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Chapter 2: Problem 84

Simplify each given expression. \(-22 \div(-22)\)

Short Answer

Expert verified
The expression simplifies to 1.

Step by step solution

01

Identify the Division Operation

The given expression is \(-22 \div (-22)\). This is a division operation where both the dividend and divisor are negative numbers.
02

Divide the Absolute Values

To simplify \(-22 \div (-22)\), we first look at the absolute values of the numbers. The absolute value of \(-22\) is 22. So, we perform the operation \(22 \div 22\).
03

Perform the Division

Divide the absolute values: \(22 \div 22 = 1\). This is because any number divided by itself equals one.
04

Apply the Rule for Negative Division

In division, when both numbers have the same sign, the result is positive. Here both numbers \(-22\) are negative, so \(-22 \div (-22) = 1\).

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Key Concepts

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

Absolute Value
The absolute value of a number is the distance between that number and zero on the number line, without taking into account its direction (positive or negative). Essentially, it transforms any number into a non-negative value. For example, the absolute value of -5 is 5, just as the absolute value of 5 is 5.
  • It is denoted by two vertical bars on either side of the number, like this: | -22 | = 22.
  • Absolute value helps simplify expressions by removing any negative signs, which allows for straightforward calculations.
This concept is particularly useful when performing operations such as division, where knowing only the size of the numbers involved, not their sign, is essential for simplifying and solving problems.
Negative Numbers
Negative numbers are those less than zero, typically found to the left of zero on the number line. They represent values below zero, such as debts, decreases, or drops in temperatures. When we perform operations with negative numbers, special rules apply:
  • Multiplying or dividing two negative numbers results in a positive number. For example, (-3) 脳 (-3) = 9 and (-9) 梅 (-3) = 3.
  • Multiplying or dividing a positive number by a negative number yields a negative result.
Understanding these rules is crucial for calculations involving negative numbers, as they can dramatically change the outcome of an expression.
Division Operation
Division is a fundamental arithmetic operation that breaks down a number into equal parts. It consists of a dividend, which is the number being divided, and a divisor, which is the number by which the dividend is divided. When dealing with division of negative numbers, such as -22 梅 -22, key considerations include:
  • First, work with the absolute values. This means ignoring the negative signs to perform the basic division: | -22 | 梅 | -22 | = 22 梅 22 = 1.
  • Next, apply the rule for division with negative numbers: if both numbers involved are negative, the result is a positive number. Hence, -22 梅 -22 = 1.
This understanding ensures that results are accurate and the math concept is correctly applied in any given situation.

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Most popular questions from this chapter

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