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Chapter 2: Problem 117

use a calculator to perform the indicated operations. $$\frac{-576,828}{-10,682}$$

Short Answer

Expert verified
54.0

Step by step solution

01

Understand the problem

The task involves dividing two numbers: -576,828 by -10,682. Since both numbers are negative, their quotient will be positive.
02

Input the numbers into the calculator

Enter the dividend (-576,828) and the divisor (-10,682) into the calculator. Perform the division operation.
03

Calculate the result

The calculator will give you the quotient. Since we are dividing a negative number by another negative number, the result will be positive.
04

Verify the result

Check the quotient to ensure the operation was performed correctly. The quotient of the division \(\frac{-576,828}{-10,682}\) is approximately 54.0

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Key Concepts

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

Division
Division is one of the basic arithmetic operations, symbolized by the forward slash (/) or the division sign (梅). It involves splitting a number, called the dividend, into equal parts defined by another number, the divisor. For example, in the exercise, we have a dividend of -576,828 and a divisor of -10,682. The division operation essentially asks, 'how many times does -10,682 fit into -576,828?' When you divide these numbers, the result is called the quotient.

To divide manually, start from the leftmost digits of the dividend and see how many times the divisor fits. However, using a calculator simplifies this process highly.
Negative Numbers
Negative numbers are less than zero and are represented with a minus sign (-). They follow different rules than positive numbers, especially in multiplication and division.

When dividing two negative numbers, the result is a positive number. This is because the negative signs cancel each other out. So, \(\frac{-576,828}{-10,682}\) will have a positive quotient. This is a crucial concept to remember: a negative divided by a negative is always positive.
Using a Calculator
Using a calculator for arithmetic operations can save time and reduce errors. Here鈥檚 a simple guide for this exercise:
  • Turn on your calculator.
  • Input the first number (dividend), making sure to include the negative sign.
  • Press the division key (梅).
  • Input the second number (divisor), also with a negative sign.
  • Press the equals key (=) to get the quotient.

This process ensures that you correctly calculate the division, reducing the chance of mistakes.
Quotient
The quotient is the result of a division problem. It tells you how many times the divisor fits into the dividend. In this exercise, dividing -576,828 by -10,682 gives a quotient of approximately 54.0.

Remember, because both numbers were negative, their signs cancel out, giving a positive outcome.

It's good practice to check the quotient by multiplying it back by the divisor to see if you get the original dividend. This ensures your division was correct.

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Most popular questions from this chapter

Simplify using the order of operations. $$14-4^{2}+2-10$$

The height of Mount Everest is \(29,029 \mathrm{ft}\). The lowest point on the surface of the Earth is \(-35,798 \mathrm{ft}\) (that is, 35,798 ft below sea level) occurring at the Mariana Trench on the Pacific Ocean floor. What is the difference in altitude between the height of Mt. Everest and the Mariana Trench?

Multiply. $$(-1)(-1)(-1)(-1)(-1)(-1)$$

a. Which is greater, \(-12\) or \(-8 ?\) b. Which is greater, \(|-12|\) or \(|-8| ?\)

Translate each English phrase to a mathematical expression. Then simplify. Subtract 24 from \(-35\)
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