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Chapter 1: Problem 112

Provide more practice on operations with fractions and decimals. Perform the indicated operations. $$-32.84 \div 8$$

Short Answer

Expert verified
-4.105

Step by step solution

01

- Identify the Operation

The exercise asks to perform a division operation. Specifically, we need to divide -32.84 by 8.
02

- Recognize the Sign

Since the dividend (-32.84) is negative and the divisor (8) is positive, the quotient will be negative.
03

- Perform the Division

Divide the absolute values: \( 32.84 \div 8 = 4.105 \).
04

- Assign the Correct Sign

Based on Step 2, apply the negative sign to the result obtained in Step 3. Thus, the quotient is -4.105.

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Key Concepts

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

division with decimals
Dividing with decimals can be tricky, but it's all about breaking it down into simple steps. When you divide one decimal number by another, start by focusing on the absolute values (ignoring the signs for now). For instance, if you're dividing 32.84 by 8, first just think about how many times 8 goes into 32.84. In our case, the result is 4.105.
This basic process can be captured in the long division format if you need more clarity:
  • Set up the division problem by aligning 32.84 inside the division bar and 8 outside.
  • Move the decimal point directly up and align it in your answer area.
  • Divide as if you're working with whole numbers.
  • After dividing, ensure the decimal is correctly placed in your quotient.
If the division isn't exact, you may need to round your answer according to the instructions given.
positive and negative numbers
When dealing with positive and negative numbers, keep a few important rules in mind:
  • If you divide a positive number by another positive number, the result is positive.
  • If you divide a negative number by a positive number, the result is negative.
  • If both numbers (dividend and divisor) are negative, the result is positive.
In the exercise, you're dividing -32.84 (a negative number) by 8 (a positive number). According to the rules, the quotient will be negative. So, after performing the division, we attach a negative sign to the result, making it -4.105. Understanding these rules helps in handling sign changes in more complex problems.
step-by-step division
Let's go through the division process step-by-step to ensure everything is crystal clear:
  • Step 1: Identify the Operation
    We need to divide -32.84 by 8.
  • Step 2: Recognize the Sign
    The dividend (-32.84) is negative, and the divisor (8) is positive, so our answer will be negative.
  • Step 3: Perform the Division
    Ignore the signs and simply divide the absolute values. 32.84 divided by 8 equals 4.105.
  • Step 4: Assign the Correct Sign
    From Step 2, we know the quotient has to be negative. So, our final answer is -4.105.
Following these structured steps aids in keeping your work organized and helps avoid mistakes. Practice makes perfect, so apply these steps repeatedly until you're comfortable with them.

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Most popular questions from this chapter

Complete each statement. The numerical coefficient in the term \(-7 y z^{2}\) is

Exercises \(91-116\) provide more practice on operations with fractions and decimals. Perform the indicated operations. $$-\frac{1}{12}+\frac{13}{16}$$

Which elements of each set are (a) natural numbers. (b) whole numbers, (c) integers, (d) rational numbers, (e) irrational numbers, (f) real numbers? See Example 3. $$ \left\\{-8,-\sqrt{5},-0.6,0, \frac{3}{4}, \sqrt{3}, \pi, 5, \frac{13}{2}, 17, \frac{40}{2}\right\\} $$

Choose the correct response The additive inverse of \(a\) is \(\mathbf{A} .-a\) \(\begin{array}{lll}{\text { B. } 0} & {\text { C. } 1} & {\text { D. } \frac{1}{a}}\end{array}\)

Complete each statement and give an example. The quotient formed by any nonzero number divided by 0 is _____ and the quotient formed by 0 divided by any nonzero number is _____.
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