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Chapter 1: Problem 43

Add. $$ -3.26+(-5.8) $$

Short Answer

Expert verified
-9.06

Step by step solution

01

Understand the operation

The problem requires finding the sum of the numbers -3.26 and -5.8.
02

Combine the numbers

When adding two negative numbers, combine their absolute values and keep the result negative. Calculate the sum: \[ | -3.26 | + | -5.8 | = 3.26 + 5.8 \]
03

Perform the addition

Add the absolute values of the numbers: \[ 3.26 + 5.8 = 9.06 \]
04

Apply the sign

Since both numbers were negative, the final result is also negative: \[ -(3.26 + 5.8) = -9.06 \]

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Key Concepts

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

Understanding Absolute Value
The absolute value of a number is the distance of that number from zero on the number line, without considering which direction it is. For example, the absolute value of -3.26 is 3.26 because it is 3.26 units away from zero. Similarly, the absolute value of -5.8 is 5.8. The symbol for absolute value is two vertical bars; for instance, \( | -3.26 | \) is 3.26.
Absolute values are always non-negative.
If you see negative numbers inside absolute value symbols, just drop the negative sign.
  • For example, \( | -7 | = 7 \)
  • Another example with a positive number: \( | 4 | = 4 \)
This concept helps to simplify problems, especially those involving addition or subtraction.
Working with Negative Numbers
Negative numbers are numbers less than zero. They are usually marked with a minus sign (-). In math, dealing with negative numbers follows specific rules:
When adding two negative numbers, their absolute values are added and the result is negative.
  • For instance, \( -3 + -5 = -(3 + 5) = -8 \)
  • Similarly: \( -2 + -7 = -(2 + 7) = -9 \)
This is because both numbers are decreasing, making the overall result more negative.
Negative numbers can be tricky, but breaking them down step-by-step can make operations like addition much simpler.
Addition of Decimals
Adding decimals involves aligning the decimal points and adding the numbers as if they were whole numbers. Here鈥檚 how to do it:
First, write down the numbers vertically, making sure the decimal points line up.
  • For example, if you want to add 3.26 and 5.8, you would write:
    3.26
    + 5.80
Next, add the numbers column by column, starting from the rightmost column.
  • In our example, 6 + 0 = 6, 2 + 8 = 10 (write 0, carry over 1), and 3 + 5 + 1 (carry over) = 9
  • So, 3.26 + 5.8 = 9.06
Finally, keep in mind to place the decimal point in the result directly below the other decimal points.
Having a strong grasp of adding decimals is crucial for handling more complex math problems.

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Most popular questions from this chapter

Write an equivalent expression using an associative law. $$ (3 x) y $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ \frac{3^{4}-(5-3)^{4}}{8-2^{3}} $$

Write an equivalent expression using an associative law. $$ -7(a b) $$

Translate to an algebraic expression. $$ \\{x | x=2 n, n \text { is an integer }\\} $$

Use set-builder notation to write each set. The set of all even numbers between 9 and 99
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