/*! 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 76 Add or subtract the fractions, a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 76

Add or subtract the fractions, as indicated, and simplify your result. $$\frac{-7}{9}-\frac{1}{9}$$

Short Answer

Expert verified
The simplified result is \( \frac{-8}{9} \).

Step by step solution

01

Identify the Fractions

We have two fractions to work with: \( \frac{-7}{9} \) and \( \frac{1}{9} \). Each fraction has the same denominator, which is 9.
02

Subtract the Numerators

Because the denominators are the same, we can directly subtract the numerators: \(-7 - 1\).
03

Calculate the New Numerator

Perform the subtraction of the numerators: \(-7 - 1 = -8\).
04

Form the New Fraction

Combine the new numerator with the common denominator to form the resulting fraction: \( \frac{-8}{9} \).
05

Simplify the Fraction

Check if the fraction \( \frac{-8}{9} \) can be simplified further. Since 8 and 9 have no common divisors other than 1, the fraction is already in its simplest form.

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.

Addition of Fractions
When adding fractions, our primary goal is to combine them into a single fraction. For this, both fractions must have a common denominator. This makes it easy to handle the numerators without affecting the value of the fractions.
  • If the denominators are already the same, it simplifies the process greatly. Just like in our task, where both fractions, \( \frac{-7}{9} \) and \( \frac{1}{9} \), share the denominator 9.
  • Add the numerators while keeping the common denominator constant. For instance, if you had to add \( \frac{-7}{9} \) and another fraction like \( \frac{2}{9} \), you would reshape it to:\[-7 + 2 = -5 \].
  • The resulting fraction is then \( \frac{-5}{9} \).
Remember, if the fractions do not share a common denominator previously, you must first find a common denominator before combining numerators. This often involves finding the least common multiple of the denominators.
Subtraction of Fractions
Just like with addition, subtraction of fractions requires them to have the same denominator. With a shared denominator, it's straightforward to subtract the numerators.
Here鈥檚 how you can subtract fractions effectively:
  • Ensure that both fractions have the same denominator, which is true in our exercise with \( \frac{-7}{9} \) and \( \frac{1}{9} \). This means we can focus directly on numerators.
  • Subtract the second fraction's numerator from the first. In our problem: \(-7 - 1 = -8\).
  • This operation results in the fraction \( \frac{-8}{9} \).
If your fractions have different denominators initially, don't worry. Simply convert them to equivalents with a common denominator before performing the subtraction. This might feel tricky at first, but practice helps every time!
Simplifying Fractions
Once you've performed addition or subtraction, simplifying the resulting fraction is essential to reach the neatest form possible.
Here are the steps to simplify fractions:
  • Identify any common factors between the numerator and the denominator. This means finding the highest number that divides evenly into both.
  • For \( \frac{-8}{9} \), check if there are any common factors between 8 and 9 beyond 1. Since there aren't any, \( \frac{-8}{9} \) is already in simplified form.
  • In circumstances where there are common factors, divide both the numerator and the denominator by that common factor.
Remember, a fraction is only fully simplified when you can no longer divide the numerator and denominator by any number other than 1. This gives the fraction its clearest and most reduced expression.

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

Solve the equation and simplify your answer. $$-\frac{5}{4} x-\frac{5}{3}=\frac{8}{7} x+\frac{7}{3}$$

Solve the equation and simplify your answer. $$-\frac{8}{9} x=-\frac{8}{3}$$

Solve the equation and simplify your answer. $$\frac{1}{4} x-\frac{4}{3}=-\frac{2}{3}$$

A trapezoid has bases measuring \(2 \frac{1}{4}\) and \(7 \frac{1}{8}\) feet, respectively. The height of the trapezoid is 5 feet. Find the area of the trapezoid.

Solve the equation and simplify your answer. $$\frac{1}{2} x+\frac{1}{3}=-\frac{5}{2} x-\frac{1}{4}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.