Problem 69 - Algebra 1

Question

Evaluate the expression. Use estimation to check your answer. $$ -13.87-(-13.87)+5.8 $$

Step-by-Step Solution

Answer

The solution to the equation is 5.8.

Step 1: Recognize the Double Negative

In the expression, -13.87 is subtracted by -13.87. Since subtraction is the addition of the negative value, this can also be interpreted as -13.87 plus 13.87.

Step 2: Simplify the Expression

Now, start by simplifying -13.87 + 13.87. These cancel each other out since they are the same number but of opposing signs. Therefore, -13.87 + 13.87 equals 0. Next, we add this result to the remaining number 5.8. So, 0 + 5.8 equals 5.8.

Step 3: Estimate to check the answer

An estimation of the equation can be achieved by rounding up the decimals to whole numbers: -14 - (-14) + 6. Simplifying this, -14 + 14 equals 0 and adding 6 gives 6. This estimated result is close to the calculated result which is 5.8. Thus, the answer is likely correct.

Key Concepts

Negative Numbers

Negative numbers can sometimes seem tricky since they involve values less than zero, but they follow the same basic arithmetic rules as positive numbers.

• A negative sign (-) in front of a number simply indicates it is less than zero.
• Subtracting a negative number is the same as adding its positive counterpart. This is because subtraction acts like adding the opposite value.
• For example, in the expression \(-13.87 - (-13.87)\), subtracting \(-13.87\) is the same as adding \(13.87\).

Understanding this concept helps simplify expressions and avoid confusion. When faced with negative numbers, it is important to apply these principles consistently.

Estimation

Estimation provides a quick way to check calculations for errors, helping to verify that answers are reasonable and likely correct.

• Rounding numbers to the nearest whole number simplifies calculations and makes them quicker to perform.
• In the given expression, \(-13.87\) can be estimated as \(-14\), and \(5.8\) as \(6\). By simplifying, the expression becomes \(-14 - (-14) + 6\).
• This estimation gives an answer of \(6\), which helps confirm that the accurate calculation of \(5.8\) is reasonable.

Using estimation effectively involves recognizing when values can be approximated, allowing you to double-check calculations efficiently.

Arithmetic Operations

Arithmetic operations are the building blocks of mathematics and include addition, subtraction, multiplication, and division. In this exercise, we see how addition and subtraction can work together.

• Simplifying expressions often requires employing multiple operations efficiently. In the expression \(-13.87 + 13.87 + 5.8\), addition and subtraction interplay to simplify the numbers.
• Although subtraction is performed first, it's actually an addition of a negative value, transforming it into \(-13.87 + 13.87\).
• Once simplified, the remaining term is added, producing the final result \(5.8\).

Mastering arithmetic operations is essential for solving various types of mathematical problems, allowing for accurate and efficient computation.