Appendix D. Mathematics Review

1. Order of Arithmetic Operations
- Certain arithmetic operations take precedence over others. In completing problems with a series of operations the following guidelines apply:
- a. Addition or subtraction may occur in any order.
  - Example: 4 + 8 − 7 + 3 = 8 or 8 + 3 + 4 − 7 = 8
- b. Multiplication or division must be completed before addition or subtraction.
  - Example: 48 ÷ 6 + 2 = 10
  - Example: 4 + (2/3)(1/2) = 4 1/3
- c. Any quantity above a division line, under a division line or a radical sign , or within parentheses or brackets must be treated as one number.
2. Fractions, Decimals, and Percents
- a. To add (or subtract) fractions, the denominator in each term must be the same. (Choose the lowest common denominator for each term. Multiply each term by the common denominator and then add [or subtract].)
  - - (lowest common denominator = 12)
  - Solution:
  - - (lowest common denominator = xc)
  - Solution:
- b. To multiply fractions, multiply the numerators by each other and the denominators by each other.
- c. To divide fractions, invert the divisor and multiply.
- d. To convert a fraction to a percentage divide the numerator by the denominator and multiply by 100.
  - Note: To convert a percentage to a decimal move the decimal point two places to the left.
- e. When dividing by a decimal divide by the integer and add sufficient zeros to move the decimal point the appropriate number of digits to the right.
  - (appropriate number of digits to right = 2)
  - When multiplying by a decimal multiply the integer and add enough zeros to move the decimal point the appropriate number of digits to the left.
  - (appropriate number of digits to left = 3)
- f. Decimals may be expressed as positive or negative powers of 10:
3. Proportions, Formulas, and Equations
- The location of values in proportions, equations, or formulas may be shifted provided that whatever addition, subtraction, multiplication, or division is performed on one side of the equation is also performed on the other side.
4. Right Triangles and Trigonometric Equations
- a. In a right triangle one angle always equals 90°. The other two angles will always be acute angles and the sum of these two angles will be 90° since the sum of the angles in any triangle is 180°.
- b. In a right triangle the sides are related to each other so that the square of the longest side or hypotenuse (c) is equal to the sum of the squares of the two sides: c2 = a2 + b2. This is the Pythagorean theorem.
- c. In triangle ABC, side a is called the side opposite angle A, side b is opposite angle B, and the hypotenuse, c, is opposite the right angle. Side b is named the side adjacent to angle A and side a is the side adjacent to angle B.
- d. Trigonometric functions are ratios between the sides of a right triangle and ...