Problem 48 - Prealgebra

Question

Divide the decimals. \(\frac{0.3306}{-0.38}\)

Step-by-Step Solution

Answer

The result of the division is approximately -0.8705.

Step 1: Understanding the problem

We need to divide the number 0.3306 by -0.38. When dividing by a negative number, the result will be negative.

Step 2: Remove Decimal by Scaling

To simplify the division, we'll eliminate the decimals by multiplying both the numerator and the denominator by 100. This converts the problem into \(\frac{33.06}{-38}\).

Step 3: Perform the Division

Now, divide 33.06 by 38, and remember the result will be negative due to the negative denominator. Perform long division or use a calculator for the division: \(33.06 \div 38 \approx 0.8705\).

Step 4: Adjust the Sign

Since we are dividing by a negative number, the quotient will be negative. Therefore, the result is -0.8705.

Key Concepts

Long Division

Long division is a powerful technique for dividing complex numbers. It involves breaking down the division process into manageable steps. Imagine you're dividing a sum of money among friends. That's the idea behind long division — methodically sharing "parts" of a number until nothing is left.

Here's how it goes:

• Start from the left: Consider the first digit(s) of the dividend which is greater or equal to the divisor.
• Determine how many times the divisor fits into those digits. Write this number above the dividend line. This is your partial quotient.
• Subtract the result from those digits and bring down the next digit of the dividend.
• Repeat the process until the dividend's digits are exhausted.

Using long division might seem lengthy, but it ensures accuracy, especially when dividing decimals. By practicing this method, you'll develop stronger arithmetic skills, making complex numbers much more manageable!

Negative Numbers

When dealing with negative numbers in mathematics, one crucial rule stands out: a negative number divided by a positive number always results in a negative quotient. Similarly, a negative divided by a negative yields a positive result. This is fundamental when performing operations involving negatives — they influence the sign of the answer.

Let's explore:

• Negative Division Rule: Dividing any number by a negative will "flip" the sign of the result.
• Keep the Outcome Negative: In our example, dividing by -0.38 implies the final answer will be negative, due to this rule.
• Sign consistency: Always keep the rules in mind to correctly determine the sign of your answer.

Understanding these rules is key to correctly solving problems involving negative numbers. They might seem tricky initially, but with practice, you'll find them to be as intuitive as positive numbers.

Scaling Decimals

Scaling decimals is a technique used to simplify complex decimal division, often making the numbers easier to work with. When you "scale" decimals, you essentially multiply both numbers by the same factor, usually 10 or 100, to eliminate decimal points.

Consider these points:

• Simplifying the Numbers: Multiplying by 100 converts 0.3306 into 33.06 and -0.38 into -38. This action removes decimals, turning them into whole numbers for easier handling.
• How it helps: By working with whole numbers, the division process becomes straightforward. Division without decimals is similar to basic arithmetic familiar from earlier lessons.
• Keeping it balanced: Remember, whatever operation you perform on the numerator, you must do the same to the denominator. This balance maintains the equation's integrity.

After simplifying through scaling, the division becomes less daunting, leaving you with clearer and quicker computations! This method keeps the math tidy and boosts confidence in solving decimal problems.