If $a+b=c$ and $b=5$, then $a+5=c$ is known as the _______ property.
A) substitution
B) reflexive
C) symmetric
D) transitive
Answer (1)
The problem involves identifying the property that allows us to replace b with 5 in the equation a + b = c , given that b = 5 . The substitution property is the correct answer, as it allows us to replace equal values in an equation. Therefore, the answer is s u b s t i t u t i o n .
Explanation
Understanding the Problem We are given the equation a + b = c and the information that b = 5 . We want to determine which property allows us to conclude that a + 5 = c .
Applying the Substitution Property The substitution property states that if two things are equal, one can be substituted for the other. In this case, since b = 5 , we can substitute 5 for b in the equation a + b = c . This gives us a + 5 = c .
Understanding the Reflexive Property The reflexive property states that any quantity is equal to itself (e.g., a = a ). This property is not relevant to the given problem.
Understanding the Symmetric Property The symmetric property states that if a = b , then b = a . While we know b = 5 , using the symmetric property would only tell us that 5 = b , which doesn't directly lead to the conclusion a + 5 = c .
Understanding the Transitive Property The transitive property states that if a = b and b = c , then a = c . This property is not directly applicable here, as we don't have a chain of equalities in that form.
Conclusion Therefore, the property that allows us to conclude a + 5 = c from a + b = c and b = 5 is the substitution property.
Examples
In cooking, if a recipe calls for 2 cups of milk, but you know that 1 cup is equal to 8 ounces, you can substitute 8 ounces + 8 ounces for 2 cups. This substitution helps you measure the ingredients accurately. The substitution property is fundamental in many areas of life where equivalent values can be interchanged without changing the outcome.
