Problem 86 - Elementary and Intermediate Algebra

Question

Add. $$ -0.9+(-1.9)+(-2.9) $$

Step-by-Step Solution

Answer

The sum is -5.7.

Step 1: Understand the problem

The problem asks us to add three negative decimal numbers: -0.9, -1.9, and -2.9.

Step 2: Add the first two numbers

Start by adding the first two numbers. Calculate: \(-0.9 + (-1.9)\)This equals \(-0.9 - 1.9 = -2.8\).

Step 3: Add the result to the third number

Now, take the result from Step 2 and add the third number:\(-2.8 + (-2.9)\)This is the same as:\(-2.8 - 2.9 = -5.7\).

Step 4: Finalize the answer

The sum of all three numbers is calculated in the previous step: \(-5.7\).

Key Concepts

Decimal Addition

Decimal addition involves summing numbers that include decimal points. When adding decimals, it's important to align the decimal points to ensure each place value is correctly added. For instance, when we have the numbers

• -0.9
• -1.9
• -2.9

Always align them vertically by their decimal points:
-0.9
-1.9
-2.9
Once aligned, you can add them similarly to whole numbers, just keep track of the decimal location in your result to avoid errors. Remember, the decimal in the result should also be directly below the decimals in the original numbers. This way ensures your addition is accurate.

Negative Numbers in Arithmetic

In arithmetic, negative numbers are simply numbers less than zero. They are represented with a minus sign (e.g., -2, -5.7). When thinking about adding negative numbers, imagine you're continuing to move backward on a number line.

• For instance, o(-0.9) indicates you're 0.9 units below zero on the number line.
• Then moving by -1.9 means you'll shift even further back by 1.9 units.
• When adding another negative number (-2.9), you keep sliding to the left.

If this is confusing, it might help to think in terms of debt. Adding a negative is like taking on more debt. So, -0.9 plus -1.9 means you owe 0.9 and you're adding more, making it a total debt of 2.8. Further adding -2.9 increases the total debt even more, resulting in -5.7. In arithmetic, the negative sign signifies moving backward or subtracting, even while adding.

Step-by-Step Addition

Understanding how to perform step-by-step addition helps with more complex calculations. Consider the problem of adding

• -0.9
• -1.9
• -2.9

One efficient technique is to take two numbers at a time.
Start by adding the first pair: \(-0.9 + (-1.9)\)which simplifies to moves in the number line and results in \(-2.8\).
Then, combine this intermediate result with the next number: \(-2.8 + (-2.9)\).
This compound addition ensures methodical progress through the problem, confirming each smaller result before tackling more complexity. Finalizing with \(-5.7\)shows careful progression and thorough checking. This method not only gives accurate results but enhances understanding, making addition of any sequence of numbers, whether positive or negative, more manageable.