1-1 Patterns and Expressions

Quick Review

You can represent patterns using words, diagrams, numbers, and algebraic expressions. You can identify a pattern by looking for the same type of change between consecutive figures or numbers. It often helps to make a table.

Example

Identify a pattern by making a table of inputs and outputs. Include a process column. 7, 14, 21, 28, 35, …

The nth output is 7n.

Exercises

Identify a pattern and find the next three numbers in the pattern.

5. 5, 10, 15, 20, …
6. 3, 4, 5, 6, …

Copy and complete the table. Then find the output when the input is n.

7. Input	Output
   1	9
   2	10
   3	11
   4	□ white square
   ⋮	⋮
   n	□ white square

8. Input	Output
   1	19
   2	38
   3	57
   4	□ white square
   ⋮	⋮
   n	□ white square

9. Finance If you put $20 in your savings account each week, how much have you saved after n weeks?

1-2 Properties of Real Numbers

Quick Review

The natural numbers, whole numbers, integers, rational numbers, and irrational numbers are all subsets of the real numbers.

You can use properties such as the ones listed below to simplify and evaluate expressions.

Example

Identify the property illustrated by the equation.

Exercises

Name the subset(s) of real numbers to which each number belongs.

10. 8.1π
11. − 79 negative 79
12. 121 square root of 121
13. 12 7 8 12 , and 7 eighths

Compare the two numbers. Use < or > . cap use less than or greater than .

14. − 60 , − 8 negative square root of 60 , comma negative 8
15. 5 , 32 5 comma square root of 32

Name the property of real numbers illustrated by each equation.

16. 9 4 ⋅ 4 9 = 1 9 fourths , dot , 4 ninths , equals 1
17. ( 8 ⋅ 1 3 ) ⋅ 12 = 8 ⋅ ( 1 3 ⋅ 12 ) open . 8 dot , 1 third . close . dot 12 equals 8 dot . open . 1 third , dot 12 . close

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