Transcript Chapter 01 – PowerPoint Presentation

Business Math
Chapter 1:
Whole Numbers
1
Learning Objectives

Read whole numbers

Write whole numbers

Round whole numbers

Add whole numbers

Subtract whole numbers

Multiply whole numbers

Divide whole numbers
2
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
3
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
4
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
5
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
6
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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).
34, 000, 892
7
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
8
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
9
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
Here’s an example
Seven million, three hundred three thousand,
nine hundred twenty eight.
7,
million
thousand
303,
928
(units)
is written 7,303,928.
10
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
11
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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
12
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
13
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
14
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
Try this example


1
3
6
7
8
5 4 6
4 5 7 0
+ __ __ __ 9
=
2
9
9





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
15
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
16
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
Try this example






Sales for last week’s
concession stand:
Monday:
Tuesday:
Wednesday:
Thursday:
Friday:
$219
$877
$455
$614
$980

What was the week’s
total to the nearest
hundred?

Answer: $3,200
17
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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
18
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
19
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
20
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
Try this example

Subtract
1
2

9
3


=
5
9
8




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
21
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
1.2.3 Multiplying whole numbers
Numbers can be multiplied in any order
without affecting the result.
8x3x4=4x3x8
96 = 96
22
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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
23
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
Multiply these numbers

Identify each:
Multiply
7
9
x
2
3
2
3
7
1
5
8
_
1
8
1
7
Multiplicand
Multiplier
Partial product
Partial product
Product
24
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
Try these examples
(without using a calculator)

123 x 466 =
?
 Answer:


67 x 120 =
348 x 27 =
57,318
?

Answer: 8,040

Answer: 9,396
?
25
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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
26
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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)
27
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
28
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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.
29
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by 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)
30
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by 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)
31
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by 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.
32
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved
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
33
Cleaves/Hobbs: Business Math, 7e Copyright 2005 by Pearson Education, Inc. Upper Saddle River, NJ 07458 All Rights Reserved