Subtract.
$\begin{array}{r}
-8-(-5)= \\
2-(-9)=
\end{array}$
Answer (1)
Subtracting a negative number is the same as adding a positive number.
Rewrite the first expression: − 8 − ( − 5 ) = − 8 + 5 = − 3 .
Rewrite the second expression: 2 − ( − 9 ) = 2 + 9 = 11 .
The results of the subtractions are − 3 and 11 .
Explanation
Understanding the Problem We are asked to perform two subtraction operations. The key to subtracting a negative number is recognizing that subtracting a negative is the same as adding a positive. In other words, a − ( − b ) = a + b . We will apply this rule to both expressions.
Calculating the First Expression Let's apply this rule to the first expression: − 8 − ( − 5 ) . This becomes − 8 + 5 . When we add these two numbers, we are adding a negative number and a positive number. Since the absolute value of -8 is greater than the absolute value of 5, the result will be negative. The difference between 8 and 5 is 3, so the result is -3. Thus, − 8 − ( − 5 ) = − 3 .
Calculating the Second Expression Now, let's apply this rule to the second expression: 2 − ( − 9 ) . This becomes 2 + 9 . When we add these two numbers, we are adding two positive numbers, so the result will be positive. The sum of 2 and 9 is 11. Thus, 2 − ( − 9 ) = 11 .
Examples
Understanding subtraction of negative numbers is crucial in many real-world scenarios. For example, if you have a debt of $8 and then you receive $5, your net worth is -$8 + $5 = -$3. Similarly, if the temperature is 2 degrees Celsius and it increases by 9 degrees Celsius, the new temperature is 2 + 9 = 11 degrees Celsius. These basic arithmetic operations are fundamental to managing finances, understanding temperature changes, and many other everyday situations.
