Transcript 3 Steps - McGraw Hill Higher Education

PROBLEM SOLVING WITH
MATH
McGraw-Hill/Irwin
Chapter One
Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.
LEARNING UNIT OBJECTIVES
LU 1-1: Reading, Writing, and Rounding Whole Numbers
1.
Read and write numeric and verbal number s using place
values.
2.
Round number s to the indicated position.
3. Dissect and solve a word problem using the blueprint aid.
LU 1-2: Basic Math Functions with Whole Number s
1.
Add whole numbers.
2.
Subtract whole numbers.
3.
Multiply whole number s.
4. Divide whole number s.
LU 1-3: Basic Math Functions with Decimals
1.
Add, subtract, multiply, and divide decimals.
2.
Multiply and divide decimals by shor tcut methods.
1-2
READING AND WRITING NUMERIC
AND VERBAL NUMBERS
1,605,743,891,412 verbalized:
One trillion, six hundred five billion, seven hundred forty-three
million, eight hundred ninety-one thousand, four hundred twelve
1-3
CONVERTING PARTS TO A REGULAR
WHOLE NUMBER
Convert 2.1 million to a
regular whole number.
Step 1. Drop the decimal
point and insert a
comma.
Step 2. Add zeros so the left most digit ends in
the word name of the amount you want
to convert. Be sure to add commas as
needed.
2,1
2,100,000
1-4
ROUNDING NUMBERS
Step 1. Identify the
place value
of the digit
you want to
round.
Step 2. Identify the digit to
the right of the
identified digit in
Step 1.
If 5 or more, increase the
identified digit by 1, if less
than 5 do not change.
Step 3. Change all digits to
the right of the
rounded identified
digit to zeros.
9362
9362
Step 4. If the digit you want
to round is to the
right of the decimal
point, drop all digits
to the right of the
identified digit af ter
following Step 2
above.
9462
9400
1-5
ROUNDING NUMBERS
Step 1. Identify the
place value
of the digit
you want to
round.
Step 2. Identify the digit to
the right of the
identified digit in
Step 1.
If 5 or more, increase
the identified digit by
1, if less than 5 do
not change.
Step 3. Change all digits to
the right of the
rounded identified
digit to zeros.
Step 4. If the digit you want
to round is to the
right of the decimal
point, drop all digits
to the right of the
identified digit af ter
67951
following Step 2
above.
67951
Example:
68951 Round .3272727 to the
nearest hundredth.
Step 1) .3272727
68000 Step 2) .3372727
Step 4) .33
1-6
ROUNDING ALL THE WAY
Step 1. Identify the left most digit.
7843
Step 2. Identify the digit to the right.
7843
If 5 or more, increase the
identified digit by 1, if less than 5
do not change.
Step 3. Change all other digits to zero.
8843
8000
1-7
HOW TO DISSECT AND SOLVE A WORD
PROBLEM
Organization and persistence
1-8
GENERAL PROBLEM-SOLVING
PROCEDURE
Step 1 . State the problem(s).
Step 2. Decide on the best method(s) to solve the problem(s).
Step 3. Does the solution make sense?
Step 4. Evaluate results.
1-9
HOW TO DISSECT AND SOLVE A
WORD PROBLEM
Tootsie Roll Industries’ sales reached one hundred ninetyfour million dollars and a record profit of twenty-two million,
five hundred fifty-six thousand dollars. Round the sales and
profit figures all the way.
Sales: One hundred ninety-four million dollars. ----------->$194,000,000 -----------> $200,000,000
Profit: Twenty-two million, five hundred fifty-six thousand dollars --------> $22,556,000 ---------> $20,000,000
1-10
ADDITION OF WHOLE NUMBERS
3 Steps
1 . Align the numbers to be added
in columns according to their
place values, beginning with the
units place at the right and
moving to the left.
2. Add the units column.
Write the sum below the
column. If the sum is more
than 9, write the units digit
and carry the tens digit.
Example
2 11
1,362
5,913
8,924
6,594
22,793
3. Moving to the left, repeat Step 2 until all
place values are added.
1-11
ALTERNATE CHECK
Add each column as a separate
total and then combine. The
end result is the same.
1,362
5,913
8,924
6,594
Ones Column
2+3+4+4
Tens Column
6+1+2+9
Hundreds Column
3+9+9+5
Thousands Column
1+5+8+6
13
18
26
20
22,793
1-12
SUBTRACTION OF WHOLE NUMBERS
3 Steps
1 . Align the minuend and subtrahend
according to their place values.
2. Begin the subtraction with the units digits.
Write the difference below the column.
If the units digit in the minuend is smaller
than the units digit in the subtrahend,
borrow 1 from the tens digit in the
minuend. One tens digit is 10 units.
3. Moving to the left, repeat Step 2 until all
place values in the subtrahend are
subtracted.
Example
414 (Minuend)
- 379 (Subtrahend)
35 Difference
Check
35
+379
414
1-13
MULTIPLICATION OF WHOLE NUMBERS—
SHORTCUT TO ADDITION
Example
4 Steps
1. Align the multiplicand and multiplier at
the right.
418 (Multiplicand)
x 52 (Multiplier)
2. Multiply the right digit of the multiplier with the
right digit of the multiplicand. Keep
multiplying as you move left through the
multiplicand.
1
836
1
2 X 418 = 836
1-14
MULTIPLICATION OF WHOLE NUMBERS
3. Your partial product right digit or first digit
is placed directly below the digit in the
multiplier that you used to multiply.
4. Continue steps 2 and 3 until the
multiplication process is complete. Add
the partial products to get the final
product.
2
2,090 (Partial Product)
3
21,736
1
(Product)
2 X 418 = 836
2
+ 50 X 418 = 20,900
3
Product = 21,736
1-15
CHECKING AND ESTIMATING
MULTIPLICATION
Check
Check the
multiplication
process by
reversing the
multiplicand and
multiplier and then
multiplying.
52
Estimate
50
x 418
416
52
x
400
20,000
20 8
21,736
1-16
MULTIPLICATION SHORTCUT WITH
NUMBERS ENDING IN ZERO
Example
3 Steps
65000 (3 zeros)
x 420 (1 zero)
1. When zeros are at the end of the
multiplicand or the multiplier, or
both, disregard the zeros and
multiply.
2. Count the number of zeros in the
multiplicand and multiplier. (4)
(4 zeros)
Solution
65
x 42
130
260
27,300,000
3. Attach the number of zeros counted in Step 2
to your answer.
1-17
MULTIPLYING A WHOLE NUMBER
BY A POWER OF 10
2 Steps
1. Count the number of zeros in the power of 10.
2. Attach that number of zeros to the right side of the other whole number to obtain
the answer. Insert commas as needed.
99 x 10
99 x 100
99 x 1,000
= 990 = 990 <----Add 1 zero
= 9,900 = 9,900 <----Add 2 zeros
= 99,000 = 99,000 <----Add 3 zeros
1-18
DIVISION OF WHOLE NUMBERS
 Count how many times
one number (Divisor) is
contained in another
number (Dividend). The
result is the Quotient.
Example
18
Divisor
15 270
Quotient
Dividend
15
120
120
0
1-19
DIVISION OF WHOLE NUMBERS
 Count how many times
one number (Divisor) is
contained in another
number (Dividend). The
result is the Quotient.
Example
24 R 1
Divisor
7
169
Quotient
Dividend
14
29
28
1
1-20
ESTIMATING AND CHECKING DIVISION
Check
138
x 36
Divisor
828
4 14
4,968
+ 111
Add remainder
Example
36 R 111
Quotient
138 5079
Dividend
414
939
828
111
5,079
Estimate
50
100 5,000
1-21
DIVISION SHORTCUT WITH NUMBERS
ENDING IN ZEROS
2 Steps
1. Count the number of ending zeros in the divisor.
2. Drop the same number of zeros in the dividend as in the divisor, counting
from right to left.
95,000 / 10 -- 95,000
95,000 / 100 -- 95,000
95,000 / 1,000 -- 95,000
= 9,500 <----Drop 1 Zero
= 950 <----Drop 2 Zeros
= 95 <----Drop 3 Zeros
1-22
ADDING DECIMALS
Add: 4 + 7.3 + 36.139 + .0007 + 8.22
4.0000
7.3000
36.1390
CHECK
.0007
4.0000
8.2200
55.6597
7.3000
36.1390
.0007
8.2200
55.6597
3-23
SUBTRACTING DECIMALS
Subtract: 45.3 - 15.273
45.300
- 15.273
30.027
CHECK
45.300
- 15.273
= 30.027
3-24
MULTIPLYING DECIMALS
8.52 (2 decimal places)
x 6.7 (1 decimal places)
= 5964
5112
57084
57.084
(3 decimal places)
2.36
x .016
1416
236
03776
Need to add zero
.03776
(5 decimal places)
3-25
DIVIDING DECIMALS
3 Steps
Example
Step 1. Make the divisor a whole
number by moving the decimal
point to the right.
2.5 32.800
Step 2. Move the decimal point in the
dividend to the right the same
number of places as in the
divisor (step 1). If there are not
enough places, add zeros to the
right of the dividend.
25. 328.00
Step 3. Place the decimal point in the
quotient above the new decimal
point in the dividend. Divide as
usual.
13.12
25. 328.00
25
78
75
30
25
50
50
3-26
DECIMALS APPLICATIONS IN
FOREIGN CURRENCY
The price of an Apple iPad 2 can be bought in Canada for $600 U.S. dollars. Using
the currencies table from the Wall Street Journal let us see what the iPad 2 would
sell for in Canadian dollars. In the table on page 74, 1 U.S. Dollar equals $1.0210
Canadian dollars . To find the cost in Canadian dollars:
1. You multiply the number of U.S. dollars ($600) times $1.0210.
$600 x $1.0210 = $612.60
2. To check your calculations, take the $612.60 Canadian dollars cost of the
iPad 2 and multiply it by $0.9794. This is what the Canadian dollar is worth
against the U.S. dollar. It equals $599.98 (this amount is off .02 due to
rounding).
Table factor from currency table
CHECK $612.60 x $1.0210 = $600.00
3-27
SHORTCUTS FOR MULTIPLES OF 10
MULTIPLICATION
Step 1. Count the zeros in the multiplier.
Step 2. Move the decimal point in the multiplicand the same
number of places to the right as you have zeros in the
multiplier.
6890
6.89 x 1000
6.89 x 100
689
6.89 x 10
68.9
3-28
SHORTCUTS FOR MULTIPLES OF 10
DIVISION
Step 1. Count the zeros in the divisor.
Step 2. Move the decimal point the same
number of spaces to the left.
.00689
6.89 / 1000
6.89 / 100
.0689
6.89 / 10
.689
3-29