Transcript Review of Whole Numbers

Learning Objectives

Read whole numbers

Write whole numbers

Round whole numbers

Add whole numbers

Subtract whole numbers

Multiply whole numbers

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

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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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: 286,418,917

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

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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.

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

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
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.
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,
million
thousand
903,
422
(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





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

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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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





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

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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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:




Business Math, Eighth Edition
Cleaves/Hobbs
$219
$877
$455
$614
$980

What was the week’s
total to the nearest
hundred?

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

The order of the numbers is important so
therefore, subtraction is not commutative.
9–4≠4–9

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

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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 Pearson Education, Inc. Upper Saddle River, NJ
07458 All Rights Reserved
Try this example
Subtract

1
2

9
3


-
5
=
9
8




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
Numbers can be multiplied in any
order without affecting the result.
8x3x4=4x3x8
96 = 96
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 Pearson Education, Inc. Upper Saddle River, NJ
07458 All Rights Reserved
Multiply these numbers

Multiply
Identify each:
7
9
x
2
3
2
3
7
1
5
8
_
1
8
1
7
Business Math, Eighth Edition
Cleaves/Hobbs
Multiplicand
Multiplier
Partial product
Partial product
Product
© 2009 Pearson Education, Inc. Upper Saddle River, NJ
07458 All Rights Reserved
Try these examples
(without using a calculator)

418 x 107 =
?


88 x 120 =
?
Answer: 10,560


348 x 27 =
?

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

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
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 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.
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)

4,750 cases of detergent will be distributed
evenly to 25 local stores. How many will each
receive?
 Answer: 190

420 bottles of fabric softener in the warehouse
are packed a dozen to case. How many cases
are there in the warehouse?
 Answer: 35
Business Math, Eighth Edition
Cleaves/Hobbs
© 2009 Pearson Education, Inc. Upper Saddle River, NJ
07458 All Rights Reserved