Problem 30 - Intermediate Algebra

Question

Perform the operations. See Example 2 . $$ 5-(-3)-2 $$

Step-by-Step Solution

Answer

The result is 6.

Step 1: Convert Subtraction of Negative to Addition

When subtracting a negative number, the operation changes to addition. Therefore, the expression becomes: \[5 - (-3) - 2 = 5 + 3 - 2\]

Step 2: Perform Addition

Next, add the numbers from the expression:\[5 + 3 = 8\]

Step 3: Perform Subtraction

Finally, subtract the remaining number:\[8 - 2 = 6\]

Key Concepts

Understanding Integer Addition

Integer addition is a fundamental math concept that is simple yet crucial. It involves combining two or more integers, which are whole numbers including zero as well as positive and negative numbers. When adding integers, if both numbers have the same sign, you simply add their absolute values. That means you ignore the signs, add the numbers, and then put the sign back to the result.
For example, adding two positive numbers like 4 and 7 results in 11. Similarly, adding two negative numbers like -4 and -7 results in -11.
- If integers have different signs, you subtract the smaller absolute value from the larger and take the sign of the number with the larger absolute value. Adding integers skillfully is a key to mastering integer operations, and helps when you perform more complex calculations in algebra and beyond.

Mastering Integer Subtraction

Integer subtraction might seem tricky at first because it includes the concept of subtracting negative numbers. But with a little practice, it becomes much simpler. The main rule to solve an integer subtraction problem is to convert it to an addition problem by changing the subtraction sign to an addition sign, and flipping the sign of the integer being subtracted.
This is because subtracting a negative is the same as adding the positive value of that number. For example, when handling an expression like 5 - (-3), you turn it into 5 + 3, because subtracting the negative number means moving in the positive direction on the number line. - With this inversion, it's easier to manage and simplifies your calculations, making subtraction a breeze.

Negative Numbers Explained

Negative numbers are a core element of mathematics. They are any numbers less than zero and are represented with a minus sign. These numbers are crucial in various applications where you need to express loss, decrease, or a direction opposite to an assumed positive direction.
When working with negative numbers in operations like addition and subtraction, it's important to follow key rules:

• Adding a negative number means moving left on the number line, or decreasing the total value.
• Subtracting a negative number translates to adding its positive opposite, effectively increasing the value.

Understanding these basics helps make processes involving negative numbers, such as the given example, straightforward and logical.