1. 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.

2. 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: per hour Here are some examples of addition, subtraction, multiplication, and division of decimal numbers. Decimal point

3. Mathematics, Decimal Examples Example Add: 6845.1 + 37.259 Solution Line up the decimal points and write extra zeros. 6 8 4 5. 1 0 0 + 3 7. 2 5 9 953 28. 6 8 1.

4. Mathematics, Decimal Examples Solution Line up decimal points and subtract, borrowing if necessary. 4 5. 1 8 0 0 – 2. 0 1 7 4 626134 7 9 10 Example Subtract: 45.18 – 2.0174.

5. 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. 7 5. 2 × 6. 3 2 2 5 6 4 5 1 2 0 4 7 3.7 6 3 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 1

6. Mathematics, Decimal Examples Solution First, we move the decimal point one place to the right and then we divide, using long division. 7.872 ÷ 9.6 = 0.82. Example Divide: 7.872 ÷ 9.6.

7. 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

8. 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%

9. Introduction to Mathematics Fraction: A fraction is part of an entire object. It is any number that can be put in the forms The top numbers are called the numerator and the bottom numbers is called the denominator.  Numerator  Denominator Example Identify the numerator and denominator. Solution

10. Introduction to Mathematics Example Multiply: a. 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. If the numerator and denominator has like numbers, we cancel them out. b.

11. Introduction to Mathematics Example Divide: a. b. Solution When dividing a number by a fraction, multiply the number by the reciprocal of the fraction. The reciprocal of 7 is a. b.

12. Introduction to Mathematics Example Add: a. Subtract: b. 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.

13. Quiz 1)105 divided by 5. a. 20 b. 21 c. 25 2) 840 divided by 40. a. 12 b. 22 c. 21 3) 296 divided by 4. a. 73 b. 74 c. 69 4)1125 divided by 15. a. 75 b. 65 c. 72 5)33.03 divided by 0.03. a. 1111 b. 1101 c. 1112

14. Quiz 6) 0.3778 divide by 0.25. a. 1.5112 b. 1.5113 c. 1.5111 7) a. 24150 b. 25251 c. 20534 8) a. b. c. 9) a. b. c. 10) Divided by a. 3 b. 5 c. 2

15. Quiz 11) a. b. c. 12) a. 779. 2867 b. 779.2876 c. 977.2876 13) a. 4.03293 b. 4.03932 c. 4.13293 Website to use for reference: 1.www.math.comwww.math.com 2.www.mathleague.com/help/fractions/fractions.htmwww.mathleague.com/help/fractions/fractions.htm 3.www.aaamath.comwww.aaamath.com 4.www.basic-mathematics.comwww.basic-mathematics.com