How is doing operations (adding, subtracting, multiplying, and

dividing) with rational expressions similar to or different from doing operations with fractions? Can
understanding how to work with one kind of problem help understand how to work another type?
When might you use this skill in real life?

We will be happy to critique your thinking on this.

You have recently found a location for your bakery and have begun implementing the first phases of your business plan. Your budget consists of an $80,000 loan from your family and a $38,250 small business loan. These loans must be repaid in full within 10 years.

a) What integer would represent your total budget?

b) Twenty-five percent of your budget will be used to rent business space and pay for utilities. Write an algebraic expression that indicates how much money will be spent on business space and utilities. Do not solve.

c) How much money will rent and utilities cost? Explain how you arrived at this answer.

d) Suppose an investor has increased your budget by $22,250. The investor does not need to be repaid. Rather, he becomes part owner of your business. Will the investor contribute enough money to meet the cost of rent and utilities? Support your answer, and write an equation or inequality that illustrates your answer.

e) This equation illustrates your remaining funds after paying for rent and utilities. How much money is left? Explain how you arrived at your answer.

$38,250 + $80,000+ $22,250-0.25($80,000 + $38,250) =         

Doing operations with rational expressions, such as adding, subtracting, multiplying, and dividing, is similar to doing operations with fractions in many ways. Both involve manipulating numerical values using mathematical operations. In fact, rational expressions can be thought of as fractions in algebraic form.

Similarities:
1. Common denominators: Like fractions, rational expressions need to have a common denominator when adding or subtracting. This involves finding a common factor that can be multiplied to both denominators to make them the same.

2. Simplification: Rational expressions, similar to fractions, can be simplified by canceling out common factors between the numerator and the denominator. This simplification helps in reducing the expression to its simplest form.

3. Distributive property and associative property: The distributive property and associative property apply similarly to rational expressions as they do to fractions. These properties allow for the rearranging of terms and operations to simplify the expressions.

Differences:
1. Variables: Rational expressions often include variables in their numerator or denominator. These variables can represent unknown quantities or real-life situations. Fractions, on the other hand, usually deal only with numerical values.

2. Complex expressions: Rational expressions can be more complex than fractions since they involve algebraic expressions. This complexity may require additional algebraic techniques, such as factoring or expanding, to simplify the expression.

Understanding how to work with fractions can certainly help in understanding how to work with rational expressions. The principles of finding common denominators, simplifying fractions, and using operations can be applied similarly to rational expressions. Once you grasp the concepts and techniques used in fractions, it becomes easier to apply them to rational expressions.

Real-life applications of these skills can be found in various fields such as economics, engineering, and science. For example, when calculating the cost of different items or comparing prices, you might need to perform operations with rational expressions. In physics or engineering, rational expressions can be used to model relationships between different variables, and operations with these expressions are required to solve problems. Additionally, solving algebraic equations involving rational expressions is often necessary in mathematical modeling and optimization in business and industry. Overall, understanding these skills can enhance problem-solving abilities in a range of practical scenarios.