Learning Objectives n Read whole numbers n Write

Learning Objectives n Read whole numbers n Write whole numbers n Round whole numbers n Add whole numbers n Subtract whole numbers n Multiply whole numbers n Divide whole numbers Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 1. 1 Read Whole Numbers n Our system of numbers, the decimal number system uses 10 symbols called digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. n Place-value system: a number system that determines the value of a digit by its position in a number. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

How to read whole numbers n Beginning with the ones place on the right, the place values are grouped in digits of three places. n For example: 286, 418, 917 n Each group is called a period. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Understanding place value n Each period has a name and a ones place, a tens place and a hundreds place. n In a number, the first period from the left may have fewer than three digits. n In many cultures, the periods are separated by commas. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Read whole numbers n Identify the period name of the leftmost group. n Read the three digit number from left to right. n Name the period. n 124, 656, 454 would read one hundred twenty four million six hundred fifty six thousand four hundred fifty four. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Note these exceptions n Do not read or name a period that is all zeros. n 34, 000, 892 would read thirty four million eight hundred ninety two. n Do not name the units period (892). 34, 000, 892 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

When reading whole numbers, remember that… n n n The period name will be read at each comma. Period names are read in the singular; (“thousand” not “thousands”). Hundreds is not a period name. Do not say the word “and” when reading whole numbers. Calculator displays ordinarily do not show commas; insert when writing the number. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 1. 2 Write Whole Numbers n Begin recording digits from left to right. n Insert a comma at each period name. n Every period after the first period must have three digits. n Insert zeros as necessary. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Here’s an example Eight million, nine hundred three thousand, four hundred twenty two. 8, 903, 422 million thousand (units) is written 8, 903, 422. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 3. 3 Rounding Whole Numbers n n n Rounding to a specific place: Identify the place (“nearest hundred”, for example) Look at the number immediately to the right. Is it 5 or higher? Round up. Is it 4 or lower? It stays the same. All digits to the right of the specified place become zeros. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples Round to the nearest hundred: 4, 856 10, 527 234, 567 8, 648, 078 And the answers are… 4, 900 10, 500 234, 600 8, 648, 100 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n Addends: numbers being added n Sum or total: The answer or result of addition. n Commutative property of addition: two or more numbers can be added in either order without changing the sum n Associative property of addition: When more than two numbers are being added, the addends can be grouped by two at a time in any way. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 2. 1 Add Whole Numbers n Write the numbers in a vertical column, aligning digits according to their places. n Beginning with the ones column, add the place digits. n Add, if necessary, to the tens column. n Repeat the operation, adding to the hundreds column, if necessary until you have reached the farthest column of digits to the left. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try this example n 1 3 5 4 5 + __ __ = 6 4 7 __ 7 6 0 9 8 2 9 9 n n n Business Math, Eighth Edition Cleaves/Hobbs Add the ones column Place the 8 the bottom of the ones column Carry the 2 to the tens column Place the 4 in the tens column. Carry the 2. Finish the operation Answer: 64, 948 © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Estimating n Estimate: to find a reasonable approximate answer for a calculation. n Use estimating as a quick tool when an exact number is not required. n Round whole numbers to the place desired for an estimate. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try this example n Sales for last week’s concession stand: n Monday: Tuesday: Wednesday: Thursday: Friday: n n Business Math, Eighth Edition Cleaves/Hobbs $219 $877 $455 $614 $980 n What was the week’s total to the nearest hundred? n 200 + 900 + 500 + 600 +1000 = $3, 200 © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 2. 2. Subtracting Whole Numbers n The order of the numbers is important so therefore, subtraction is not commutative. 9– 4≠ 4– 9 n Grouping in subtraction is important. Subtraction is not associative. (8 - 3) -1 = 5 – 1 = 4 but 8 - (3 -1) = 8 - 2 = 6 4≠ 6 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n Minuend: the beginning amount or number that a second number is being subtracted from. n Subtrahend: the number being subtracted. n Difference: the answer or result of subtracting n Borrow: regroup digits in the minuend by borrowing 1 from the digit to the left of the specified place and adding 10 to the specified place. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Using rounding in subtraction n Subtract 128 from 1, 345 by rounding each number to the nearest hundred to estimate the difference. n 128 would become 100. n 1, 345 would become 1, 300. n The estimated difference would be 1, 200. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try this example Subtract n 1 2 n 9 3 n n - 5 = 9 8 n n Business Math, Eighth Edition Cleaves/Hobbs Borrow 1 from the tens column. Subtract 8 from 13. Borrow 1 from the hundreds column Subtract 9 from 18 Borrow 1 from the thousands column Subtract 5 from 11 Answer: 695 © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 2. 3 Multiplying Whole Numbers can be multiplied in any order without affecting the result. 8 x 3 x 4=4 x 3 x 8 96 = 96 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key terms n Multiplicand: the number being multiplied n Multiplier: the number multiplied by n Factor: each number involved in multiplication n Product: the answer or result of multiplication n Partial product: the product of one digit of the multiplier and the entire multiplicand Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Multiply these numbers n Multiply Identify each: 7 9 x 2 3 7 1 5 8 _ 1 8 1 7 Business Math, Eighth Edition Cleaves/Hobbs Multiplicand Multiplier Partial product Product © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples (without using a calculator) n 418 x 107 = ? n n 88 x 120 = ? Answer: 10, 560 n n 348 x 27 = ? n Business Math, Eighth Edition Cleaves/Hobbs Answer: 44, 726 Answer: 9, 396 © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

1. 2. 4 Divide Whole Numbers n Division is used to find the number of equal parts a whole quantity can be separated into. n A $40 tip is shared equally among 5 servers. How much does each server receive? n $40 ÷ 5 servers = $8 each Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n Dividend: the number being divided or the total quantity n Divisor: The number to divide by n Quotient: The answer or result of the operation n Whole-number part of the quotient: the quotient without regard to its remainder Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Key Terms n Remainder of quotient: a number that is smaller than the divisor that remains after division is complete. n Partial dividend: the part of the dividend that is being considered at a given step of the process. n Partial quotient: the quotient of the partial dividend and the divisor. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Remainders n There will be a remainder if an amount is too small to be further divided by the divisor. For example: 152 ÷ 3 = 50 R 2 n That amount may be expressed as a remainder (R 2), a fraction, or a decimal. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

How to divide whole numbers 1235 ÷ 5 = ? 1. Beginning with its leftmost digit, identify the first group of digits of the dividend that is larger than or equal to the divisor. Is it 1? No. Is it 12? Yes. 5 goes into 12 two times. Place the 2 above the 2 in the dividend. (Go on to next slide) Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Division step by step 2. Multiply 2 by the divisor. Place 10 under the 12 and subtract. The result is 2. 3. Bring down the following digit which is 3 and divide 5 into 23. The result is 4. 4. Place the 4 directly above the 3 in the dividend. Multiply 4 by the divisor. (Go on to next slide) Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Finish the problem 5. Place 20 under the 23 and subtract. The result is 3. 6. Bring down the last digit which is 5 and divide 5 into 35. The result is 7. Place 7 directly above the 5. 7. You have finished and the answer is 247. Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved

Try these examples (without a calculator) n 4, 750 cases of detergent will be distributed evenly to 25 local stores. How many will each receive? n Answer: 190 n 420 bottles of fabric softener in the warehouse are packed a dozen to case. How many cases are there in the warehouse? n Answer: 35 Business Math, Eighth Edition Cleaves/Hobbs © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved