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]
