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 substitution property is used when one quantity is replaced with an equal quantity. Since b = 5 , substituting 5 for b in the equation a + b = c gives a + 5 = c . Therefore, the answer is s u b s t i t u t i o n .
Explanation
Understanding the Problem We are given that a + b = c and b = 5 . We want to identify the property that 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 .
Concluding the Property Substituting b = 5 into a + b = c gives us a + 5 = c . Therefore, the property used is the substitution property.
Examples
In cooking, if a recipe calls for 2 cups of milk and you know that 1 cup is equal to 8 ounces, you can substitute 8 ounces for 1 cup to get 16 ounces of milk. This is an example of the substitution property in action. Understanding the substitution property is crucial in many areas, from balancing chemical equations to managing your budget.
