Problem 42 - Algebra 1

Question

Find the sum. Use a calculator if you wish. $$-7344.28+2997.65+(-255.11)$$

Step-by-Step Solution

Answer

The sum of given numbers is -4601.74.

Step 1: Identify And Arrange The Numbers

The numbers given are -7344.28, 2997.65 and -255.11. Take note of the negative sign before the first and the last numbers. Arrange them for addition as -7344.28 + 2997.65 + (-255.11).

Step 2: Addition of The Numbers (with calculator)

With the help of a calculator, add the numbers together. Start by adding the first two numbers (-7344.28 + 2997.65) which gives -4346.63. Then add the previous result with the next number (-4346.63 + -255.11).

Step 3: Final Result Calculation

After executing the final addition step in step 2, find the result. By adding -4346.63 with -255.11, we get -4601.74.

Key Concepts

Real Numbers

In mathematics, real numbers are a fundamental concept used in various calculations, from basic arithmetic to complex analysis. A real number can be any number on the continuous number line, which includes both rational and irrational numbers.

Real numbers are represented by the symbol \( \mathbb{R} \). They include:

• Positive numbers, like 3, 15, or 202.8
• Negative numbers, like -5, -20.17, or -7344.28, which are crucial in our context
• Zero, which is the neutral element in addition
• Fractions and decimals, both positive and negative

Understanding real numbers is essential because they provide a way to express a wide range of quantities. Whether dealing with distances, temperatures, or financial figures, real numbers help us model the real world in a mathematical form.

In the given problem, we are adding real numbers that include negative decimals. Handling these numbers accurately is key to solving the exercise.

Addition

Addition is one of the basic operations in arithmetic and algebra, and it involves combining two or more numbers to get a sum. When adding real numbers, it is important to consider the signs of these numbers, especially when they are negative.

In the exercise, you encounter negative numbers like \(-7344.28 \) and \(-255.11 \). Adding negative numbers involves understanding that these numbers reduce the total sum because you are essentially adding a deficit.

• To add two negative numbers, sum their absolute values and prefix the result with a negative sign.
• To add a negative and a positive number, determine which has the greater absolute value; the sign of the larger absolute value will be the sign of the result.

For example:

• \( -7344.28 + 2997.65 = -4346.63 \) (the result takes the sign of the larger number, which is negative).
• \(-4346.63 + (-255.11) = -4601.74\) (summing two negative numbers).

Understanding addition of real numbers allows learners to solve problems that involve combining various quantities, ensuring accurate mathematical computations.

Algebraic Operations

Algebraic operations are the procedures we follow to manipulate and solve equations involving variables and constants. Addition, subtraction, multiplication, and division are key concepts tied to algebraic operations.

For this exercise, the focus is on adding real numbers, an operation that requires careful attention to signs and sequence in algebra. The numbers presented, like \(-7344.28 \), must be calculated with the understanding of how negative values affect the result.

• Negative numbers subtract from the total sum due to their lesser value compared to positive numbers.
• Calculators can assist but understanding the math behind the operation is vital for error-free calculations.

In the example given:

• Identify each number and its sign.
• Use a calculator to handle the decimal places effectively. This ensures accuracy in basic algebraic operations.

Ultimately, mastering algebraic operations provides a foundation for advanced mathematical topics and practical problem-solving skills, irrespective of complex or simple equations.