Let's go through each equation and identify the
property of real numbers used. Here's a breakdown with explanations:
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1. $ 3 \times 5 = 5 \times 3 $
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Property Used:
Commutative Property of Multiplication
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Explanation: This property states that changing the order of the numbers being multiplied does not change the product. So, $ a \times b = b \times a $.
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2. $ 9 + 0 = 9 $
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Property Used:
Identity Property of Addition
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Explanation: Adding zero to any number leaves the number unchanged. The number 0 is the
additive identity.
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3. $ (-12 + 3) + 4 = -12 + (3 + 4) $
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Property Used:
Associative Property of Addition
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Explanation: This property allows us to group numbers differently when adding without changing the sum. So, $ (a + b) + c = a + (b + c) $.
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4. $ 28 \times \frac{1}{28} = 1 $
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Property Used:
Inverse Property of Multiplication
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Explanation: A number multiplied by its reciprocal equals 1. The multiplicative inverse of $ a $ is $ \frac{1}{a} $, so $ a \times \frac{1}{a} = 1 $.
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5. $ 2c + 5 - 3d = 2c - 3d + 5 $
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Property Used:
Commutative Property of Addition
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Explanation: The order of adding terms can be changed. Even though variables are involved, this is still rearranging addends: $ a + b = b + a $. Here, 5 is moved past $ -3d $, which is valid due to commutativity.
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6. $ 19 \times 1 = 19 $
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Property Used:
Identity Property of Multiplication
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Explanation: Multiplying any number by 1 leaves it unchanged. The number 1 is the
multiplicative identity.
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7. $ (2 \times 8) \times 5 = 2 \times (8 \times 5) $
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Property Used:
Associative Property of Multiplication
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Explanation: This property allows us to regroup factors in multiplication without changing the product. So, $ (a \times b) \times c = a \times (b \times c) $.
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8. $ 22 + (-22) = 0 $
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Property Used:
Inverse Property of Addition
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Explanation: Adding a number to its opposite (additive inverse) results in zero. So, $ a + (-a) = 0 $.
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✔ Final Answer Table:
| Equation | Property Used |
|--------|----------------|
| 1. $ 3 \times 5 = 5 \times 3 $ | Commutative Property of Multiplication |
| 2. $ 9 + 0 = 9 $ | Identity Property of Addition |
| 3. $ (-12 + 3) + 4 = -12 + (3 + 4) $ | Associative Property of Addition |
| 4. $ 28 \times \frac{1}{28} = 1 $ | Inverse Property of Multiplication |
| 5. $ 2c + 5 - 3d = 2c - 3d + 5 $ | Commutative Property of Addition |
| 6. $ 19 \times 1 = 19 $ | Identity Property of Multiplication |
| 7. $ (2 \times 8) \times 5 = 2 \times (8 \times 5) $ | Associative Property of Multiplication |
| 8. $ 22 + (-22) = 0 $ | Inverse Property of Addition |
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Parent Tip: Review the logic above to help your child master the concept of number property worksheet.
