Transcript Introduction to Mathematics - University of Antelope Valley

Introduction to Mathematics
This prep course introduces decimals,
percents, and fractions. Some reference
websites can be found on the last slide of
this presentation.
After you finish the course, please
complete the multiple-choice quiz at the
end, and bring your answers to the first
day of class.
Introduction to Mathematics
Decimal:
A decimal is not a whole number (0, 1, 2, 3,…). It is a part of a
number. We use decimals most often when we use money.
The following hourly wage is an example of a decimal:
$7.35 per hour
Decimal point
Here are some examples of addition, subtraction,
multiplication, and division of decimal numbers.
Mathematics, Decimal Examples
Example Add: 6845.1 + 37.259
Solution Line up the decimal points and write extra zeros.
1
6 8 4 5
+
3 7
6 8 82
. 1 0 0
. 2 5 9
. 3 5 9
Mathematics, Decimal Examples
Example Subtract: 45.18 – 2.0174
Solution Line up decimal points and subtract, borrowing if
necessary.
7
9
10
4 5 . 1 8 0 0
– 2 . 0 1 7 4
4 3
.
1 6 2 6
Mathematics, Decimal Examples
Example Multiply: 6.3 × 75.2.
Solution We can set this up as if it were a multiplication problem
with whole numbers. We multiply and then place the decimal
point in the
correct position in the answer .
3
1
75.2
×
6.3
2256
45120
4 7 3.7 6
1 decimal place to the right of decimal point
1 decimal place to the right of decimal point
the decimal point is placed so that there are 1+1=2
places to its right
Mathematics, Decimal Examples
Example Divide: 7.872 ÷ 9.6.
Solution First, we move the decimal point one place to the right
and then we divide, using long division.
.82
96. 78.72
768
192
192
0
7.872 ÷ 9.6 = 0.82.
Introduction to Mathematics
Percent:
Percent means “out of 100.” Writing a number as a percent is
a way of comparing the number with 100. For example,
instead of saying “12 out of every 100 professional basketball
players are female,” we can say “12% of professional
basketball players are female.”
Example Change 34.2% to a decimal.
Solution we drop the % symbol and move the decimal point
two places to the left, inserting zeros as placeholders if
needed.
.34.2% = 0.342
Introduction to Mathematics
Example Change 1.23 to a percent.
Solution we move the decimal point two places to the right
and write a % symbol.
1.23 = 123%
Introduction to Mathematics
Fraction:
A fraction is part of an entire object. It is any number that can
1 3 7
be put in the forms 2 , 5 , 8 , 
The top numbers are called the numerator and the bottom
numbers is called the denominator.
Example Identify the numerator and denominator
Solution
9
16
 Numerator
 Denominator
9
16
.
Introduction to Mathematics
4 5
Example Multiply: a. 7  11
14 15

15 17
b.
Solution When two fractions are multiplied, the result is a
fraction with a numerator that is the product of the fractions’
numerators and a denominator that is the product of the
fractions’ denominators.
a.
4 5
4  5 20
 

7 11 7 11 77
If the numerator and denominator has like numbers, we
cancel them out.
b. 14  15  14 15  14
15 17 15 17 17
Introduction to Mathematics
Example Divide: a. 7  1
5
b.
5 11

4 7
Solution When dividing a number by a fraction, multiply the
number by the reciprocal of the fraction. The reciprocal of 7 is
1
7
1
5
5
1
7 5
1 1
a. 7   7    
b.
5 11 5 7 35
   
4 7 4 11 44
35
 35
1
Introduction to Mathematics
Example Add: a. 3  2
8 8
Subtract: b.
9 5

2 2
Solution When the fraction have the same denominator,
their sum is the sum of the numerators over the
denominator, and their difference is the difference of the
numerators over the denominator.
a.
b.
3 2 5
 
8 8 8
9 5 95 4
 
 2
2 2 2 2
Quiz
1) 105 divided by 5.
a. 20
b. 21
2) 840 divided by 40.
a. 12
b. 22
3) 296 divided by 4.
a. 73
b. 74
4) 1125 divided by 15.
a. 75
b. 65
5) 33.03 divided by 0.03.
a. 1111
b. 1101
c. 25
c. 21
c. 69
c. 72
c. 1112
Quiz
6) 0.3778 divide by 0.25.
a. 1.5112
b. 1.5113
7) 345  70.
a. 24150
b. 25251
8) 23  74 .
8
a. 108
b. 21
9) 19  23 .
1
2
a. 27
b. 27
10) 23 Divided by 13 .
a. 3
b. 5
c. 1.5111
c. 20534
c.
c.
21
8
27
2
c. 2
Quiz
11)
1 3

20 20
a.
1
5
b.
4
20
c.
5
4
12) 35.23  22.12
a. 779. 2867 b. 779.2876
c. 977.2876
13) 1.21  3.333 .
a. 4.03293
b. 4.03932
c. 4.13293
Website to use for reference:
1. www.math.com
2. www.mathleague.com/help/fractions/fractions.htm
3. www.aaamath.com
4. www.basic-mathematics.com