Find the value of $-12+8-(-9)$.
Answer (2)
Rewrite the expression: − 12 + 8 − ( − 9 ) = − 12 + 8 + 9 .
Add the first two numbers: − 12 + 8 = − 4 .
Add the result to the remaining number: − 4 + 9 = 5 .
The final answer is 5 .
Explanation
Understanding the Problem We are asked to find the value of the expression − 12 + 8 − ( − 9 ) . This involves adding and subtracting integers. Let's break it down step by step.
Rewriting the Expression First, we can rewrite the expression to remove the double negative. Recall that subtracting a negative number is the same as adding the positive number. So, − ( − 9 ) becomes + 9 . The expression now is − 12 + 8 + 9 .
Adding the First Two Numbers Next, we perform the addition from left to right. First, we add − 12 and 8 . Since − 12 is negative and 8 is positive, we subtract their absolute values: ∣ − 12∣ − ∣8∣ = 12 − 8 = 4 . Since the number with the larger absolute value is − 12 , the result is negative: − 4 . So, − 12 + 8 = − 4 .
Adding the Result to the Remaining Number Now, we add the result, − 4 , to the remaining number, 9 . Again, we have a negative number and a positive number. We subtract their absolute values: ∣9∣ − ∣ − 4∣ = 9 − 4 = 5 . Since the number with the larger absolute value is 9 , the result is positive: 5 . So, − 4 + 9 = 5 .
Final Answer Therefore, the value of the expression − 12 + 8 − ( − 9 ) is 5 .
Examples
Understanding how to add and subtract integers is crucial in managing finances. For example, if you have a bank account with a starting balance of $0, and you deposit $8, then spend $12, and then receive a refund of $9, the expression -12+8-(-9) helps you calculate your final balance, which would be $5.
The evaluated expression − 12 + 8 − ( − 9 ) becomes − 12 + 8 + 9 , which equals 5 . Step-by-step, we calculate − 12 + 8 to get − 4 , and then − 4 + 9 gives us the final answer of 5 . Thus, the value of the expression is 5 .
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