Holt Algebra 1: 1.1 Variables and Expressions - Vanguard Algebra
Holt Algebra 1: 1.1 Variables and Expressions
variable: __________________________________________________________________________________
constant: __________________________________________________________________________________
numerical expression: _______________________________________________________________________
5 + 4
8 ? 2
____________
_____________
algebraic expression: ________________________________________________________________________
15 ? x
1 + y ? 15
_____________
______________
Example 1: Translating from Algebra to Words
Give two ways to write each algebraic expression in words.
A. x ? 5
B. j ? 10
C. 3 ? k
D. 13 + w
1
Example 2: Translating from Words to Algebra A. John types 62 words per minute. Write an expression for the number of words he types in m minutes.
B. Roberto is 4 years older than Emily, who is y years old. Write an expression for Roberto's age.
C. Joe runs a mile in 6 minutes. Write an expression for the number of miles that Joe runs in m minutes.
D. Angela is a inches shorter than Georgia, who is 59 inches tall. Write an expression for Angela's height.
evaluate: __________________________________________________________________________________
Example 3: Evaluating Algebraic Expressions
Evaluate each expression for x = 4, y = 2, and z = 10
A. x + y
B.
C. xy
D. z ? x
2
Holt Algebra 1: 1.2 Adding and Subtracting Real Numbers
When using a number line, it is important to remember the following rules:
If the symbols are the same, _________
Ex: + + means +
? ? means +
If the symbols are different, ______________
Ex: + ? means ?
? + means ?
When subtracting two numbers, take the sign of the ______________________ number.
1. If two symbols are next to each other in the expression, ________________________________________
Ex: -9 + (-2)
4 ? (-5)
2. Start at ____________ 3. The ___________ _______________ means move to the left 4. The ___________ _______________ means move to the right
Example 1: Adding and Subtracting Numbers on a Number Line
Add or subtract using a number line.
A. 4 ? 7
B. 3 ? (?2)
C. ?2 ? (?7)
D. ? 1 ? 6
3
Example 2: Adding Real Numbers A. ? 7 + 10 = C. 8 ? (+6) = E. 5 + (+6) = G. ? 2 ? (?10) = I. 8 ? 15 =
B. ? 11 + 5 = D. ?4 + (?12) = F. 5 ? (? 6) = H. 3 + (? 9) = J. ? 16 ? (?4) =
Example 3: Evaluating Expressions for a Given Value of the Variable
Evaluate.
A. x + 8 for x = ? 14
B. y ? 20 for y = ? 2
C. 3 + k for k = 12
D. h + (?9) for h = ?6
E. 13 ? g for g = 30
F. ?3 ? f for f = ?2
4
Holt Algebra 1: 1.3 Multiplying and Dividing Real Numbers
When you multiply or divide numbers with the same sign, the answer is _____________________
Example:
10 ? 5 = ________
? 12 ? ? 2 = _________
When you multiply or divide numbers with different signs, the answer is ____________________
Example:
6(?3) = _________
? 18 ? 2 = _________
Example 1: Multiplying and Dividing Signed Numbers
Find the value of each expression.
A. ?11 ? 5
B. 6y for y = ?1.5
C. ? 80 ? ? 10
D. 11 ? ? 5
E. 4 for w = 12
F.
?
20b
for
b
=
?
3 4
*Flip ONLY the second fraction, then multiply. Worry about the negative symbol at the end.
Example 2: Dividing by Fractions
Divide.
A.
3 ? (? 4)
7
5
B.
? 10 ? 20
3
C.
? 5 ? (? 15)
4
8
D.
2 ? 17
8
5
................
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