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Algebra II & Trigonometry
Date ________________________________________
Properties of Real Numbers
1. Disprove the following statement by giving a counterexample. A counterexample is a specific case that shows that a
statement is false. Explain.
Every real number has a multiplicative inverse.
Name the sets of numbers to which each number belongs.
2. – 4
3. 45
4. 6.23
5.
6.
121
Name the property illustrated by each equation.
2 3
7.   1
8. (a + 4) + 2 = a + (4 + 2)
3 2
10. 5a + (-5a) = 0
11. (3  4)  25 = 3  (4  25)
13. 2 3  5 3  2  5 3
 2  7 
14.  1    1
 7  9 
Identify the additive inverse and multiplicative inverse for each number.
1
15. – 8
16.
3
10
9. 4x + 0 = 4x
12. ab = 1ab
17. 1.5
Determine whether each statement is true or false. If false, give a counterexample.
18. Every whole number is an integer.
19. Every integer is a whole number.
20. Every real number is irrational.
21. Every integer is a rational number.
Simplify each expression.
22. 7a + 3b – 4a – 5b
23. 3x + 5y + 7x – 3y
24. 3(15x – 9y) + 5(4y – x)
25. 2(10m – 7a) + 3(8a – 3m)
26. 8(r + 7t) – 4(13t + 5r)
27. 4(14c – 10d) – 6(d + 4c)
28. 4(0.2m – 0.3n) – 6(0.7m – 0.5n)
29. 7(0.2p + 0.3q) + 5(0.6p – q)
30.
1
6  20 y   1 19  8y 
4
2
31.
1
3x  5y   2  3 x  6y 
6
35
