Problem 45 - Elementary Algebra

Question

For exercises 15-100, evaluate. $$ -6 \div(-2) $$

Step-by-Step Solution

Answer

-6 divided by -2 equals 3.

Step 1: Identify the operation

The operation to be performed is division, as indicated by the division symbol \( \div \).

Step 2: Identify the numbers

The numbers involved in the operation are -6 and -2.

Step 3: Apply the division rule

When dividing two negative numbers, the result is positive. Therefore, \( -6 \div (-2) = 3 \).

Key Concepts

headline of the respective core concept

Arithmetic operations are fundamental mathematical actions we use to calculate values, such as addition, subtraction, multiplication, and division. These operations allow us to solve a variety of mathematical problems and are the building blocks for more advanced topics.

• Addition: Combining two numbers to get a larger number (e.g., 3 + 4 = 7).
• Subtraction: Finding the difference between two numbers (e.g., 7 - 4 = 3).
• Multiplication: Adding a number to itself a certain number of times (e.g., 3 x 4 = 12).
• Division: Splitting a number into equal parts (e.g., 12 ÷ 4 = 3).

In the given exercise, our focus is on the division of two negative numbers. Performing division correctly with negative numbers relies on understanding certain rules, which we'll explore below.

headline of the respective core concept

Division is the arithmetic operation of distributing a number into equal parts. In mathematical notation, we represent division using the symbols \( \div \) or \( / \). The number being divided is called the dividend, while the number you divide by is the divisor. The result of the division is called the quotient.

To illustrate this, in the exercise we have the division expression \( -6 \div -2 \). Here:

• Dividend: -6
• Divisor: -2
• Quotient: The result we need to find.

When performing division, if both the dividend and divisor are negative, the quotient becomes positive. This is because dividing two negative numbers cancels out the negative signs, resulting in a positive quotient. Thus, \( -6\div (-2) = 3 \).

This rule is essential for correctly solving problems involving the division of negative numbers.

headline of the respective core concept

Negative numbers are numbers less than zero. They are used to represent values like debts, temperatures below zero, or elevations below sea level. Negative numbers are marked with a minus sign (–).

When it comes to arithmetic operations involving negative numbers:

• Adding a negative number is like subtracting its positive counterpart (e.g., \( 5 + (-3) = 2 \)).
• Subtracting a negative number is like adding its positive counterpart (e.g., \( 5 - (-3) = 8 \)).
• Multiplying two negative numbers gives a positive result (e.g., \( -4 \times -2 = 8 \)).
• Dividing two negative numbers also results in a positive quotient, as seen in our exercise with \( -6 \div -2 = 3 \).

Understanding these rules can help you confidently handle arithmetic operations involving negative numbers. Remember that the presence of two negative signs (either in multiplication or division) cancels out, resulting in a positive outcome.