Grade 12 Math: Properties of Numbers
Explore and apply fundamental properties of real numbers including commutative, associative, distributive, identity, and inverse properties, along with their applications in algebraic expressions and equations.
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Grade 12 Math: Properties of Numbers
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. Which property is demonstrated by the equation 5 + (3 + 2) = (5 + 3) + 2?
Commutative Property of Addition
Associative Property of Addition
Distributive Property
Identity Property of Addition
2. The multiplicative inverse of a non-zero real number 'a' is:
-a
0
1/a
a
3. The property states that for any real numbers a, b, and c, a(b + c) = ab + ac.
4. The additive identity for real numbers is because for any real number a, a + 0 = a.
5. The set of irrational numbers is closed under multiplication.
True
False
6. The associative property applies to both addition and subtraction.
True
False
7. Explain the difference between the commutative property of addition and the associative property of addition.
8. Use the distributive property to simplify the expression 3(x + 5y - 2).
Match each property with its example.
9. Identity Property of Multiplication
a. (ab)c = a(bc)
10. Commutative Property of Multiplication
b. 7 * 1 = 7
11. Associative Property of Multiplication
c. 4 * 5 = 5 * 4
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