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Chapter 4: Problem 58

Simplify by dividing. See Examples 14 through 19. $$\frac{-3}{-3}$$

Short Answer

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Step by step solution

01

Recognize the Division

Understand that the expression \(\frac{-3}{-3}\) involves the division of \(-3\) by \(-3\).
02

Simplify the Negative Divisors

When both the numerator and the denominator are negative, the negatives cancel each other out. Thus, dividing \(-3\) by \(-3\) simplifies to \(\frac{3}{3}\).
03

Simplify the Fraction

The fraction \(\frac{3}{3}\) simplifies to 1, since any number divided by itself is 1.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers less than zero. A negative sign indicates that a number is less than zero. It is important when working with negative numbers, especially in arithmetic, to pay close attention to their signs. Here are a few key points about negative numbers:
  • Negative numbers can be integers, fractions, or decimals, like o-3, o\(-\frac{1}{2}\), or o-0.75.
  • Multiplying or dividing two negative numbers results in a positive number.
  • When subtracting negative numbers, it鈥檚 like adding the positive equivalent.
      • Understanding how negative numbers interact is crucial. In the exercise, both the numerator and denominator were negative. Their division results in a positive outcome.
Basics of Division
Division is one of the four fundamental arithmetic operations. It involves determining how many times one number is contained within another. For example, dividing 6 by 2, as in \(\frac{6}{2}\), equals 3, because 2 fits into 6 exactly three times.
In division:
  • The number being divided is called the dividend.
  • The number by which the dividend is divided is the divisor.
  • The result of the division is known as the quotient.
      • When both numbers in a fraction (the dividend and the divisor) are the same negative number, like in our exercise o\(\frac{-3}{-3}\), the result (the quotient) is 1. This happens because dividing a number by itself always results in 1, except when the number is zero.
The Role of Basic Arithmetic
Basic arithmetic encompasses addition, subtraction, multiplication, and division. Understanding these operations allows us to perform various mathematical tasks and problem-solving. In the context of the given exercise, a firm grasp of division and recognizing patterns with numbers can help simplify problems quickly and efficiently. Remember:
  • Addition and subtraction deal with combining or removing quantities.
  • Multiplication and division address repeated addition and subtraction.
      • With this exercise, basic arithmetic teaches us that dividing any non-zero number by itself, whether positive or negative, results in 1. This simplifies complex expressions and helps in the simplification process.

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Most popular questions from this chapter

Write each improper fraction as a mixed number or a whole number. See Example 21. $$\frac{17}{5}$$

The perimeter of the square below is \(23 \frac{1}{2}\) feet. Find the length of each side.

Use the following numbers: \(\begin{array}{llllllll}8691 & 786 & 1235 & 2235 & 85 & 105 & 22 & 222 & 900 & 1470\end{array}\); List the numbers that are divisible by both 3 and 5.

Write each improper fraction as a mixed number or a whole number. See Example 21. $$\frac{13}{7}$$

Solve. A student asked you to check his work below. Is it correct? If not, where is the error? \(3 \frac{2}{3} \cdot 1 \frac{1}{7} \stackrel{?}{=} 3 \frac{2}{21}\)
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