Why can a subtraction problem be rewritten as an additional problem without changing the outcome? Give a real-world scenario where this might be modeled.
You have $10. You spend $4.00 for a cup of coffee. How much do you have left?
10 - 4 = 6
6 + 4 = 10
oh okay thanks Ms. Sue
A subtraction problem can be rewritten as an addition problem without changing the outcome because subtraction is the inverse operation of addition. This means that adding a number and subtracting the same number will result in the initial value.
To understand why this works, let's take an example: 8 - 3.
To rewrite this as an addition problem, we can change the operation to addition and use the same value to be subtracted but with a negative sign. So, 8 - 3 can be written as 8 + (-3).
If we calculate both equations, we find that 8 - 3 equals 5, and 8 + (-3) also equals 5. So, by rewriting the subtraction problem as an addition problem, we obtain the same result.
A real-world scenario where this might be modeled is tracking someone's bank balance. Suppose someone has $100 in their bank account, and they withdraw $30. We can model this situation as a subtraction problem, 100 - 30.
However, we can also model it as an addition problem by considering the withdrawal as a negative amount, -$30, and adding it to the initial balance. So, 100 - 30 is equivalent to 100 + (-30).
Both approaches lead to the same result, which is $70, representing the person's updated bank balance.