Problem 34 - Beginning and Intermediate Algebra

Question

Find each sum. $$ -1.25+(-6.88) $$

Step-by-Step Solution

Answer

-8.13

Step 1 - Understand the Addition of Negative Numbers

When adding two negative numbers, the sum will also be negative. Each of the numbers remains in the negative range, making the final result more negative.

Step 2 - Write Down the Addition Problem

Write the equation: -1.25 + (-6.88)

Step 3 - Combine the Numbers

Combine -1.25 and -6.88 by aligning their decimal points. Add them as you would with positive numbers: -1.25 + (-6.88) = -8.13

Step 4 - Add Negative Sign

Since both numbers are negative, keep the negative sign in the final answer.

Step 5 - Write the Final Answer

The final sum of the addition is -8.13.

Key Concepts

negative numbers

When we talk about negative numbers, we refer to numbers less than zero. These are usually identified with a minus sign (-) in front of them. For example, -3, -0.75, and -25 are all negative numbers. Understanding negative numbers is important because they show up in various fields, such as temperatures below zero or bank overdrafts.
When you add negative numbers together, think of it as moving further away from zero in the negative direction.
For instance, if you add -2 and -3, you go from -2 to -5, which is further away from zero. This can be confusing at first, but remember: adding two negative numbers always results in a more negative number.

decimal addition

Decimal addition may seem tricky, but it's similar to whole number addition.
When you add decimal numbers, make sure to line up the decimal points. This ensures that you add corresponding place values correctly, such as tenths with tenths and hundredths with hundredths. For instance, if adding 1.25 and 3.67, you would align them like this:

1.25
+3.67
______
It's also helpful to handle any empty spaces by filling them with zeros if needed. This won’t change the number’s value but makes the addition clearer. Make sure to keep the decimal point in the aligned spot to get an accurate result. For example, adding 0.5 and 0.75:

0.50
+0.75
_____

negative sum

A negative sum occurs when the result of adding two or more numbers gives you a negative number. In our exercise, -1.25 + (-6.88) results in -8.13.
Why? Because both numbers are already negative, so you're combining two negative amounts.
Think of it as like owing money: if you owe \(1.25 and then you owe an additional \)6.88, you now owe $8.13 in total. That's why the sum is negative and indicates a greater deficit. It doesn't matter how many negative numbers you add together; the result will always be more negative.

number alignment

Proper number alignment is essential in performing accurate arithmetic operations. For adding decimals, line up the numbers by their decimal points.
This means all the digits should be in the correct place value column. This will make it easier to add corresponding digits:

-1.25
-6.88
_____
Notice how the decimal points are stacked vertically. This ensures that tenths align with tenths, and hundredths with hundredths.
When all digits are correctly placed, you can then proceed with straightforward addition, treating the numbers as if they were positive, but remembering to keep the result negative if adding negative numbers.