To solve this problem, we need to match each given expression with the appropriate property of real numbers. Let's analyze each expression step by step:
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1. \( 11 + 0 = 11 \)
- This expression shows that adding 0 to any number leaves the number unchanged.
- This is the definition of the
additive identity.
-
Answer: \( e \) (additive identity)
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2. \( x \times (y \times z) = (x \times y) \times z \)
- This expression demonstrates that the way in which numbers are grouped during multiplication does not affect the result.
- This is the
associative property of multiplication.
-
Answer: \( d \) (associative property of multiplication)
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3. \( 8 + (-8) = 0 \)
- This expression shows that adding a number to its opposite (negative) results in 0.
- This is the definition of the
additive inverse.
-
Answer: \( h \) (additive inverse)
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4. \( 14 + 20 = 20 + 14 \)
- This expression demonstrates that the order in which numbers are added does not affect the result.
- This is the
commutative property of addition.
-
Answer: \( a \) (commutative property of addition)
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5. \( 2 \times \frac{1}{2} = 1 \)
- This expression shows that multiplying a number by its reciprocal (multiplicative inverse) results in 1.
- This is the definition of the
multiplicative inverse.
-
Answer: \( i \) (multiplicative inverse)
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6. \( 22 \times 1 = 22 \)
- This expression demonstrates that multiplying any number by 1 leaves the number unchanged.
- This is the definition of the
multiplicative identity.
-
Answer: \( f \) (multiplicative identity)
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7. \( (19 + 12) + 8 = 19 + (12 + 8) \)
- This expression shows that the way in which numbers are grouped during addition does not affect the result.
- This is the
associative property of addition.
-
Answer: \( c \) (associative property of addition)
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8. \( a \times 9 = 9 \times a \)
- This expression demonstrates that the order in which numbers are multiplied does not affect the result.
- This is the
commutative property of multiplication.
-
Answer: \( b \) (commutative property of multiplication)
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9. \( 7(4 + 11) = 7(4) + 7(11) \)
- This expression shows that multiplying a number by a sum is the same as multiplying the number by each term in the sum and then adding the results.
- This is the
distributive property.
-
Answer: \( g \) (distributive property)
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Final Answer:
\[
\boxed{
\begin{array}{ll}
1. & e \\
2. & d \\
3. & h \\
4. & a \\
5. & i \\
6. & f \\
7. & c \\
8. & b \\
9. & g \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of properties of real numbers worksheet answers.
