/*! 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 19 Simplify. See Examples 1 through... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 19

Simplify. See Examples 1 through \(10\). $$ \frac{24}{10+(-4)} $$

Short Answer

Expert verified
The simplified expression is 4.

Step by step solution

01

Simplify the Denominator

First, focus on simplifying the expression in the denominator. You have the expression \(10 + (-4)\). This is the same as \(10 - 4\). Calculate this to get \(10 - 4 = 6\). Now, the expression becomes \(\frac{24}{6}\).
02

Divide the Numerator by the Simplified Denominator

Now, divide the numerator, \(24\), by the simplified value of the denominator, \(6\). So, \(24 \div 6 = 4\).
03

Write the Final Answer

The simplified form of the original expression \(\frac{24}{10+(-4)}\) is just \(4\).

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.

Simplifying the Denominator
When simplifying fractions, one of the first actions to take is making the denominator as simple as possible. Simplifying the denominator involves dealing with any arithmetic operations within it.
Start by analyzing the expression in the denominator. In our case, we have:
  • Identify the arithmetic operation: The original denominator expression is \(10 + (-4)\). Adding a negative number is equivalent to subtraction.
  • Calculate carefully: Transition from \(10 + (-4)\) to \(10 - 4\).
Perform the subtraction to conclude that the denominator is simplified to \(6\). By completing this step, you transform the fraction to \(\frac{24}{6}\), ready for the next phase.
Numerator Calculation and Simplification
Now that your denominator is simplified, the next focus is on the numerator, which remains constant in this particular problem.
With the expression reduced to \(\frac{24}{6}\), numerical simplification requires dividing the numerator by the now simplified denominator. Start by identifying the calculation:
Perform a division operation, \(24 \div 6\), which results in the value \(4\).
  • Understand that the simplification process does not alter the numerical value of the numerator itself prior to division.
  • The primary goal is translating the calculation from the previously stepped-down expression into a straightforward, easy-to-understand numerical form.
This step results in your simplified fraction having a single number rather than an expression.
Applying Arithmetic Operations
Arithmetic operations are fundamental in simplifying fractions. These operations allow us to break down complex expressions into simpler components step by step.
Understanding arithmetic operations in the context of fraction simplification involves:
  • Handling operations within the denominator: We first needed to address the \(10 + (-4)\), which means respecting the order of operations and interpreting symbols carefully.
  • Executing division for simplification: Once the denominator was simplified to \(6\), arithmetic operations helped in evaluating \(24 \div 6\), further reducing complexity.
Grasping these basics - addition, subtraction, and division - is crucial. They play essential roles in transforming expressions into their simplest forms, breaking down complex tasks into straightforward calculations, and achieving a clearer final result.

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

Find the opposite of each integer. $$ 5 $$

Add. $$ 0+13 $$

Evaluate. $$ -|x| \text { if } x=7 $$

Simplify. $$ -|-18| $$

Insert \(<,>,\) or \(=\) between each pair of numbers to make a true statement. $$ -22 \quad-(-38) $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.