/*! 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 30 Subtract. See Examples 1 through... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 30

Subtract. See Examples 1 through 5 $$ -\frac{1}{10}-\frac{7}{8} $$

Short Answer

Expert verified
The result of the subtraction is -\(\frac{39}{40}\).

Step by step solution

01

Make Fractions Like Denominators

Convert both fractions to have a common denominator. In this case, the lowest common denominator (LCD) of 10 and 8 is 40. Convert \(-\frac{1}{10}\) to \(-\frac{4}{40}\) and \(-\frac{7}{8}\) to \(-\frac{35}{40}\).
02

Subtract Fractions

Now that both fractions have the same denominator, subtract the numerators: \(-4\) - (35) = -39. The result is \(-\frac{39}{40}\).
03

Simplify the Result

Check if the resulting fraction can be simplified. Since there are no common factors for 39 and 40, \(-\frac{39}{40}\) 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.

Common Denominator
When dealing with fractions, especially in subtraction or addition, finding a common denominator is crucial. This ensures that the fractions have the same bottom number, making them easier to work with. To find a common denominator:
  • Identify the denominators of each fraction you are dealing with, in this case, 10 and 8.
  • Find the least common multiple (LCM) of these denominators. The LCM is the smallest number that both denominators can divide into without a remainder. Here, the LCM of 10 and 8 is 40.
Once the common denominator is found, adjust the numerators accordingly so that the value of the fractions remains unchanged. For example, \(-\frac{1}{10}\) becomes \(-\frac{4}{40}\) and \(-\frac{7}{8}\) becomes \(-\frac{35}{40}\). Now, with a common denominator of 40, you can easily perform operations like subtraction.
Simplify Fractions
After performing any operations with fractions, it is essential to check if the resulting fraction can be simplified. Simplification means reducing the fraction to its simplest form, where the numerator and the denominator no longer have any common factors except 1. For instance:
  • Examine the greatest common divisor (GCD) of the numerator and denominator.
  • Divide both the numerator and the denominator by the GCD to simplify.
In the solution \(-\frac{39}{40}\), there are no common factors between 39 and 40 besides 1. Thus, this fraction is already in its simplest form. Remembering to simplify ensures your final answer is clear and concise.
Like Denominators
The concept of like denominators aligns closely with having a common denominator. By converting fractions to have like denominators, you simplify operations between them, such as addition or subtraction. "Like denominators" merely means that each of the fractions shares the same denominator:
  • This uniformity contrasts the fractions only by their numerators, making computations straightforward.
  • Once you have transformed fractions into having like denominators, proceed with direct operations on the numerators.
For example, in the problem \(-\frac{1}{10}-\frac{7}{8}\), using a common denominator of 40 achieved like denominators: \(-\frac{4}{40}\) and \(-\frac{35}{40}\), allowing you to subtract the numerators easily, resulting in \(-\frac{39}{40}\). Understanding and applying this makes fraction operations more efficient and less prone to errors.

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

Fill in the table with the opposite (additive inverse), and the reciprocal (multiplicative inverse). Assume that the value of each expression is not 0 $$ 7 x $$

Perform the following operations. Write answers in lowest terms. $$ \frac{3}{4} \div \frac{7}{12} $$

Tyson Industries stock posted a loss of 1.625 points yesterday. If it drops another 0.75 point today, find its overall change for the two days.

Evaluate each expression when \(x=-5, y=4,\) and \(t=10 .\) See Example 6. $$ x-y $$

In forensics, the density of a substance is used to help identify it. The expression \(\frac{M}{V}\) represents the density of an object with a mass of \(M\) grams and a volume of \(V\) milliliters. Find the density of an object having a mass of 29.76 grams and a volume of 12 milliters.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete 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.