1. This document provides examples and guided practice problems involving properties of numbers and algebraic expressions. 2. Example 1 names properties like the commutative property and order of operations illustrated in equations. Example 2 involves using mental math to simplify expressions. 3. The guided practice problems that follow involve applying skills like adding numbers mentally to find a total, identifying mistakes in solutions, and setting up and solving multi-step word problems.

1. Standards Practice AF 1.3
A Practice by Example Name the property each equation illustrates.
Example 1 1. k 5 6 5 k 6 Guided Practice
(page 27) The order of the factors changes, so This exercise has been
started for you!
the equation illustrates the 9.
2. 1 h h 3. ( e d) f e (d f)
4. t 7 c t c 7 5. 4 (wx) ( 4 w)x
6. ab ba 7. m 0 m
Example 2 Mental Math Use mental math to simplify each expression.
(page 27)
8. 5 47 2 Guided Practice
This exercise has been
5 47 2 5 2 47 started for you!
9. 3 . 5 9 6.5 10. 70 1 4
11. 40 ( 33 25) 12. (17 24) 18
For: Examples 1–2 13. 5 . 75 0 18. 25 14. 20 19 5
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15. A train started a trip pulling 9 cars. At the first stop, 17 cars were
added to the train. At the second stop, 11 more cars were added.
Use mental math to find the number of cars the train was pulling
after the second stop.
B Apply Your Skills 16. Guided Problem Solving Four running clubs raised money in a
24-hour relay race. Club A ran 183 mi, Club B ran 144 mi, Club C
ran 117 mi, and Club D ran 146 mi. What was the total number of
miles that all four clubs ran?
• Which pairs of numbers can you add easily using mental math?
• What is the sum of each of those pairs?
Use R, , or S to complete each statement.
17. 41 29 70 18. 737 373 4 11 25
19. Writing in Math At the
right is your friend’s 100 (5 9) (100 5) 9
incorrect solution to a 500 9
problem. Explain your 509
friend’s mistake.
20. In a student art contest there are 14 drawings, 22 sculptures, and
some paintings. There are 18 more paintings than sculptures. What
is the total number of art pieces?
28 Chapter 1 Variables and Algebraic Expressions 1-5 Properties of Numbers