Problem 87 Translate to an algebraic expres... [FREE SOLUTION] (2024)

Short Answer

quotient

In math, the term 'quotient' is a way to describe the result of dividing one number by another. It's essentially the answer you get when you perform division.
The quotient can be represented as a fraction in algebra. For example, if you have two numbers, let's call them \( x \) and \( y \), dividing \( x \) by \( y \) gives the quotient \( \frac{x}{y} \).
In our exercise, we took the quotient of two expressions: the sum of \( x \) and \( y \) and their difference. So, we're dividing one expression by another, forming \( \frac{x + y}{x - y} \).
This type of quotient is important in algebra because it shows how we manipulate and compare different expressions.

sum and difference

When we talk about 'sum and difference,' we refer to the results of addition and subtraction operations. The sum of two numbers is what you get when you add them together.
In our example, we have two numbers, \( x \) and \( y \). Adding these numbers gives us their sum: \( x + y \).
On the other hand, the difference is what you get when you subtract one number from another. For \( x \) and \( y \), the difference is \( x - y \).
Understanding sum and difference is fundamental in algebra because it allows us to construct and deconstruct expressions, making it easier to solve complex problems and find relationships between variables.

variables

Variables are symbols used in algebra to represent numbers whose values are not yet known. They are usually denoted by letters like \( x \) and \( y \).
In our exercise, we used variables to denote two unknown numbers. Variables are useful because they allow us to create general rules and equations that work for any numbers.
For example, we used \( x \) and \( y \) to represent the two numbers whose sum and difference we were interested in. By doing this, we created a flexible expression that can be used in multiple situations.
Variables make algebra a powerful tool for solving a wide range of mathematical problems.