Problem 75 - Prealgebra and Introductory Algebra

Question

Divide. $$-49 \div 1$$

Step-by-Step Solution

Answer

The answer is \(-49\).

Step 1: Identify the dividend and divisor

In this problem, \(-49\) is the dividend (the number to be divided) and \(1\) is the divisor (the number by which we are dividing).

Step 2: Perform the division

Divide \(-49\) by \(1\). The result is \(-49\) because any number divided by \(1\) is the number itself.

Step 3: Include the sign

Since we are dividing a negative number by a positive number, the result is a negative number, so the answer is \(-49\).

Key Concepts

Negative Numbers

Negative numbers are values less than zero. They are commonly used to represent loss, debt, or temperatures below freezing. When handling calculations involving negative numbers, it's important to consider the signs. For example, if you multiply or divide a negative number by a positive number, the result will be negative. Conversely, if both numbers are negative, the result will be positive. Negative numbers are critical in various real-world situations:

• Temperature: Below zero indicates freezing conditions.
• Banking: Negative balances show overdrafts or debts.
• Coordinates: They define positions on a graph's axes.

Understanding how to handle negative numbers will help in many mathematical operations and real-life scenarios.

Dividend

In division, the dividend is the number you want to divide. It's the starting point before you break it into parts or groups. In the problem, (-49) is the dividend. The division operation aims to "split" this number by the divisor.
Think of the dividend as a total amount that you distribute or share:

• In (-49 ÷ 1), (-49) is what you're dividing into parts.
• In a real-world context, this could be dividing something tangible, like money or items.

Efficiently identifying the dividend helps you set up the division correctly and understand the problem's starting point.

Divisor

The divisor is the number by which you divide another number. It tells you how many parts or groups the dividend should be split into. In our example, (1) is the divisor. Dividing by (1) doesn't change the value of the dividend. The basic role of the divisor includes:

• Indicating how many equal parts to create from the dividend.
• Determining the scale of division; larger divisors shrink the result.

By consistently identifying the divisor, you understand the division operation's structure and results. It's essential to solving math problems accurately.

Integer Division

Integer division involves dividing numbers without focusing on fractions or decimals. It aims for whole number results. In our problem, (-49 ÷ 1) results in (-49). The integer division focuses on:

• Whole number outcomes: No fractions or remainders.
• Simplicity: Results that are easily understandable, especially useful in basic math.

Integer division often comes up in various real-life applications where only whole numbers make sense, like counting objects or splitting items among people.