Final answer:
The algebraic property of equality used when stating that if 6 = 60, then 1 = 10, is the Division Property of Equality. This property allows division of both sides of an equation by the same non-zero number while maintaining the truth of the equation.
Step-by-step explanation:
The question asks to identify the algebraic property of equality that is being used when we infer that if 6 = 60, then 1 = 10. Looking at the given statement, the correct algebraic property is the Division Property of Equality, which states that if we divide both sides of an equation by the same non-zero number, the equality remains true. Applying this property to the equation 6 = 60, we can divide both sides by 6, which gives us 1 = 10 after applying the property correctly.
Let us consider the equation step-by-step:
- We start with the given equation: 6 = 60.
- To find the value that corresponds to 1, we divide both sides of the equation by 6.
- Dividing both sides by 6 gives us: \(\frac{6}{6} = \frac{60}{6}\)
- Perform the division: 1 = 10.
This shows that the Division Property of Equality is used to maintain the balance in the equation and allows us to find that if 6 = 60, then 1 = 10. None of the other options (Substitution, Transitive, or Additive Property of Equality) describe this operation.
Thermodynamics is not directly related to this question, but it is interesting to note that the concept of equality and balance is a common theme in both algebra and physics. In thermodynamics, principles like the conservation of energy or the transitive property of thermal equilibrium ensure that there is a balance in the transfer of energy and heat.