1-1 Evaluating Expressions

P

EMDAS

arentheses

xponents

ultiplication

ivision

ddition

ubtraction

}}

(in order: left to right)

(in order: left to right)

To remember the order think of this phrase:

(in order: left to right)

Please Excuse My Dear Aunt Sally

(or other grouping symbols)Within grouping symbols, or if there are no grouping symbols.

1.2.

a.

b.

c.

Important definitions & properties.•Algebraic Definition of Subtraction: For all real #s a and b, a – b = a + -b.

•Algebraic Definition of Division: For all real #s a and b, with b 0, a ÷ b = a 1 . b•Associative Property of Multiplication: For any real #s a, b, & c, (ab)c = a(bc) .

•Associative Property of Addition: For any real #s a, b, & c, (a + b) + c = a + (b + c) .

•Transitive Property of Equality: For any real #s a,b, & c, if a = b & b = c, then a = c .

1. Let n = 2. Evaluate

a. -4n3

-4 • 23

-4 • 8

-32

b. (-4n)3

(-4 • 2)3

(-8)3

-512

Problems that______ to bethe _____ arequite ________with the addition of__________ .

appearsame

different

parentheses

1-4

2. Use a calculator to evaluate , when a = 7 and b = 2.

Step 3: round the result to the nearest thousandths.

.566649587... .567

1-4

( ( 7 + 10 ) / ( 2³ + 7 – 1.5 ) ) ^ 2

a + 10 ² b³ + a - 1.5( ) 7 + 10 ² 2³ + 7 – 1.5( )Step 1: substitute given values

for the variables.Step 2: Enter into the calculator using proper notation.

The outer ( ) makes sure that the calculator squares the expression as the last operation performed.

The inner ( ) makes sure that the calculator calculates the numerator & denominator before division.

3. Find the volume of a rectangular solid using the formula V = lwh. Let l = 4 cm, w = 6 cm, & h = 7 cm.

lw

hV = lwhV = 4 6 7V = 168 cm³