Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 1 The Whole Numbers

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

Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers An electronics store received a shipment of two boxes of iPod nanos one day and an additional four boxed of iPod nanos the next day. The total shipment in the two days can be found by adding 2 and 4. The sum (or total) is 6 boxes. 2 and 4 are called addends, and the process of finding the sum is called addition.

Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers To add whole numbers, we add the digits in the ones place, then the tens place, then the hundreds place, and so on. Example: Line up numbers vertically so that the place values correspond. Then add the digits in corresponding place values, starting with the ones place.

Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers 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, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Add: 32, ,761

Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers Addition Property of 0 The sum of 0 and any number is that number. For example, = = 7 Next, notice that we can add any two whole numbers in any order and the sum is the same. For example, = 9 and = 9. We call this special property of addition the commutative property of addition.

Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers Commutative Property of Addition Changing the order of two addends does not change their sum. For example, = 5 and = 5.

Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Adding Whole Numbers 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.

Martin-Gay, Developmental Mathematics, 2e 10 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.

Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the perimeter of the polygon. 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. 5 in 8 in 4 in 3 in 6 in

Martin-Gay, Developmental Mathematics, 2e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Solving Problems by Adding 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

Martin-Gay, Developmental Mathematics, 2e 13 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)