Problem 41 - Prealgebra and Introductory Algebra

Question

Simplify. $$-3.09-4.6-27.3$$

Step-by-Step Solution

Answer

-34.99

Step 1: Identify the operation

The operation given in the problem is subtraction. This involves subtracting a decimal number from another, then subtracting the result from a negative number.

Step 2: Subtract the numbers

Start by performing the subtraction from left to right. First, subtract 4.6 from -3.09. The result is -7.69. Next, subtract 27.3 from -7.69. Since subtraction of a number is equivalent to the addition of its opposite, this is equivalent to adding -27.3 to -7.69.

Step 3: Add the negative numbers

Finally, add the negative numbers -7.69 and -27.3 together. Adding negative numbers is just like adding positive numbers, so -7.69 + -27.3 = -34.99.

Key Concepts

Subtraction of Decimals

Subtraction of decimals might seem daunting at first, but with a few easy steps, it becomes much simpler. When you subtract decimals, it’s important to keep track of the decimal points. Align the numbers vertically so that the decimal points are in a straight line. This ensures that you're subtracting the correct values in each place.

Here's how you can think about it:

• Align the numbers by their decimal points.
• Fill in any empty decimal places with zeros to maintain consistency.
• Subtract each column starting from the rightmost (smallest value) towards the left.

To tackle operations like \(-3.09 - 4.6\), remember you're actually doing \(-3.09 + (-4.6)\). In this case, manage both as negative values when they are subtracted.
After you get the first result, continue using the same logic for additional terms.

Negative Numbers

Understanding negative numbers is essential, especially when dealing with more complex arithmetic like decimal operations. Negative numbers are the values less than zero, typically represented with a minus sign ("). They can initially be tricky to work with, but a few fundamental concepts can help.

Here are the essentials to remember:

• A negative number \(e.g. -3\) indicates a movement below zero.
• Subtracting a negative translates into adding its corresponding positive value.
• Opposite of a negative number is a positive number and vice versa.

In practical terms, when you have an expression like \(-3.09 - 4.6 - 27.3\), each subtraction after the first can be treated as adding a larger negative number, simplifying your calculation process.

Addition of Negative Numbers

Adding negative numbers might seem unusual at first, but it's very similar to adding positive numbers. It involves combining amounts that are below zero, essentially moving further into negative territory.

Consider these key points:

• Adding negative numbers involves summing them as if they were positive, then keeping the negative sign.
• The more you add, the further below zero you go (e.g. \(-7 + -5 = -12\)).
• The concept is the same for both whole numbers and decimals.

In an expression like \(-7.69 + (-27.3)\), treat both values as positives first (i.e., \(7.69 + 27.3\) = 34.99), and then apply the negative sign to get \(-34.99\). This way, you're simply following a logical approach, making the process much more straightforward.