/*! 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 9 Simplify. $$-\frac{5}{8}-\left... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 9

Simplify. $$-\frac{5}{8}-\left(-\frac{11}{12}\right)$$

Short Answer

Expert verified
After simplifying the expression, the final answer is \(\frac{7}{24}\).

Step by step solution

01

Treat Subtraction of Negative as Addition

To simplify the expression, first, identify the negative sign in front of the second fraction. This means you add instead of subtract, i.e., \(-\frac{5}{8}+ \frac{11}{12}\). The expression becomes positive since subtracting a negative number is equivalent to adding a positive number.
02

Make Denominators Same

To add fractions, the denominators have to be the same. In this case, they are not. The Lowest Common Multiple (LCM) of 8 and 12 is 24, so the fractions can be adjusted to have this common denominator. It becomes \(-\frac{15}{24}+ \frac{22}{24}\).
03

Add the fractions

Adding the two fractions \(-\frac{15}{24}+ \frac{22}{24}\) gives us \(\frac{7}{24}\).

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.

Subtraction of Negatives
When you see a negative sign in front of a number or fraction, you can think of it as the opposite direction on the number line. If you have to subtract a negative, you are essentially moving in the positive direction on the number line. This is because subtracting a negative is the same as adding its positive counterpart.

For instance, if you have the expression
  • \(-\frac{5}{8} -(-\frac{11}{12})\)
You should treat the second negative sign as an addition. Therefore, the expression changes to:
  • \(-\frac{5}{8} + \frac{11}{12}\)
Understanding this will help you easily manage operations involving several consecutive negative signs in any equation.
Lowest Common Multiple
Adding fractions requires having a common denominator. The common denominator is often found by identifying the Lowest Common Multiple (LCM) of the denominators of the fractions you are working with. The LCM is the smallest multiple that is evenly divisible by each denominator.

In the case of fractions \(\frac{5}{8}\) and \(\frac{11}{12}\), their denominators are 8 and 12, respectively.
  • List the multiples of 8: 8, 16, 24, 32, ...
  • List the multiples of 12: 12, 24, 36, 48, ...
  • The smallest multiple they share is 24.
This means the common denominator for these fractions is 24.
Transform each fraction:
  • \(-\frac{5}{8} = -\frac{15}{24}\) by multiplying both the numerator and the denominator by 3
  • \(\frac{11}{12} = \frac{22}{24}\) by multiplying both the numerator and the denominator by 2
Now you have fractions with a common denominator!
Adding Fractions
Once the fractions have the same denominator, it's much easier to add them. When adding fractions, you only add the numerators together while keeping the common denominator unchanged.

Examine the fractions
  • \(-\frac{15}{24}\)
  • \(\frac{22}{24}\)
To perform the addition:
  • Add the numerators: \(-15 + 22 = 7\)
The denominator remains the same. So, the result of the addition is:
  • \(\frac{7}{24}\)
Thus, the simplified expression of the given problem is \(\frac{7}{24}\). This result can't be simplified further since 7 is a prime number and does not share any factors with 24. Understanding how to handle numerators and denominators separately keeps the process straightforward.

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 temperature after a rise of \(9^{\circ} \mathrm{C}\) from \(-6^{\circ} \mathrm{C}\)

Find the multiplier in the geometric sequence. Then find the next four numbers of the sequence. $$2,-4,8, \dots$$

Golf Use the equation \(S=N-P,\) where \(S\) is a golfer's score relative to par in a tournament, \(N\) is the number of strokes made by the golfer, and \(P\) is par, to find a golfer's score relative to par when the golfer made 49 strokes and par is 52 .

Subtract. $$-9-4$$

Simplify. $$6-(-13)-14+7$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics 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.