/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 84 Evaluate \(\frac{a}{1-b}\) for t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 11: Problem 84

Evaluate \(\frac{a}{1-b}\) for the given values of \(a\) and \(b\) $$ a=-1, b=0.5 $$

Short Answer

Expert verified
The value is -2.

Step by step solution

01

Identify the Formula

The expression given is \( \frac{a}{1-b} \). Our task is to substitute the values of \(a\) and \(b\) into this expression.
02

Substitute Values

Substitute \( a = -1 \) and \( b = 0.5 \) into the expression. This gives us \( \frac{-1}{1-0.5} \).
03

Simplify the Denominator

Calculate \( 1 - 0.5 \), which simplifies to \( 0.5 \).
04

Evaluate the Expression

With the calculation from the previous step, we substitute back into the expression, which is now \( \frac{-1}{0.5} \). Simplifying this gives us \( -2 \) since dividing by 0.5 is the same as multiplying by 2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Substitution
Substitution is a key concept in algebra that involves replacing variables in an algebraic expression with their given values. This allows us to evaluate the expression or solve equations easily. In our exercise, we are given the expression \( \frac{a}{1-b} \) and the values \( a = -1 \) and \( b = 0.5 \). By substituting these values into the expression, we change its form to \( \frac{-1}{1-0.5} \). Substitution is performed step-by-step:
  • First, identify each variable in the expression.
  • Next, replace each variable with the specified number.
This helps in reducing complex expressions into simple numerical ones that are easier to handle. It's an essential skill for solving a variety of math problems.
Simplifying Expressions
Simplifying expressions is the process of making an expression easier to understand and work with by reducing it to its simplest form. In our example, after substitution, we have the fractional expression \( \frac{-1}{1-0.5} \). To simplify:
  • First, perform operations in the denominator: \( 1 - 0.5 \), which results in \( 0.5 \).
  • Next, complete the division: \( \frac{-1}{0.5} \), which simplifies the expression to \( -2 \).
Reducing fractions like \( \frac{-1}{0.5} \) means finding a simpler equivalent value, often transforming the problem by considering multiplication (since dividing by 0.5 is the equivalent of multiplying by 2). Simplification enhances clarity and makes further calculations much easier.
Rational Expressions
A rational expression is an algebraic expression that can be written as a fraction where both the numerator and the denominator are polynomials. These can look like common fractions, but instead of integers, they involve algebraic terms. In the given problem, \( \frac{a}{1-b} \) is a rational expression. Key characteristics include:
  • The numerator and denominator may include variables like \( a \) or \( b \), numbers, and algebraic operations such as addition and subtraction.
  • The denominator cannot be zero, as division by zero is undefined and results in invalid expressions.
Understanding rational expressions helps in seamlessly evaluating and simplifying them, which involves careful attention to any restrictions, like excluding any values that might lead to a zero denominator. This ensures that the expression is always valid for evaluation.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

PUZZLES Show that a \(2^{n}\) by \(2^{n}\) checkerboard with the top right square missing can always be covered by nonoverlapping L-shaped tiles like the one at the right.

Find the indicated term of each expansion. fourth term of \(\left(x+\frac{1}{3}\right)^{7}\)

Find the indicated term of each expansion. seventh term of \((x+y)^{12}\)

Ofelia is taking ten shots in the intramural free-throw shooting competition. How many sequences of makes and misses are there that result in her making eight shots and missing two?

Prove that each statement is true for all positive integers. \(9^{n}-1\) is divisible by 8
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.