/*! 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 21 Divide and simplify. \(12 \div... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 21

Divide and simplify. \(12 \div \frac{3}{2}\)

Short Answer

Expert verified
8

Step by step solution

01

Rewrite the Division as Multiplication

Rewrite the division problem using multiplication by the reciprocal of the divisor. Reciprocal of \( \frac{3}{2} \) is \( \frac{2}{3} \). So, \( 12 \div \frac{3}{2} \) becomes \( 12 \times \frac{2}{3} \).
02

Simplify the Multiplication

Multiply 12 by the reciprocal of \( \frac{3}{2} \), which is \( \frac{2}{3} \). This gives: \[ 12 \times \frac{2}{3} = \frac{12 \times 2}{3} \].
03

Perform the Multiplication and Simplification

Multiply the numbers in the numerator: \( 12 \times 2 = 24 \). Simplify the fraction by dividing the numerator by the denominator: \[ \frac{24}{3} = 8 \].

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.

Reciprocal
To divide one fraction by another, we use a helpful concept called the 'reciprocal.' A reciprocal is simply what you get when you flip a fraction upside down.
For example, the reciprocal of \( \frac{3}{2} \) is \( \frac{2}{3} \). This means the numerator (top number) becomes the denominator (bottom number), and vice versa.
  • Reciprocals are essential when changing a division problem into a multiplication problem.
  • Always find the reciprocal of the divisor鈥攖he number you are dividing by鈥攖o continue solving.
Multiplication
Once you have the reciprocal of the fraction, you replace the division sign with a multiplication sign. This is because dividing by a fraction is the same as multiplying by its reciprocal.
In our example, \( 12 \div \ \frac{3}{2} \) becomes \( 12 \times \ \frac{2}{3} \). Note how the operation switches from division to multiplication.
  • Multiplication is often easier to handle than division, especially with fractions.
  • Make sure to carefully replace the operations to avoid confusion.
Simplification
Simplification makes math problems easier to handle and understand.
After multiplying, you might get a fraction that can be reduced to its simplest form.
In our step-by-step example, multiplying \( 12 \times \ \frac{2}{3} \) results in \( \frac{24}{3} \).
Here, you simplify by dividing the numerator (24) by the denominator (3), giving \( 8 \).
  • Always check if the fraction can be reduced by finding common factors for the numerator and denominator.
  • This makes the number easier to understand and work with in further calculations.
Fraction
A fraction represents a part of a whole.
It consists of two numbers: the numerator (top number) and the denominator (bottom number). For example, in \( \frac{3}{2} \), 3 is the numerator, and 2 is the denominator.
  • Fractions can sometimes look tricky, but understanding their components and how to manipulate them can make solving problems much simpler.
  • Operations such as addition, subtraction, multiplication, and division can be applied to fractions just like whole numbers.

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 prime factorization of each number. $$ 70 $$

Use \(<\) or \(>\) for \(\square\) to write a true sentence. $$ 34 \square 43 $$

Simplify. $$ \frac{0}{16} $$

Find the prime factorization of each number. $$ 42 $$

Determine whether 4227 is divisible by \(9 .\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Statistics

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.