Holt Algebra 1: 1.1 Variables and Expressions

Holt Algebra 1: 1.1 Variables and Expressions

variable: __________________________________________________________________________________

constant: __________________________________________________________________________________

numerical expression: _______________________________________________________________________

8?2

5+4

____________

_____________

algebraic expression: ________________________________________________________________________

15 ¨C x

1 + y ¡Â 15

_____________

______________

Example 1: Translating from Algebra to Words

Give two ways to write each algebraic expression in words.

A.

x¨C5

B.

j ¡Â 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¨Cx

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 +

¨C ¨C means +

If the symbols are different, ______________

Ex: + ¨C means ¨C

¨C + means ¨C

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 ¨C (-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¨C7

B.

3 ¨C (¨C2)

C.

¨C2 ¨C (¨C7)

D.

¨C1¨C6

3

Example 2: Adding Real Numbers

A.

¨C 7 + 10 =

B.

¨C 11 + 5 =

C.

8 ¨C (+6) =

D.

¨C4 + (¨C12) =

E.

5 + (+6) =

F.

5 ¨C (¨C 6) =

G.

¨C 2 ¨C (¨C10) =

H.

3 + (¨C 9) =

I.

8 ¨C 15 =

J.

¨C 16 ¨C (¨C4) =

Example 3: Evaluating Expressions for a Given Value of the Variable

Evaluate.

A.

x + 8 for x = ¨C 14

B.

y ¨C 20 for y = ¨C 2

C.

3 + k for k = 12

D.

h + (¨C9) for h = ¨C6

E.

13 ¨C g for g = 30

F.

¨C3 ¨C f for f = ¨C2

4

Holt Algebra 1: 1.3 Multiplying and Dividing Real Numbers

When you multiply or divide numbers with the same sign, the answer is _____________________

10 ? 5 = ________

Example:

¨C 12 ¡Â ¨C 2 = _________

When you multiply or divide numbers with different signs, the answer is ____________________

Example:

¨C 18 ¡Â 2 = _________

6(¨C3) = _________

Example 1: Multiplying and Dividing Signed Numbers

Find the value of each expression.

A.

¨C11 ? 5

B.

D.

11 ? ¨C 5

E.

6y for y = ¨C1.5

?

4

for w = 12

C.

¨C 80 ¡Â ¨C 10

F.

¨C 20b for b = ¨C

3

4

*Flip ONLY the second fraction, then multiply. Worry about the negative symbol at the end.

Example 2: Dividing by Fractions

Divide.

A.

C.

3

7

¨C

4

¡Â (¨C 5)

5

4

15

¡Â (¨C 8 )

10

B.

¨C

D.

2 ¡Â 18

3

¡Â 20

7

5

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