Page 765 - Basic College Mathematics with Early Integers

BIGGER PICTURE—STUDY GUIDE OUTLINE 741

3. Divide: First fraction times the reciprocal of the second fraction.
2 3 2 4 8
, = # =
11 4 11 3 33
4. Add or Subtract: Must have same denominators. If not, find the LCD, and
write each fraction as an equivalent fraction with the LCD as denomina-
tor.
2 1 2 3 1 6 1 7
+ = # + = + =
5 15 5 3 15 15 15 15
D. Decimals
1. Add or Subtract: Line up decimal points. 1.27
+ 0.6
1.87

2. Multiply: 2.56 2 decimal places
* 3.2 1 decimal place
512 2 1 3
768
8.192 3 decimal places
0.7 1.31
3. Divide: 8 5.6 0.6 0.786
II. Solving Equations
A. Proportions: Set cross products equal to each other.Then solve.
14 2 6 3
#
#
#
= ,or14 n = 3 2,or14 n = 6,orn = =
3 n 14 7
B. Percent Problems
1. Solved by Equations: Remember that “of” means multiplication and “is”
means equals.
“12% of some number is 6” translates to
6
# #
12% n = 6 or 0.12 n = 6 or n = or n = 50
0.12
2. Solved by Proportions: Remember that percent, p, is identified by % or
percent; base, b, usually appears after “of”; and amount, a, is the part
compared to the whole.
“12% of some number is 6” translates to
6 12 600
#
#
= or 6 100 = b 12 or = bor 50 = b
b 100 12
C. Equations in General: Simplify both sides of the equation by removing paren-
theses and adding any like terms. Then use the Addition Property to write
variable terms on one side, constants (or numbers) on the other side.Then use
the Multiplication Property to solve for the variable by dividing both sides of
the equation by the coefficient of the variable.
Solve: 2(x - 5) = 80
2x - 10 = 80 Use the distributive property.
2x - 10 + 10 = 80 + 10 Add 10 to both sides.
2x = 90 Simplify.
2x 90
= Divide both sides by 2.
2 2
x = 45 Simplify.