/*! 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 48 Simplify. See Sections 1.5 and \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 48

Simplify. See Sections 1.5 and \(1.6 .\) \(\frac{12-3}{10-9}\)

Short Answer

Expert verified
The expression simplifies to 9.

Step by step solution

01

Simplify the Numerator

The numerator of the fraction is \(12 - 3\). Compute the subtraction: \(12 - 3 = 9\).
02

Simplify the Denominator

The denominator of the fraction is \(10 - 9\). Compute the subtraction: \(10 - 9 = 1\).
03

Perform Division

With the numerator being \(9\) and the denominator being \(1\), divide to simplify the fraction: \(\frac{9}{1} = 9\).

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.

Numerator
In a fraction, the numerator plays an essential role as it sits above the line, representing the number of parts we are interested in. When simplifying a fraction like \( \frac{12-3}{10-9} \), the first step involves focusing on this top figure. Here, the numerator is expressed as \( 12 - 3 \). To simplify, we simply perform the arithmetic operation involved鈥攕ubtraction. We calculate \( 12 - 3 = 9 \).
Understanding how to determine and simplify the numerator is crucial. Remember:
  • The numerator is the top part of the fraction.
  • It tells you how many parts you have or are considering.
  • It requires performing the designated arithmetic operation to simplify it.
Denominator
The denominator is equally important in a fraction. It appears below the line and tells us into how many parts the whole is divided. In this example, we have the fraction \( \frac{12-3}{10-9} \), with \( 10 - 9 \) as the denominator. Simplifying this involves solving the subtraction, which gives \( 10 - 9 = 1 \).
Key things to remember about the denominator:
  • It is the bottom number, indicating the division of the whole.
  • A smaller denominator means larger pieces, and a larger denominator means smaller pieces in terms of division.
  • Without simplifying the denominator properly, the fraction's value may not be accurately represented.
Arithmetic Operations
Simplifying fractions often involves basic arithmetic operations: addition, subtraction, multiplication, and division. In our example, the operations simplify both the numerator and the denominator.
  • A fraction is essentially a division operation \( \frac{a}{b} \), where \( a \) is divided by \( b \).
  • In the fraction \( \frac{12-3}{10-9} \), we subtract to simplify both the numerator and the denominator separately.
  • Once both parts are simplified, the division is straightforward: \( \frac{9}{1} = 9 \).
Arithmetic operations allow for the reduction and simplification of fractions, which is vital for easier calculation and clearer understanding of the quantity represented. Being comfortable with these operations will make manipulating fractions far simpler.

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 an equation of each line described. Write each equation in slope- intercept form when possible. Slope \(-5, y\) -intercept (0,7)

Assume each exercise describes a linear relationship. Write the equations in slope-intercept form. The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at \(\$ 3,\) sales will reach 10,000 Fun Noodles per day during the summer. Raising the price to \(\$ 5\) will cause sales to fall to 8000 Fun Noodles per day. a. Assume that the relationship between price and number of Fun Noodles sold is linear and write an equation describing this relationship. Use ordered pairs of the form (price, number sold). b. Predict the daily sales of Fun Noodles if the price is \(\$ 3.50\)

Write an equation in standard form of the line that contains the point (4,0) and is perpendicular to the line \(y=-2 x+3\)

Find an equation of each line described. Write each equation in slope- intercept form when possible. Through (5,-6) and (-6,5)

Solve. See Example 4. The table shows the amount of money (in billions of dollars) that Americans spent on their pets for the years shown. (Source: American Pet Products Manufacturers Association) $$ \begin{array}{|c|c|} \hline \text { Year } & \begin{array}{c} \text { Pet-Related Expenditures } \\ \text { (in billions of dollars) } \end{array} \\ \hline 2005 & 36.3 \\ \hline 2006 & 38.5 \\ \hline 2007 & 41.2 \\ \hline 2008 & 43.4 \\ \hline \end{array} $$ a. Write this paired data as a set of ordered pairs of the form (year, pet- related expenditures). b. In your own words, write the meaning of the ordered pair (2007,41.2) c. Create a scatter diagram of the paired data. \(\mathrm{Be}\) sure to label the axes appropriately. d. What trend in the paired data does the scatter diagram show?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.