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Chapter 2: Problem 13

Evaluate each expression. $$-64 \div(-8)$$

Short Answer

Expert verified
The result is 8.

Step by step solution

01

Understand the Division of Two Negative Numbers

When you divide two negative numbers, the result is positive. This is because a negative divided by a negative gives a positive result.
02

Divide the Absolute Values

Now, divide the absolute values of the numbers involved: \(64 \div 8 = 8\).
03

Apply the Sign Rule

Since both numbers in the division are negative, the result will be positive, so \(-64 \div -8 = 8\).

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero, often encountered in everyday life, like temperatures below freezing or bank overdrafts. When dealing with negative numbers, it's essential to understand that they represent a value in the opposite direction from positive numbers on the number line.

When dividing negative numbers, it's crucial to recall that the sign rules for multiplication and division are the same.
  • Negative divided by negative gives a positive result. For example, \(-64 \div -8 = 8\), because the negatives cancel each other out.
  • Negative divided by positive, or positive by negative, results in a negative outcome. For instance, if you have \(-64 \div 8\), the result is \(-8\).
  • Always remember, two negatives make a positive when dividing or multiplying.
Absolute Values
Absolute value is a mathematical concept used to analyze the distance a number is from zero on the number line, regardless of its direction. Therefore, it is always non-negative. The absolute value is denoted by vertical bars, for example, \(|-64| = 64\) and \(|8| = 8\).

To find the absolute value, simply ignore the sign of the number and remember:
  • The absolute value of a positive number is the number itself.
  • The absolute value of a negative number is the number without its negative sign.
Understanding absolute values is particularly useful in operations like addition, subtraction, multiplication, and division, as it helps simplify and standardize calculations involving negative numbers.
Division Rules
Division is one of the basic arithmetic operations. When it comes to dividing numbers, knowing the division rules is essential for accurately solving math problems. For integer division, you often deal with whole numbers.

Here are some basic division rules to always keep in mind:
  • When dividing two numbers with the same sign, either both positive or both negative, the result is positive.
  • When dividing two numbers with different signs, the result is negative.
  • When you divide any number by itself, the result is always 1. However, zero divided by any number is zero, and any number divided by zero is undefined.
  • For example, with \(-64 \div -8\), both numbers have the same negative sign, producing a positive result of \(8\).
By keeping these division rules in mind, you can efficiently solve division problems involving integers and avoid common mistakes.

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