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Chapter 2: Problem 29

Find the sum. $$-11.6+6.4+(-3.0)$$

Short Answer

Expert verified
The sum of \(-11.6+6.4+(-3.0)\) is \(-8.2\)

Step by step solution

01

Addition of positive and negative numbers

Firstly, separate the positive and negative numbers. We have \(-11.6\) and \(-3.0\) as negative numbers, and \(6.4\) as positive number.
02

Add negative numbers together

When we add the negative numbers, \(-11.6 + -3.0\) we get \(-14.6\)
03

Add result from Step 2 to the positive number

Afterwards, we add the sum of the negative numbers from step 2 to the positive number, \(-14.6 + 6.4\). The answer is \(-8.2\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Addition of Negative Numbers
Working with negative numbers can seem challenging at first, but it becomes simple once you understand the rules. When we add two negative numbers, we are finding the total value of their negative contributions. For example, in the exercise \(-11.6 + (-3.0)\), we combine the negatives by adding their absolute values: \(11.6 + 3.0 = 14.6\), then we apply the negative sign to the result, giving us \(-14.6\).
  • The key is to ignore the negative signs temporarily while adding the numbers.
  • Then, reapply the negative sign to the final sum.
Thinking of negative numbers as money owed can help in visualizing this process. Adding debts together results in a larger total debt.
Combining Positive and Negative Numbers
Combining positive and negative numbers is a fundamental concept in operations with real numbers. It involves either increasing or decreasing a quantity depending on the signs of the numbers involved. In the solution, we combined -14.6 (the sum of two negative numbers) with 6.4, a positive number.

  • The rule to remember is:
    • When the signs are different, subtract the smaller absolute value from the larger absolute value.
    • The result takes the sign of the number with the larger absolute value.
Applying this to our example, we have \(-14.6 + 6.4\). The absolute values 14.6 and 6.4 are compared, subtracted, and because 14.6 is larger, we keep the negative sign. This results in \(-8.2\).
Visualizing this process can highlight the importance of not just the numbers themselves, but the signs they carry.
Number Line Interpretation
A number line is a powerful tool for visualizing operations involving real numbers. It allows us to see where numbers fall relative to each other and how they combine. Consider the exercise again: \(-11.6 + 6.4 + (-3.0)\).
  • Start at zero, move left for negative numbers, and right for positive numbers.
  • For \(-11.6\), move 11.6 units to the left.
  • Then for \(6.4\), move 6.4 units back to the right.
  • Finally, move 3 units to the left for \(-3.0\).
The endpoint on the number line illustrates the sum, which in this case, is \(-8.2\). This visual approach can help clarify the effect of each step in the operation, making more abstract concepts tangible and easier to grasp.

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Most popular questions from this chapter

LEAVING A TIP In Exercises \(83-85\), use the following information. You and a friend decide to leave a \(15 \%\) tip for restaurant service. You compute the tip, \(T,\) as \(T=0.15 C,\) where \(C\) represents the cost of the meal. Your friend claims that an easier way to mentally compute the tip is to calculate \(10 \%\) of the cost of the meal plus one half of \(10 \%\) of the cost of the meal. Will both methods give the same results? Explain.

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ (2 x-4)(-3) $$

MULTI-STEP PROBLEM A customer of your flower shop wants to send flowers to 23 people. Each person will receive an \(\$ 11.99\) "sunshine basket" or a \(\$ 16.99\) "meadow bouquet." a. Let \(s\) represent the number of people who will receive a sunshine basket. Which function can you use to find \(C\), the total cost of sending flowers to all 23 people, depending on how many of each arrangement is sent? (A) \(C=16.99(23-s)+11.99 s\) (B) \(C=11.99 s+16.99(23)\) b. If 8 people receive a sunshine basket, what is the total cost of the flowers? c. If 13 people receive a meadow bouquet, what is the total cost of the flowers? d. CRITICAL THINKING If your customer can spend only \(\$ 300\), what is the greatest number of people that can receive a meadow bouquet?

DISTRIBUTIVE PROPERTY Use the distributive property to rewrite the expression without parentheses. $$ 4 x(x+8) $$

SIMPLIFYING EXPRESSIONS Simplify the expression by combining like terms. $$ 1.3 t-2.1 t $$
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