/*! 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 477 In the following exercises, perf... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 477

In the following exercises, perform the indicated operation and write the result as a mixed number in simplified form. $$6-\frac{2}{5}$$

Short Answer

Expert verified
5 \( \frac{3}{5} \)

Step by step solution

01

Convert the Whole Number to a Fraction

First, write the whole number 6 as a fraction with the same denominator as \(\frac{2}{5}\). The whole number 6 can be written as \(\frac{30}{5}\).
02

Subtract the Fractions

Now subtract the fractions: \(\frac{30}{5} - \frac{2}{5}\). Since the fractions have the same denominator, subtract the numerators: \(\frac{30-2}{5} = \frac{28}{5}\).
03

Convert to Mixed Number

Convert the improper fraction \(\frac{28}{5}\) to a mixed number. Divide 28 by 5 to get 5 with a remainder of 3. Therefore, \(\frac{28}{5}\) is 5 \(\frac{3}{5}\).
04

Simplify the Mixed Number

The fraction \(\frac{3}{5}\) is already in its simplest form, so the final answer is 5 \(\frac{3}{5}\).

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.

Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. They are used to represent values that lie between whole numbers. For example, instead of writing an improper fraction like \(\frac{28}{5}\), we often prefer to use a mixed number. This makes it easier to understand and manage. Here鈥檚 how you convert an improper fraction to a mixed number:
  • Divide the numerator by the denominator to get the whole number part.
  • The remainder becomes the numerator of the fractional part.
  • Keep the same denominator for the fractional part.
So, \(\frac{28}{5}\) converts to 5 \(\frac{3}{5}\), because 28 divided by 5 is 5 with a remainder of 3.
Improper Fractions
An improper fraction has a numerator that is larger than or equal to its denominator. This means the fraction's value is 1 or greater. Improper fractions are useful in calculations, but we often convert them to mixed numbers for practical use. Here are the steps for converting a whole number to an improper fraction:
  • Multiply the whole number by the denominator of the fraction you are working with.
  • Write the result as the numerator over the same denominator.
For example, to convert 6 to a fraction with a denominator of 5:
  • Multiply: 6 * 5 = 30.
  • Write as a fraction: \(\frac{30}{5}\).
Simplification of Fractions
Simplifying fractions makes them easier to understand and compare. A fraction is simplified when the numerator and denominator have no common factors other than 1. Here鈥檚 how you can simplify fractions:
  • Find the greatest common divisor (GCD) of the numerator and denominator.
  • Divide both the numerator and the denominator by their GCD.
For instance, the fraction 6/8 simplifies to 3/4 because the GCD of 6 and 8 is 2. Here's another example: The fraction \(\frac{3}{5}\) is already in its simplest form because 3 and 5 have no common factors other than 1.

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, simplify. $$\left(\frac{3}{4}+\frac{1}{6}\right) \div\left(\frac{5}{8}-\frac{1}{3}\right)$$

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

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x-\frac{1}{3}\) when (a) \(x=\frac{2}{3} \quad\) (b) \(x=-\frac{2}{3}\)

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\frac{2}{3}\) when (a)\(x=-\frac{1}{6} \quad\) (b) \(x=-\frac{5}{3}\)

In the following exercises, simplify. $$ \frac{9 a}{10} \div \frac{15 a}{8} $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.