/*! 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 39 Divide. Find the product of \(... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 39

Divide. Find the product of \(2 \frac{2}{3}\) and \(1 \frac{1}{2}\).

Short Answer

Expert verified
The product of \(2 \frac{2}{3}\) and \(1 \frac{1}{2}\) is 4.

Step by step solution

01

Convert Mixed Numbers to Improper Fractions

Firstly, convert the mixed numbers into improper fractions. To convert \(2 \frac{2}{3}\), multiply the whole number (2) by the denominator (3), and add the numerator (2). This gives \(2\cdot3+2=8\), so \(2 \frac{2}{3} = \frac{8}{3}\). For \(1 \frac{1}{2}\), multiply the whole number (1) by the denominator (2), and add the numerator (1). This gives \(1\cdot2+1=3\), so \(1 \frac{1}{2} = \frac{3}{2}\).
02

Multiply the Improper Fractions

Now multiply the improper fractions \(\frac{8}{3}\) and \(\frac{3}{2}\) by multiplying their numerators together and their denominators together. So the product is \(\frac{8 \cdot 3}{3 \cdot 2} = \frac{24}{6}\).
03

Simplify the Resulting Fraction

The fraction \(\frac{24}{6}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6. Therefore, \(\frac{24\div 6}{6\div 6} = \frac{4}{1} = 4\).

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.

Improper Fractions
An improper fraction is a type of fraction where the numerator (top number) is greater than or equal to the denominator (bottom number). This typically means that the fraction is greater than or equal to one whole. Understanding improper fractions is important because they often appear when converting mixed numbers.

Mixed numbers combine a whole number with a fraction, making computation a bit tricky. So, converting them to improper fractions simplifies many operations.
  • To convert a mixed number, multiply the whole number by the denominator of the fractional part.
  • Add the numerator of the fractional part to the result.
  • This sum becomes the new numerator, and the denominator stays the same.
For example, converting the mixed number \(2 \frac{2}{3}\) involves calculating \(2 \times 3 + 2 = 8\), so it becomes \(\frac{8}{3}\).
Multiplying Fractions
Multiplying fractions involves a straightforward method:
  • Multiply the numerators (top numbers) together.
  • Multiply the denominators (bottom numbers) together.
This simple process contrasts other fraction operations like addition and subtraction, which need a common denominator. Once you multiply the fractions, you get a new fraction that may need further simplification.

Consider the example: multiplying \(\frac{8}{3}\) and \(\frac{3}{2}\). By multiplying the numerators (8 and 3) and the denominators (3 and 2) separately, you get \(\frac{24}{6}\). Notice how this product is an improper fraction, which is common when dealing with multiplication of fractions.
Simplifying Fractions
Simplifying fractions makes them easier to understand and work with. The goal is to find the simplest form, where the numerator and denominator are as small as possible while still representing the same value. This is done by:
  • Finding the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
In our example, the fraction \(\frac{24}{6}\) is simplified by identifying the GCD of 24 and 6, which is 6. Dividing both terms by 6, the fraction becomes \(\frac{4}{1}\), or simply \(4\). Simplification not only makes fractions clearer, but also more convenient for further calculations.

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

Divide. $$378.9 \div 21.05$$

Divide. Find the difference of \(2 \frac{2}{3}\) and \(1 \frac{1}{2}\).

A new graphics card can increase the resolution of a computer's monitor. Suppose a monitor has a horizontal resolution of 640 pixels and a vertical resolution of 480 pixels. By adding a new graphics card, the resolutions remain in the same proportions, but the vertical resolution increases to 786 pixels. What is the new horizontal resolution?

Find the following quotients. (Divide.) $$6.99 \div 2.33$$

Solve each equation by finding a number to replace \(n\) that will make the equation a true statement. $$650=10 \cdot n$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.