- 1. Order of Arithmetic Operations
- Certain arithmetic operations take precedence over others.
In completing problems with a series of operations the following
- 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
- Example: 48 ÷ 6 + 2 = 10
- Example: 4 + (2/3)(1/2) = 4
- 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)
- (lowest common denominator = xc)
- 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
- 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
- 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
- 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 ...
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