/*! 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 40 Multiply. Simplify, if possible.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 40

Multiply. Simplify, if possible. $$ 4 \frac{1}{10} \cdot 3 \frac{1}{3} $$

Short Answer

Expert verified
The simplified product is \(\frac{41}{3}\).

Step by step solution

01

Convert Mixed Numbers to Improper Fractions

First, convert the mixed numbers to improper fractions. For the mixed number \(4 \frac{1}{10}\), multiply the whole number (4) by the denominator (10) and add the numerator (1): \[ 4 \frac{1}{10} = \frac{4 \times 10 + 1}{10} = \frac{40 + 1}{10} = \frac{41}{10} \] For the mixed number \(3 \frac{1}{3}\), multiply the whole number (3) by the denominator (3) and add the numerator (1): \[ 3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3} \]
02

Multiply the Improper Fractions

Next, multiply the improper fractions: \[ \frac{41}{10} \times \frac{10}{3} \] Multiply the numerators: \[ 41 \times 10 = 410 \] Multiply the denominators: \[ 10 \times 3 = 30 \] So the product is: \[ \frac{410}{30} \]
03

Simplify the Fraction

To simplify \(\frac{410}{30}\), find the greatest common divisor (GCD) of 410 and 30. The GCD is 10. Divide both the numerator and the denominator by 10: \[ \frac{410 \text{ 梅 } 10}{30 \text{ 梅 } 10} = \frac{41}{3} \]

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 fraction where the numerator (the top number) is greater than or equal to the denominator (the bottom number). For instance, in the mixed number \(4 \frac{1}{10}\), when we convert it to an improper fraction, we get \(\frac{41}{10}\). This is because 41 is greater than 10.
Numerator
The numerator is the top number in a fraction. It indicates how many parts of a whole are being considered. For example, in the fraction \(\frac{41}{10}\), 41 is the numerator, showing that we have 41 parts out of 10.
Denominator
The denominator is the bottom number in a fraction. It represents the total number of equal parts the whole is divided into. In the fraction \(\frac{41}{10}\), 10 is the denominator, denoting that the whole is divided into 10 equal parts. Understanding the denominator helps us grasp the size of each part compared to the whole.
Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that can exactly divide both the numerator and the denominator of a fraction. For the fraction \(\frac{410}{30}\), the GCD of 410 and 30 is 10. By dividing both the numerator and the denominator by their GCD, we simplify the fraction \(\frac{410}{30}\) to \(\frac{41}{3}\), which is easier to understand and work with.

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

Solve. $$ \frac{\frac{1}{5}}{\frac{1}{10}}=\frac{\frac{1}{10}}{x} $$

The number of golf courses in the United States has declined steadily since its peak in the early 2000 s. In \(2015,\) there were 15,372 golf courses in the United States. This was 680 fewer courses than the peak number. What was the peak number of golf courses in the United States? \([1.8 \mathrm{a}]\)

Solve. Round the answer to the nearest thousandth. $$ \frac{12.0078}{56.0115}=\frac{789.23}{y} $$

Solve. $ \frac{5}{\frac{1}{3}}=\frac{3}{x} $$

Joanna filled her van's gas tank and noted that the odometer read 42,598.2 . After the next fill-up, the odometer read 42,912.1. It took 14.6 gal to fill the tank. How many miles per gallon did the van get? \([4.7 a]\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

Read Explanation

Decision 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.