P 20

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.4 Subtracting Whole Numbers

Martin-Gay, Basic Mathematics, 4e 24 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Subtracting Whole Numbers To subtract whole numbers, we subtract the digits in the ones place, then the tens place, then the hundreds place, and so on. Example: 7826 – 505 Line up numbers vertically so that the place values correspond. Then subtract the digits in corresponding place values, starting with the ones place. P 29

Martin-Gay, Basic Mathematics, 4e 25 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Subtracting by Borrowing When subtracting vertically, if a digit in the second number (subtrahend) is larger than the corresponding digit in the first number (minuend), borrowing is necessary. DefinitionExample Borrowing: Necessary when subtracting vertically if a digit in the second number is larger than the corresponding digit in the first number. P 30

Martin-Gay, Basic Mathematics, 4e 26 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Subtracting Whole Numbers Example: 900 – 174 P 30

Martin-Gay, Basic Mathematics, 4e 27 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Subtracting Key Words or Phrases ExampleSymbols subtract subtract 2 from 7 7 – 2 difference the difference of 13 and 1 13 – 1 less 19 less 5 19 – 5 less than 3 less than – 3 take away 16 take away 4 16 – 4 decreased by 8 decreased by 7 8 – 7 subtracted from 6 subtracted from – 6 P 31

Martin-Gay, Basic Mathematics, 4e 28 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Subtracting Example Dyllis King is reading a 503-page book. If she has just finished reading page 239, how many more pages must she read to finish the book? P 32

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 1.5 Rounding and Estimating

Martin-Gay, Basic Mathematics, 4e 30 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rounding Whole Numbers Rounding a whole number means approximating it. 26 is closer to 30 than 20, so 26 is rounded to the nearest ten is is closer to 50 than 60, so 52 is rounded to the nearest ten is 50. P 39

Martin-Gay, Basic Mathematics, 4e 31 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rounding Whole Numbers 25 is halfway between 20 and 30. It is not closer to either number. In such a case, we round to the larger ten, that is, to 30. P 39

Martin-Gay, Basic Mathematics, 4e 32 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Rounding Whole Numbers Round 32 to the nearest 10 th Round 36 to the nearest 10 th Round 35 to the nearest 10 th Round to 30 Round to 40 Rounding Whole Numbers to a Given Place Value Step1: Locate the digit to the right of the given place value. Step 2: If this digit is 5 or greater, add 1 to the digit in the given place value and replace each digit to its right by 0. Step 3: If this digit is less than 5, replace it and each digit to its right by 0. P 39

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Examples 1. Round 568 to the nearest ten. 2. Round 278,362 to the nearest thousand. 3. Round 248,982 to the nearest hundred , ,000 P 40

Martin-Gay, Basic Mathematics, 4e 34 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Estimating Sums and Differences Example Estimate the sum by rounding each number to the nearest hundred. P 41

Martin-Gay, Basic Mathematics, 4e 35 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Estimating Example Jared Nuss scored 89, 92, 100, 67, 75 and 89 on his biology tests. Round each score to the nearest ten to estimate his total score. P 41

Martin-Gay, Basic Mathematics, 4e 36 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. DONE