Problem 38 - Algebra 1

Question

Find the sum. Use a calculator if you wish. $$10.97+(-51.14)+(-40.97)$$

Step-by-Step Solution

Answer

The sum of \(10.97\), \(-51.14\), and \(-40.97\) is \(-81.14\).

Step 1 - Identify the Numbers

Identify the three numbers that needs to be added: \(10.97\), \(-51.14\), and \(-40.97\). Remember that adding a negative number is the same as subtracting its absolute value.

Step 2 - Add the Positive Number and the First Negative Number

First, add the positive number \(10.97\) and the first negative number \(-51.14\). Which is equivalent to subtracting \(51.14\) from \(10.97\), giving us \(-40.17\).

Step 3 - Add the Result with the Second Negative Number

Next, add the result \(-40.17\) with the second negative number \(-40.97\). This is also equivalent to subtracting \(40.97\) from \(-40.17\), which gives us \(-81.14\).

Key Concepts

Understanding Basic Arithmetic

Basic arithmetic is the foundation of all mathematics and includes operations such as addition, subtraction, multiplication, and division. These operations are used to perform calculations on numbers, which can be positive, negative or even zero. It's crucial to master basic arithmetic to make progress in more advanced math topics.

When dealing with basic arithmetic, remember the following points:

• Always start by identifying the numbers and their signs.
• Group similar types of numbers (positive with positive, and negative with negative) for easier calculation.
• Use the number line concept to help visualize addition and subtraction.
• Remember the key property that adding a negative number is equivalent to subtracting the positive value of that number.

Using arithmetic correctly requires careful attention to these fundamental principles which will help you approach more complex problems with confidence.

Adding Negative Numbers

Adding negative numbers can sometimes be confusing, but it's an important concept in mathematics. When you add a negative number to another number, you're essentially moving to the left on the number line.

Consider these tips for adding negative numbers:

• Adding a negative number is like subtracting its positive counterpart. For instance, \( 5 + (-3) \) is the same as \( 5 - 3 \).
• When adding two negative numbers, combine their absolute values, and give the result a negative sign.
• Using a number line can help visualize why adding a negative number decreases the overall value.

Understanding how to add negative numbers will not only aid in solving basic equations but also in dealing with real-world situations, like calculating debts or temperature changes.

Algebraic Operations and Negative Numbers

Algebraic operations, which include addition, subtraction, multiplication, and division, are not limited to positive numbers. Negative numbers can be involved in these operations too, often leading to results that might initially seem counterintuitive.

When performing algebraic operations with negative numbers, keep these points in mind:

• The sum of a positive and negative number will have the sign of the number with the larger absolute value.
• Subtracting a negative number is equivalent to adding its positive value—this can be thought of as the 'double negative' rule.
• In multiplication and division, two negative numbers result in a positive product or quotient, while a positive and a negative number give a negative result.

Mastering algebraic operations with negative numbers expands your capability to solve a wider range of mathematical problems effectively.