/*! 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 160 Divide, and write the answer in ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 160

Divide, and write the answer in simplified form. \(-5 \div \frac{1}{2}\)

Short Answer

Expert verified
-10

Step by step solution

01

- Rewrite the Division as Multiplication

To divide by a fraction, multiply by its reciprocal. The reciprocal of \(\frac{1}{2}\) is \(\frac{2}{1}\). Thus, rewrite -5 \/ \(\frac{1}{2}\) as \( -5 \times \frac{2}{1} \).
02

- Multiply the Numbers

Now, multiply -5 by the reciprocal of \(\frac{1}{2}\), which is \(\frac{2}{1}\). This step becomes \(-5 \times 2\).
03

- Simplify

Perform the multiplication: \(-5 \times 2 = -10\). Therefore, \(-5 \/ \(\frac{1}{2}\) = -10\).

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.

dividing fractions
Dividing fractions might seem tricky at first. But remember: divisions can be turned into multiplications!
Instead of dividing, you multiply by the reciprocal of the fraction.
For the exercise \(-5 \div \frac{1}{2}\), this means transforming it into a multiplication problem.
It's easier to understand with the steps below.
  • Step 1: Change the division to multiplication.
  • Step 2: Find the reciprocal of the divisor fraction.
  • Step 3: Multiply the whole number by the reciprocal.

This makes dividing by fractions much more straightforward!
reciprocal
The reciprocal of a number is basically what you multiply the number by to get 1. For fractions, it鈥檚 simple.
You just flip the numerator and the denominator.
So, the reciprocal of \(\frac{1}{2}\) is \(\frac{2}{1}\).
When you divide by a fraction, you can think of it as multiplying by its reciprocal. This is because division is the same as multiplying by the inverse.
Let's look at another example:
  • The reciprocal of \(\frac{3}{4}\) is \(\frac{4}{3}\).
  • If we need to divide 5 by \(\frac{3}{4}\), it鈥檚 the same as multiplying 5 by \(\frac{4}{3}\).

Working with reciprocals not only simplifies division but also makes other operations with fractions easier!
simplifying fractions
Simplifying fractions is all about making a fraction as simple as possible.
It's helpful for understanding and comparing numbers.
Here鈥檚 how you do it:
  • Find the greatest common divisor (GCD) of the numerator and denominator.
  • Divide both the numerator and the denominator by the GCD.
Let's simplify \(\frac{20}{28}\):
  • First, find the GCD of 20 and 28, which is 4.
  • Divide both parts by 4: \(\frac{20 梅 4}{28 梅 4} = \frac{5}{7}\).

That鈥檚 it! The fraction \(\frac{20}{28}\) simplifies to \(\frac{5}{7}\).
Simplifying makes fractions easier to work with and to understand.
Remember, practice makes perfect!

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

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{5}{12}-w\) when (a) \(w=\frac{1}{4} \quad\) (b) \(w=-\frac{1}{4}\)

In the following exercises, perform the indicated operations and simplify. $$-\frac{9}{10}-\frac{3}{4}$$

In the following exercises, simplify. $$ -5 \frac{7}{12} \cdot 4 \frac{4}{11} $$

Translate and solve. The sum of two-thirds and \(n\) is \(-\frac{3}{5}\)

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{a+b}{a-b}\) when \(a=-3, b=8\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.