Quiz - Properties of Real Numbers worksheet - Free Printable

Problem Overview:

The task is to match each given example with the property of real numbers that it illustrates. The properties listed are:

- Additive Identity (a)
- Additive Inverse (b)
- Associative Property of Addition (c)
- Associative Property of Multiplication (d)
- Commutative Property of Addition (e)
- Commutative Property of Multiplication (f)
- Distributive Property of Multiplication over Addition (g)
- Multiplicative Identity (h)
- Multiplicative Inverse (i)

We will analyze each example and determine which property it represents.

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Solution:

#### 1. \( m + 3 = 3 + m \)
- This shows that the order of addition does not matter.
- Property: Commutative Property of Addition (e)

#### 2. \( w \cdot 1 = w \)
- Multiplying any number by 1 leaves the number unchanged.
- Property: Multiplicative Identity (h)

#### 3. \( a + (b + c) = (a + b) + c \)
- This shows that the grouping of terms in addition does not affect the result.
- Property: Associative Property of Addition (c)

#### 4. \( (2 \cdot x) \cdot y = (x \cdot 2) \cdot y \)
- This shows that the grouping of terms in multiplication does not affect the result.
- Property: Associative Property of Multiplication (d)

#### 5. \( 2x(x + 3) = 2x^2 + 6x \)
- This demonstrates distributing a factor over a sum.
- Property: Distributive Property of Multiplication over Addition (g)

#### 6. \( k + (-k) = 0 \)
- Adding a number to its opposite results in zero.
- Property: Additive Inverse (b)

#### 7. \( (a + b) + c = a + (b + c) \)
- This shows that the grouping of terms in addition does not affect the result.
- Property: Associative Property of Addition (c)

#### 8. \( u + 0 = u \)
- Adding zero to any number leaves the number unchanged.
- Property: Additive Identity (a)

#### 9. \( r \cdot \frac{1}{r} = 1 \)
- Multiplying a number by its reciprocal results in 1.
- Property: Multiplicative Inverse (i)

#### 10. \( m \cdot a \cdot t \cdot h = h \cdot a \cdot m \cdot t \)
- This shows that the order of multiplication does not matter.
- Property: Commutative Property of Multiplication (f)

#### 11. \( (-y) + y = 0 \)
- Adding a number to its opposite results in zero.
- Property: Additive Inverse (b)

#### 12. \( ab + xy = ba + yx \)
- This shows that the order of multiplication does not matter for both terms.
- Property: Commutative Property of Multiplication (f)

#### 13. \( \frac{1}{n} \cdot n = 1 \)
- Multiplying a number by its reciprocal results in 1.
- Property: Multiplicative Inverse (i)

#### 14. \( (2 + m) + 3 = 3 + (2 + m) \)
- This shows that the order of addition does not matter.
- Property: Commutative Property of Addition (e)

#### 15. \( a \cdot (j \cdot e) = (a \cdot j) \cdot e \)
- This shows that the grouping of terms in multiplication does not affect the result.
- Property: Associative Property of Multiplication (d)

#### 16. \( (2 \cdot a) \cdot b = 2 \cdot (a \cdot b) \)
- This shows that the grouping of terms in multiplication does not affect the result.
- Property: Associative Property of Multiplication (d)

#### 17. \( 2x + 6 = 2(x + 3) \)
- This demonstrates factoring out a common factor, which is the reverse of distribution.
- Property: Distributive Property of Multiplication over Addition (g)

#### 18. \( 0 + h = h \)
- Adding zero to any number leaves the number unchanged.
- Property: Additive Identity (a)

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & \text{(e)} \\
2. & \text{(h)} \\
3. & \text{(c)} \\
4. & \text{(d)} \\
5. & \text{(g)} \\
6. & \text{(b)} \\
7. & \text{(c)} \\
8. & \text{(a)} \\
9. & \text{(i)} \\
10. & \text{(f)} \\
11. & \text{(b)} \\
12. & \text{(f)} \\
13. & \text{(i)} \\
14. & \text{(e)} \\
15. & \text{(d)} \\
16. & \text{(d)} \\
17. & \text{(g)} \\
18. & \text{(a)} \\
\end{array}
}
\]