Problem 66 - Elementary and Intermediate Algebra

Question

Divide. See Example 5. $$ \frac{-1.7}{10} $$

Step-by-Step Solution

Answer

The result is \(-0.17\).

Step 1: Understand the Problem

The exercise asks us to divide \(-1.7\) by 10. This requires understanding how a negative decimal is divided by a whole number.

Step 2: Determine the Division Process

To divide \(-1.7\) by 10, we need to move the decimal point one place to the left. This process is equivalent to dividing by 10.

Step 3: Execute the Division

Move the decimal in \(-1.7\) one place to the left to get \(-0.17\). This is because dividing by 10 scales down the number by one decimal place.

Step 4: Confirm the Sign

Ensure the result is negative because the original numerator \(-1.7\) is negative.

Step 5: State the Result

After performing the division, the answer is \(-0.17\). Ensure all steps align logically to confirm accuracy.

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero and are usually represented with a minus sign (-). They are used to signify a decrease, temperature drop, or financial debt. When working with negative numbers, especially in division, it’s crucial to remember certain rules.

• When you divide a negative number by a positive number, the result is always negative. For example, dividing \(-4\) by \(2\) gives \(-2\).
• If both the dividend and the divisor are negative, the result is positive, such as dividing \(-4\) by \(-2\) gives \(2\).
• If a negative number is divided by zero, it is undefined, just like any number divided by zero.

These rules will help keep your calculations accurate and ensure you understand how negative values behave in arithmetic.

Performing Decimal Division

Decimal division may seem tricky at first, but it follows the basic principles of division. Here are the key steps:

• When dividing a decimal by a whole number, like \(-1.7\) divided by \(10\), move the decimal point to the left as many places as there are zeros in the divisor. In the case of \(10\), you move it one place.
• Keep the negative sign if the original number is negative, ensuring the division result reflects the correct sign.
• The key is recognizing that moving the decimal translates into 'scaling down' the number by powers of 10. Thus, \(-1.7\) becomes \(-0.17\).

Being comfortable with the idea of moving decimal points makes division with decimal numbers much more manageable.

Breaking Down Mathematical Steps

The process of dividing decimals involves a series of logical steps, which if followed correctly, guarantee a correct answer.

• Read and understand the problem: Knowing what is being asked helps to focus on the required operation, in this case, division.
• Identify decimal movement: Knowing that dividing by \(10\) means moving the decimal one position to the left helps simplify the task.
• Perform the division: Execute the division operation by shifting the decimal place correctly. Here, it means \(-1.7\) becomes \(-0.17\).
• Check the sign: Reinforce the negative sign in your result if the original number was negative.
• Validate your outcome: Ensure every step is in alignment by checking that the final result makes logical sense.

By understanding each mathematical step, you not only solve the problem but also build confidence in handling similar questions in the future.