Problem 41 - Prealgebra

Question

Add or subtract the decimals, as indicated. \(-4.47+(-2)\)

Step-by-Step Solution

Answer

The result of the addition is -6.47.

Step 1: Understand the Problem

We have to add two numbers: a decimal and an integer. The numbers in the equation are: -4.47 and -2. The operation we need to perform is addition.

Step 2: Convert the Problem into a Simple Equation

Express the problem directly as an addition of the two numbers: \(-4.47 + (-2) \) This can be rewritten as \(-4.47 - 2 \) as adding a negative is the same as subtracting.

Step 3: Align the Decimal Points

When dealing with decimals, it's important to align the decimal points of the numbers while performing the operation:\(\begin{array}{r} -4.47 \ -2.00 \ \hline ?\end{array}\)

Step 4: Perform the Subtraction

Subtract the numbers as you would do for whole numbers, keeping in mind to align the decimal point in the result as well:\(\begin{array}{r} -4.47 \ -2.00 \ \hline -6.47\end{array}\)

Step 5: Check the Sign of the Result

Both numbers are negative, so the result will also be negative. Therefore, \(-4.47 + (-2) = -6.47\).

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They appear to the left of zero on the number line. This is important to know because negative numbers behave differently than positive numbers in arithmetic operations. For example, adding two negative numbers means you're actually moving further left on the number line. If you add

• -4.47
• -2

You're essentially combining their distances in the negative direction. Always remember: - **Adding two negative numbers** results in a larger negative number. - **Subtracting a negative number** is equivalent to adding its positive counterpart. Recognizing and correctly handling negative numbers in equations is crucial for accurate calculations. Feel free to visualize negative numbers on a number line as they can help you see their relationships clearly.

Decimal Subtraction

Decimal subtraction involves taking one decimal number away from another. The challenge often lies in ensuring the decimal points are properly aligned during the operation. This helps prevent calculation errors. Let's consider the decimal subtraction example from the solution:

• -4.47
• -2

First, rewrite the addition equation as a subtraction:

• \(-4.47 + (-2)\)
• becomes \(-4.47 - 2\)

Usually, when performing subtraction, make sure:- Align the decimal points.- Fill in zeros if necessary to make decimal places even.By carefully subtracting each column, starting from the rightmost part to the left, and ensuring decimal alignment, you can arrive at the correct results. In the given solution:

• -4.47 - 2.00 = -6.47

Don't forget to carry over if the top digit is smaller than the bottom. Decimal subtraction is similar to whole numbers but with an extra focus on lining up the decimals.

Integer Addition

Integer addition involves summing two numbers, regardless of whether they are positive or negative. With negative numbers, the usual rules apply but keep in mind the direction on the number line. Take

• -4.47
• -2

When you add these, you are adding two negatives, which will result in a larger negative number due to the nature of integer arithmetic. When combining integers:- If both integers are negative, the sum is negative, and you add their absolute values.- If both are positive, the sum is positive, and you also add their absolute values.- If they differ in sign, subtract the smaller absolute value from the larger one, and take the sign of the number with the larger absolute value.The operations become even simpler when interpreted visually using a number line:- Adding a negative integer, like adding \(-2\) to (-4.47) , pulls the total further away from zero. This understanding will make integer addition, even when decimals are involved, straightforward.