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Which of these expressions demonstrates the identity property? Check all that apply.

A. [tex]$25(0)=25$[/tex]
B. [tex]$25(1)=25$[/tex]
C. [tex]$25+0=25$[/tex]
D. [tex]$25+1=25$[/tex]

Sagot :

GinnyAnswer
To determine which of these expressions demonstrates the identity property, let’s examine each expression individually.

1. Expression: [tex]\( 25(0) = 25 \)[/tex]
- Evaluate the left-hand side: [tex]\( 25 \times 0 = 0 \)[/tex].
- Compare it with the right-hand side: [tex]\( 0 \neq 25 \)[/tex].
- Conclusion: This does not demonstrate the identity property.

2. Expression: [tex]\( 25(1) = 25 \)[/tex]
- Evaluate the left-hand side: [tex]\( 25 \times 1 = 25 \)[/tex].
- Compare it with the right-hand side: [tex]\( 25 = 25 \)[/tex].
- Conclusion: This demonstrates the identity property for multiplication.

3. Expression: [tex]\( 25 + 0 = 25 \)[/tex]
- Evaluate the left-hand side: [tex]\( 25 + 0 = 25 \)[/tex].
- Compare it with the right-hand side: [tex]\( 25 = 25 \)[/tex].
- Conclusion: This demonstrates the identity property for addition.

4. Expression: [tex]\( 25 + 1 = 25 \)[/tex]
- Evaluate the left-hand side: [tex]\( 25 + 1 = 26 \)[/tex].
- Compare it with the right-hand side: [tex]\( 26 \neq 25 \)[/tex].
- Conclusion: This does not demonstrate the identity property.

The identity properties in mathematics state:
- Additive Identity: Adding 0 to any number does not change the number ([tex]\( a + 0 = a \)[/tex]).
- Multiplicative Identity: Multiplying any number by 1 does not change the number ([tex]\( a \times 1 = a \)[/tex]).

Based on the evaluation, the expressions that demonstrate the identity property are:
- [tex]\( 25(1) = 25 \)[/tex]
- [tex]\( 25 + 0 = 25 \)[/tex]

Therefore, the expressions that demonstrate the identity property are:
[tex]\[ 25(1)=25 \][/tex]
[tex]\[ 25+0=25 \][/tex]
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