Final answer:
The number 24 shows the age difference between Timmy and his dad and works in both the addition and subtraction equations due to the inverse property of addition and subtraction. Adding 24 to Timmy's age gives us his dad's age, while subtracting 24 from the dad's age gives us Timmy's age.
Step-by-step explanation:
To determine how much older Timmy's dad is than Timmy, we start with Timmy's age, which is 8 years old, and hop up to his dad's age, which is 32 years old. By adding 24 to Timmy's age, we reach his dad's age: 8 + 24 = 32. Conversely, if we start with the dad's age and want to find out Timmy's age, we would subtract 24: 32 - 24 = 8.
The number 24 works in both equations because of the relationship between addition and subtraction; they are inverse operations. This means that if you add a number to another number and then subtract the same number, you are back to where you started. This concept is a basic property in arithmetic known as the inverse property of addition and subtraction.
The mathematical principle behind this is that addition or subtraction of the same number on both sides of an equation does not change the equality. An equation represents a balance, and performing the same operation on both sides keeps the balance intact. This is why 24 can be added to Timmy's age or subtracted from the father's age to show the age difference between them.