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Chapter 1: Problem 526

Evaluate. $$ \frac{r-s}{r+s} \text { when } r=10, s=-5 $$

Short Answer

Expert verified
3

Step by step solution

01

Understand the given formula

The given formula to evaluate is \ \ \ \( \frac{r-s}{r+s} \), where r and s are variables.
02

Substitute the given values

We are given that \( r = 10 \) and \( s = -5 \). Substitute these values into the formula: \ \ \( \frac{r-s}{r+s} = \frac{10 - (-5)}{10 + (-5)} \).
03

Simplify the numerator

Simplify the numerator by performing the subtraction: \ \ \( 10 - (-5) = 10 + 5 = 15 \).
04

Simplify the denominator

Simplify the denominator by performing the addition: \ \ \( 10 + (-5) = 10 - 5 = 5 \).
05

Divide the simplified numerator by the simplified denominator

Now, divide the results: \ \ \( \frac{15}{5} = 3 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution
Substitution is a key concept in algebra where you replace variables in an expression with given values. In this exercise, we substitute the values of variables \( r \) and \( s \) into the expression \[ \frac{r-s}{r+s} \]. We were given \( r = 10 \) and \( s = -5 \). By substituting these values, the expression becomes \ \[ \frac{10 - (-5)}{10 + (-5)} \]. When substituting, ensure you replace each instance of the variable systematically to avoid errors.
Simplifying Expressions
Simplifying an expression means reducing it to its simplest form. After substitution, our task is to simplify the numerator and the denominator separately. Let's break it down:
First, the numerator: \ \[ r - s \] becomes \ \[ 10 - (-5) \] which simplifies to \ \[ 10 + 5 \].
This gives us \ \[ 15 \].

Next, the denominator: \ \[ r + s \] becomes \ \[ 10 + (-5) \] which simplifies to \ \[ 10 - 5 \].
This gives us \ \[ 5 \].

Finally, we simplify the whole expression by dividing the simplified numerator by the simplified denominator. So, \ \[ \frac{15}{5} = 3 \].
By taking it step by step, we can simplify complex fractions easily.
Numerator and Denominator
Understanding the terms numerator and denominator is crucial when working with fractions.
The numerator is the top part of a fraction, which represents how many parts we have. In our example, after substitution, \ \[ r - s = 10 - (-5) = 15 \]. So, 15 is our numerator.

The denominator is the bottom part of a fraction, indicating the total parts into which the whole is divided. In our example, \ \[ r + s = 10 + (-5) = 5 \]. So, 5 is our denominator.
Having simplified both, our fraction becomes \ \[ \frac{15}{5} \], which can be further simplified to 3. This step-by-step approach demystifies how fractions represent parts of a whole and the process to simplify them.

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