Problem 32 - Algebra A Combined Function

Question

Subtract. \(4.3-(-0.87)\)

Step-by-Step Solution

Answer

The result is 5.17.

Step 1: Recognize the Double Negative

In the expression \(4.3 - (-0.87)\), notice the double negative. Subtracting a negative number is the same as adding its positive counterpart.

Step 2: Rewrite as Addition

Transform the expression to addition. Thus, \(4.3 - (-0.87)\) becomes \(4.3 + 0.87\).

Step 3: Perform the Addition

Add the two numbers together: \(4.3 + 0.87\). Make sure to align the decimal points when adding.\[\begin{array}{c} 4.30 \+ 0.87 \\hline 5.17 \\end{array}\]

Step 4: Confirm the Result

The result of the addition is \(5.17\). Ensure no arithmetic errors occurred during addition by revisiting the calculation if necessary.

Key Concepts

Understanding Negative Numbers

Negative numbers are essential in algebra and appear frequently in real-world scenarios, such as temperatures below zero or bank overdrafts. A negative number is less than zero and is represented by a minus sign (e.g., -5). Understanding their properties is critical for operations like subtraction and addition.

When subtracting a negative number, it's crucial to know that the operation is equivalent to addition. This comes from the rule that subtracting something is the same as adding its opposite. Thus, subtracting a negative becomes adding its positive value. For example, in the expression \(4.3 - (-0.87)\), converting it to addition simplifies the calculation to \(4.3 + 0.87\).

• Remember: two negatives make a positive.
• Use the idea of opposite directions on a number line to help visualize: moving left (negative) and right (positive).

Addition of Numbers

Addition is a basic arithmetic operation where two or more numbers are combined to make a sum. It is one of the four fundamental operations in mathematics, alongside subtraction, multiplication, and division. In algebra, addition is often used to combine values or solve equations.

When dealing with signed numbers (positive and negative), the signs must be carefully managed. As seen in the problem \(4.3 + 0.87\), the conversion from subtraction to addition due to the double negative made the operation straightforward because both numbers are positive.

• Align the numbers vertically by their decimal points to ensure accuracy.
• Change subtraction of a negative to addition, as two negatives make a positive.
• Double-check your sum for simple arithmetic errors, especially when decimals are involved.

Working with Decimal Arithmetic

Decimals are numbers with a fractional part separated from the whole number by a decimal point. They are prevalent in both everyday life, such as in monetary transactions, and in scientific notation. Understanding how to work with decimals is crucial for mathematical accuracy and precision.

In the example given, \(4.3 + 0.87\), dealing with the decimal point requires extra care. Align the decimal points vertically before adding. Each digit should line up precisely for correct computations.

• Always keep the decimal points aligned to maintain place value.
• Add zeros if necessary to ensure all decimal places are filled (as with \(4.3\) becoming \(4.30\)).
• Re-calculate to verify the accuracy when you work with decimals as small deviations can affect the result significantly.