Problem 31 - Algebra A Combined Function

Question

Subtract. 3-(-0.62)$

Step-by-Step Solution

Answer

The result is 3.62.

Step 1: Understand the Operation

The given expression is the subtraction of a negative number: 3 - (-0.62). When you subtract a negative number, it's equivalent to adding the positive version of that number.

Step 2: Convert Subtraction to Addition

Convert the expression 3 - (-0.62) into an addition operation. This becomes 3 + 0.62. This step simplifies the problem by getting rid of the negative sign.

Step 3: Perform the Addition

Now, calculate the result of the conversion you did earlier, which is 3 + 0.62. Align the numbers by their decimal points and add them together: \(3.00 + 0.62 = 3.62\).

Key Concepts

Subtracting Negative Numbers

Understanding subtraction with negative numbers can seem tricky at first, but it's simpler than you might think. In mathematics, subtracting a negative number is the same as adding its positive counterpart. This is because the negative of a negative number is positive.

For instance, consider the problem 3 - (-0.62). Here, we are subtracting -0.62 from 3. Instead of taking away a negative number, which can be confusing, we can flip the process. We transform this operation into an addition: 3 + 0.62. This is the essence of handling the subtraction of negative numbers.

This core idea is fundamental in basic arithmetic and helps simplify calculations, making them more intuitive and straightforward.

Conversion to Addition

Converting subtraction of negative numbers into addition is an essential skill in arithmetic. When you see a problem like 3 - (-0.62), the goal is to turn it into something we are more comfortable with: addition.

Essentially, the expression 3 - (-0.62) turns into 3 + 0.62. This conversion happens because subtracting a negative is the same as adding a positive. Once converted, the problem becomes straightforward, and we apply the rules of addition to solve it.

This technique is particularly useful in algebra and calculus, where such expressions commonly appear. Mastering this conversion can greatly enhance your arithmetic skills and accuracy.

Decimal Addition

Adding decimal numbers might seem challenging, but with a systematic approach, it becomes quite manageable. When presented with an addition like 3 + 0.62, the key is to align the decimal points.

Start by writing each number vertically, ensuring the decimal points are in a straight line. For the problem 3 + 0.62:

• 3 is rewritten as 3.00 to match the format, ensuring all decimal places are aligned.
• Then, perform the addition as you would with whole numbers, column by column, starting from the rightmost digit.

The result is straightforward:

• 3.00 + 0.62 = 3.62.

Understanding decimal addition through alignment ensures precision and accuracy in your results.

Basic Arithmetic Operations

Basic arithmetic operations—addition, subtraction, multiplication, and division—form the foundation of mathematics. Grasping these operations is the key to solving more complex math problems.

Each operation follows specific rules, and understanding these can simplify problem-solving processes. For subtraction and addition, it’s important to remember how they relate to each other, especially when negative numbers are involved.

For example, transforming 3 - (-0.62) into an addition problem allows us to handle it easily using decimal addition. Moreover, consistently practicing these operations helps sharpen calculation skills, builds confidence in handling mathematical problems, and prepares you for more advanced mathematics.