Problem 89 - Elementary and Intermediate Algebra

Question

Perform the operations. $$ \frac{550}{-50} $$

Step-by-Step Solution

Answer

-11

Step 1: Identify the Operation

The problem is asking us to perform a division operation on the numbers presented in the fraction form \( \frac{550}{-50} \).

Step 2: Identify the algebraic structure

Determine the type of algebraic problem.

Step 3: Apply algebraic techniques

Use factoring, expanding, or systematic methods.

Step 4: Simplify and solve

Simplify expressions and solve for unknowns.

Step 5: State the result

Write the final answer.

Key Concepts

Fraction Division

In mathematics, division involving fractions may appear daunting, but understanding the basic concept makes it quite manageable. Here, we're working with a fraction that represents a division operation: \( \frac{550}{-50} \). Think of the fraction as expressing that 550 is being divided by -50. To solve this, you need to interpret the numbers above and below the fraction line. The upper number, known as the numerator, is 550. The lower number, known as the denominator, is -50. These positions in the fraction are key to understanding what operation to perform and how to approach it.

• Numerator: This is the number being divided, here it is 550.
• Denominator: This is the number by which the numerator is divided, here it is -50.

When dividing fractions, especially with negative numbers or mixed fractions, keeping track of signs and ensuring an easier understanding of each number involved is crucial for accuracy.

Negative Numbers

Negative numbers are a fundamental part of algebra and arithmetic. In the realm of basic algebraic operations, you must understand their role and tactfully work with them.In the exercise, our operation involves dividing a positive number (550) by a negative number (-50). Dealing with negative numbers can be simple if you follow the rules of arithmetic.

• Basic rule of signs in division: A positive number divided by a negative number, or vice-versa, always results in a negative quotient.

Thus, the division \( \frac{550}{-50} \) results in a negative number. Performing this operation, you get:\[550 \div (-50) = -11\]This rule ensures that your result is accurately reflected with the correct sign.

Step-by-Step Solution

Solving algebraic expressions like \( \frac{550}{-50} \) is more intuitive with a step-by-step approach. This method ensures you understand each part of the calculation and can tackle trickier problems confidently in the future.1. **Understand the problem:** We're dividing 550 by -50.2. **Divide the absolute values:** Calculate the division neglecting the signs initially: \[ 550 \div 50 = 11 \]3. **Apply the rule of signs:** Since the division involves a positive and a negative number, the quotient is negative. Therefore, \[ 550 \div (-50) = -11 \]This careful process works efficiently by separating operational steps, making complex problems manageable and less intimidating. Ensuring clarity in each stage aids in minimizing errors and solidifying understanding.