IMA 101: Basic Math
1
LECTURE 4
IMA101: Basic Mathematics
6/17/2010
Lecture Outline
2
 HW/Journal overview
 Wrapping up mixed numbers
 Decimals
 Square roots
IMA101: Basic Mathematics
6/17/2010
Mixed Numbers: Addition
3
3
1
168  85
4
5
2
4
45  96
3
5
IMA101: Basic Mathematics
6/17/2010
Mixed Numbers: Subtraction
4
 Remember to distribute the subtraction sign to the
whole part and the fraction of the subtracted mixed
number
2
10  2
3
1
2
34  11
5
3
11
419  53
16
IMA101: Basic Mathematics
6/17/2010
Complex Fractions
5
 Recall: A fraction is just a number (numerator)
divided by another number (denominator)
3
4  37
7 4 8
8
 Simplify the following:
1  1
 
8  2
1 3

4 8
IMA101: Basic Mathematics
1  5
  
3  6
1
1
3
6/17/2010
Order of Operations
6
3
7 1 
    2 
 8 4   16 
3
1 
1
  2   2 
16
4 
8
8 1  4

  1      10 
5 3  5

IMA101: Basic Mathematics
6/17/2010
Decimals
7
IMA101: Basic Mathematics
6/17/2010
Introduction to Decimals
8
 Decimals as fractions
 -1.5
 8361.2759
 Fractions as Decimals
 5/10

3/4

1/5
IMA101: Basic Mathematics
6/17/2010
Understanding Decimals
9
 Place values
 Writing whole numbers as decimals
 42
 Comparing two decimals
 1.99
2.99
 1.999
1.99
 -0.58
-0.57
IMA101: Basic Mathematics
6/17/2010
Rounding decimals
10
 Similar to rounding whole numbers
 >,=5  1
 <5 0
 3.14159265
 Round to the nearest…
 Tenth
 Hundredth
 Thousandth
 Ten-thousandth
 …
IMA101: Basic Mathematics
6/17/2010
Addition and Subtraction with Decimals
11
 Same as with whole numbers
 Line up the decimal points, and pull it down to the
result
 Examples
 382.5 – 227.1 =

2.56 – (-4.4) =
IMA101: Basic Mathematics
6/17/2010
Dividing to get a decimal
12
 5/8  use long division
IMA101: Basic Mathematics
6/17/2010
Multiplication with decimals
13
 IGNORE the decimal point
 First multiply by the numbers, just like you would a
whole number
 Then count the number of places (in BOTH
numbers)
 Move the decimal of the result over that number of
places
 Examples:

5.9 * 0.2
IMA101: Basic Mathematics
1.4 * 0.006
6/17/2010
Multiplication with decimals
14
 Student Practice:
 67.164 * 31

46.28 * .0098

6981 * .097
IMA101: Basic Mathematics
6/17/2010
Decimals: Multiplication by 10
15
 Decimals represent fractions of 10, 100, 1000…
 So multiplying a decimal by 10 means we just divide
the denominator of each fraction by 10
 8361.2759
 Notice: we just move the decimal point to the right by 1
IMA101: Basic Mathematics
6/17/2010
Decimals: Multiplication by powers of 10
16
Count the number of zeros and move the decimal point
to the right that many spaces
 3.14159265 * 10 =
 3.14159265 * 100 =
 3.14159265 * 1000 =
 3.14159265 * 10000 =
IMA101: Basic Mathematics
6/17/2010
Dividing a Decimal by a whole number
17
 Long division: move decimal point in the same spot
 71.68/ 28
IMA101: Basic Mathematics
6/17/2010
Dividing a Decimal by a Decimal
18
 Move decimal point over (for BOTH numbers) until
you are dividing by a whole number.
 0.2592/ 0.36
IMA101: Basic Mathematics
6/17/2010
Dividing by a Decimals
19
 Student Practice:
-5.714/ 2.4
0.02201/ 0.08
12.243 / 0.90
0.003164/0.04
IMA101: Basic Mathematics
6/17/2010
Dividing a Decimal by 10
20
 Same idea as multiplication, except this time we
move the decimal point to the _____.
 Example
 9.0 / 10 =

4592.13 / 10 =
IMA101: Basic Mathematics
6/17/2010
Fractions and Decimals: Revisited
21
 Writing fraction as the equivalent decimal
 Use long division with decimals
 5/8
IMA101: Basic Mathematics
6/17/2010
Repeating decimals
22
 Numbers that are never factors of a power of 10 (i.e.
whose factors are not 2 or 5) do not form FINITE
decimals
 Use a bar to indicate repeated digits
 Example:
 1/3
IMA101: Basic Mathematics
6/17/2010
Repeating Decimals
23
 Student examples
1/11
4/7
2/9
4/13
[Rounding repeating decimals]
IMA101: Basic Mathematics
6/17/2010
Fractions and Decimals
24
 Decide if it’s easiest to work in terms of decimals or
in terms of fractions
 Are the decimals easily divided by the denominator?
 (3/4) * 0.88 + (1/3) * 6.60
IMA101: Basic Mathematics
6/17/2010
Square roots
25
IMA101: Basic Mathematics
6/17/2010
Square roots
26
 Recall:
 92 = 81
 81 is a perfect square
 9 is the Square ROOT of 81
 √81 = 9
 Recall:
 -9 * -9 = 81 so -9 is also a square root of 81


We denote this as - √81 = -9
-9 * 9 = -81, but since -9≠ 9, -81 is NOT a square

We can NEVER take the square root of a negative number. Why?
IMA101: Basic Mathematics
6/17/2010
Perfect Squares
27
 32 = 9
IMA101: Basic Mathematics
92=81
6/17/2010
Perfect squares: memorize these
28
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100
110
120
11
11
22
33
44
55
66
77
88
99
110
121
132
12
12
24
36
48
60
72
84
96
108
120
132
144
IMA101: Basic Mathematics
6/17/2010
Properties of Square Root
29
 Note that we cannot “distribute” the square root
when we add or subtract two terms

√ 15 = √ (4+9) ≠ √4 + √9 = 2 + 3 = 5
 However, when we multiply or divide the square root
 6 = 2*3 = (√4) * (√ 9) =√ (4*9) = √ (36) = 6
IMA101: Basic Mathematics
6/17/2010
How to find the square root of a number
30
 Using prime factorization
 √400
 √2304 =
 √3136=
IMA101: Basic Mathematics
6/17/2010