Mathematical Review Fractions & Decimals A fraction represents division, the numerator is divided by the denominator. 2/3 is read as 2 divided by 3 Proper fraction: numerator is smaller than denominator. Example: 3/5 Improper fraction: numerator is larger than the denominator. Example: 5/3 A decimal is a fraction with the division carried out. A decimal is a fraction expressed in powers of 10. 0 . 0 0 1 ones . Tenths hundredths thousandths

Mathematical Review Algebraic Equations Variables are the symbols used to represent a measurement. For example; T is the variable for temperature while t is the variable for time. To isolate one variable of an equation remember to divide if the unwanted variable is on top and to multiply if the variable is on the bottom. An asterisk * represents multiplication. A = B / C to isolate C first rearrange the equation to it will read C=? Do this by multiplying both sides by C (since it is on the bottom of a fraction (denominator). C * A = B * C / C note: C/C = 1 C * A = B Now to isolate C we need to divide by A (it is on top of a fraction; A/1 = A) C * A / A = B / A Remember: what ever you do to one side you must do it to the other side. C = B / A

Mathematical Review Algebraic Equations When multiplication & division is mixed with adding & subtracting, try the multiplication or division first. (A - D) / (C + F) = B to solve for C, first rearrange the equation to it will read C=? Do this by multiplying both sides by C + F (since it is on the bottom of a fraction (denominator). (A - D) * (C + F) / (C + F) = B * (C + F) (A - D) = B * (C + F) Now to isolate C we need to divide by B (A - D) / B = B * (C + F) / B (A - D) / B = C + F Now you can subtract F from both sides. [(A - D) / B] - F = C + F - F [(A - D) / B] - F = C which is the same as C = [(A-D) / B] -F If A = 8, D = 2, B = 3, & F = 7 then C must = [(8-2) / 3] - 7 = -5

Mathematical Review Exponents An exponent is a number written as a superscript. X2 is X-squared or “X to the power of 2” The base (X) is multiplied by itself the number of times represented in the exponent(superscript, 2 in this example). 23 or two cubed (2 is the base and 3 is the exponent) 23 is 2 * 2 * 2 = 4 * 2 = 8 A positive exponent represents a large number (greater than one). 1 x 103 is 10 *10 *10 = 1000 thousand A negative exponent represents a small number (less than one). 1 x 10-3 is (1/10) * (1/10) * (1/10) = 0.001 thousandths When multiplying numbers written with exponents, add the exponents. If dividing then subtract the exponents. x4 * x6 = x (4+6) = x10 or (2 x 103)(3 x 106) = 6 x 10(3+6) = 6 x 109 2x6/7x3 = 0.2857 x(6-3) = 0.2857 x3

Practice Questions D B B B C 1. 2,533 The five is in the ____ place. 1. 2,533 The five is in the ____ place. a) thousands b) tens c) ten thousands d) hundreds 2. 2.533 The five is in the ___ place. a) tens b) tenths c) oneths d) hundredths 3. Round 0.18948 to the nearest thousandths. a) 0.18 b) 0.189 c) 0.190 d) 0.1895 4. 216/2 = a) 18 b) 108 c) 1008 d) 432 5. Student A scored 45 on the first exam, 67 on the second exam and 51 on the third exam. What was the average score? a) 67.1 b) 81 c) 54.3 d) 49.3 D B B B C

Practice Questions C D D B A 6. 3/8 x 8/5 = a) 5/9 b) 5/7 c) 3/5 d) 15/4 7. 5/3 + 1/9 = a) 3/7 b) 3/12 c) 2/7 d) 16/9 8. 0.006/ 0.0002 = a) 0.03 b) 0.3 c) 3.0 d) 30 9. What is 36% of 19? a) 1.9 b) 6.8 c) 53 d) 684 10. Solve for x: 6x + 4 = 16 a) 2 b) 3 c) 4 d) 5 C D D B A

Practice Questions A B B B 11. Factor: x2 + 20x + 10 = a) (x + 10)(x + 10) b) (x + 20)(x + 10) c) (x - 10)(x - 20) d) (x + 10)(x - 10) 12. Solve for y: y2 - 6y + 9 = 0 a) -1 b) 3 c) 1 d) -2 13. The correct value for the expression [(1 x 10-21 x 1 x 1035)5] / (1 x 1014)2 a. 1 x 10-58 b. 1 x 1047 c. 1 x 1026 d. 1 x 1012 14. Change the following decimal to a fraction in its lowest term: 0.625 a) 1/8 b) 5/8 c) 1/6 d) 3/4 A B B B