Problem 31 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ \frac{25}{-5} $$

Step-by-Step Solution

Answer

The result is -5.

Step 1: Set Up the Division Problem

The exercise requires you to divide 25 by -5. Write this as a fraction: \( \frac{25}{-5} \).

Step 2: Divide the Numerator by the Denominator

Divide 25 (the numerator) by -5 (the denominator). This involves dividing two numbers, which gives \( 25 \div (-5) \).

Step 3: Calculate the Division

Perform the division: dividing a positive number by a negative number results in a negative quotient. Thus, \( 25 \div (-5) = -5 \).

Step 4: Verify with a Calculator

Use a calculator to ensure the result is correct. Enter 25 divided by -5, and the calculator should show the result as -5.

Key Concepts

Negative Numbers

When working with negative numbers, it's important to understand their rules in arithmetic operations. Negative numbers are simply numbers with a minus sign in front of them, indicating they are less than zero. In division, negative numbers can affect the sign of your result. Here's a key point to remember:

• When you divide a positive number by a negative number, the result is a negative number.
• If both numbers are negative, the result is positive.
• Kee in mind, the absolute values are divided just like positive numbers, it's the sign that changes.

Calculating with negative numbers can initially seem confusing. However, once you understand the pattern of signs, it becomes much simpler. Practice dividing different combinations of positive and negative numbers to get familiar with their outcomes.

Division Process

The division process involves showing how many times one number, the divisor, can fit into another number, the dividend. In this exercise, you are dividing 25 by -5. Breaking down the division process:

• Step 1: Write the division as a fraction: \( \frac{25}{-5} \).
• Step 2: Focus on dividing the absolute values: 25 divided by 5 equals 5.
• Step 3: Since you are dividing by a negative, remember to change the sign to negative, giving you \( -5 \).

Continue practicing this process with various numbers to strengthen your understanding. You'll find that approaching division in a step-by-step manner helps in reducing errors, especially when dealing with negative signs.

Calculator Verification

Using a calculator is an effective way to verify your results in mathematical calculations. It acts as a double-check to ensure your manual computations are correct. Here’s how to incorporate calculator verification in your division:

• After manually finding the quotient, input the division equation into your calculator.
• For this exercise, type in 25 divided by -5 on the calculator.
• The display should read -5, confirming that your calculated result is accurate.

It’s important to rely on calculators not just to get the answer quickly but also to understand the steps leading to the answer. This practice helps develop both your computational skills and your ability to check your work autonomously. Watching how your manual calculations align with automated results builds confidence in your arithmetic abilities.