Problem 31 - Beginning and Intermediate Algebra

Question

Find each sum. $$ -3.5+12.4 $$

Step-by-Step Solution

Answer

8.9

Step 1 - Understand the problem

Identify the numbers involved in the problem, which are -3.5 and 12.4, and understand that you need to find their sum.

Step 2 - Align the numbers for addition

Make sure that the numbers are lined up correctly by their decimal points: -3.5 +12.4

Step 3 - Perform the addition

Add the numbers starting from the rightmost digits: -3.5 +12.4 = 8.9

Key Concepts

Understanding Negative Numbers

Negative numbers can be a little tricky at first, but once you understand them, they're not so bad! A negative number is a number less than zero and is often used to represent things like debt or temperatures below freezing.
In our example exercise, we are adding -3.5 and 12.4. The minus sign in front of 3.5 indicates that this number is negative.
When you add a negative number to a positive number, you essentially subtract the magnitude of the negative number from the positive number.
So in our exercise, adding -3.5 to 12.4 means subtracting 3.5 from 12.4.
This is why getting a good grip on negative numbers is so important!

Aligning Decimal Points

To add or subtract decimals, it's crucial to align the decimal points of the numbers you are working with.
This ensures that each digit is in the correct place value column (ones, tenths, hundredths, etc.).
Let's look at our exercise: we need to add -3.5 and 12.4. To do this:
- Write down -3.5.
- Underneath, write 12.4, making sure the decimal points are one below the other.
These steps help prevent errors and make it easier to perform the arithmetic operations accurately. Proper alignment of decimal points keeps everything in order and ensures the answer is correct.

Performing Arithmetic Operations

Once the numbers are aligned by their decimal points, you can proceed to perform the arithmetic operations.
In this case, we are adding -3.5 and 12.4. Here’s how:
- Start from the rightmost column (i.e., the tenths place).
- Add the tenths place digits: 4 (from 12.4) and -0.5 (from -3.5).
- This gives 3.9.
- Move to the next left column, which is the ones place.
- Add 2 (from 12.4) and -3 (from -3.5).
- This gives -1.
Combining these results, we have 8.9.
The key to success here is to take it step by step, aligning everything correctly and adding/subtracting each place value carefully. This approach ensures accuracy and helps you build confidence in handling decimal arithmetic.