1. 1 Business Math Chapter 1: Whole Numbers

2. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 2 Learning Objectives Read whole numbers Write whole numbers Round whole numbers Add whole numbers Subtract whole numbers Multiply whole numbers Divide whole numbers

3. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 3 1.1.1 Read whole numbers Our system of numbers, the decimal number system uses 10 symbols called digits: 0,1, 2, 3, 4, 5, 6, 7, 8, and 9. Place-value system: a number system that determines the value of a digit by its position in a number.

4. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 4 How to read whole numbers Beginning with the ones place on the right, the place values are grouped in digits of three places. For example: 145,874,322 Each group is called a period.

5. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 5 Understanding place value Each period has a name and a ones place, a tens place and a hundreds place In a number, the first period from the left may have fewer than three digits. In many cultures, the periods are separated by commas.

6. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 6 Read whole numbers Identify the period name of the leftmost group. Read the three digit number from left to right. Name the period. 34,786,654 would read thirty four million seven hundred eighty six thousand six hundred fifty four.

7. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 7 Note these exceptions Do not read or name a period that is all zeros. 34,000,892 would read thirty four million eight hundred ninety two. Do not name the units period (892). 000,892 34,

8. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 8 When reading whole numbers, remember that… 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.

9. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 9 1.1.2 Write whole numbers. Begin recording digits from left to right. Insert a comma at each period name. Every period after the first period must have three digits. Insert zeros as necessary.

10. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 10 Here’s an example Seven million, three hundred three thousand, nine hundred twenty eight. 7,million 303,thousand 928(units) is written 7,303,928.

11. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 11 1.3.3 Rounding whole numbers 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.

12. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 12 Try these examples Round to the nearest hundred: 2,345 12,517 234,567 12,345,078 And the answers are… 2,300 12,500 234,600 12,345,100

13. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 13 1.2.1 Add whole numbers. Write the numbers in a vertical column, aligning digits according to their places. Beginning with the ones column, add the place digits. Add, if necessary, to the tens column. Repeat the operation, adding to the hundreds column, if necessary until you have reached the farthest column of digits to the left.

14. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 14 Key Terms Addends: numbers being added Sum or total: The answer or result of addition. Commutative property of addition: two or more numbers can be added in either order without changing the sum 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.

15. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 15 Try this example 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 13678 5462 45709 +__ 99 =

16. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 16 Estimating Estimate: to find a reasonable approximate answer for a calculation. Use estimating as a quick tool when an exact number is not required. Round whole numbers to the place desired for an estimate.

17. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 17 Try this example Sales for last week’s concession stand: Monday: $219 Tuesday:$877 Wednesday:$455 Thursday:$614 Friday:$980 What was the week’s total to the nearest hundred? Answer: $3,200

18. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 18 1.2.2. Subtracting whole numbers The order of the numbers is important so therefore, subtraction is not commutative. 8 – 3 ≠ 3 – 8 Grouping in subtraction is important. Subtraction is not associative. (8 - 3) -1 = 5 – 1 = 4 but 8 - (3 -1) = 8 - 2 = 6 4 ≠ 6

19. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 19 Key Terms Minuend: the beginning amount or number that a second number is being subtracted from. Subtrahend: the number being subtracted. Difference: the answer or result of subtracting 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.

20. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 20 Using rounding in subtraction Subtract 128 from 1,345 by rounding each number to the nearest hundred to estimate the difference. 128 would become 100. 1,345 would become 1,300. The estimated difference would be 1,200.

21. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 21 Try this example Subtract 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 1293 -598 =

22. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 22 1.2.3 Multiplying whole numbers Numbers can be multiplied in any order without affecting the result. 8 x 3 x 4 = 4 x 3 x 8 96 = 96

23. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 23 Key terms Multiplicand: the number being multiplied Multiplier: the number multiplied by Factor: each number involved in multiplication Product: the answer or result of multiplication Partial product: the product of one digit of the multiplier and the entire multiplicand

24. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 24 Multiply these numbers Multiply Identify each: 79 x23 237 158_ 1817 Multiplicand Multiplier Partial product Product

25. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 25 Try these examples (without using a calculator) 123 x 466 = ? Answer: 57,318 67 x 120 = ? Answer: 8,040 348 x 27 = ? Answer: 9,396

26. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 26 1.2.4 Divide whole numbers Division is used to find the number of equal parts a whole quantity can be separated into. A $40 tip is shared equally among 5 servers. How much does each server receive? $40 ÷ 5 servers = $8 each

27. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 27 Key Terms Dividend: the number being divided or the total quantity Divisor: The number to divide by Quotient: The answer or result of the operation Whole-number part of the quotient: the quotient without regard to its remainder (continued on the next slide)

28. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 28 Key Terms Remainder of quotient: a number that is smaller than the divisor that remains after division is complete. Partial dividend: the part of the dividend that is being considered at a given step of the process. Partial quotient: the quotient of the partial dividend and the divisor.

29. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 29 Remainders 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 That amount may be expressed as a remainder (R 2), a fraction, or a decimal.

30. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 30 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)

31. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 31 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)

32. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 32 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.

33. Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved 33 Try these examples (without a calculator) 6,750 cases of detergent will be distributed evenly to 25 local stores. How many will each receive? Answer: 270 420 bottles of fabric softener in the warehouse are packed a dozen to case. How many cases are there in the warehouse? Answer: 35