/*! 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 8 Simplify. $$\left(3-1 \frac{3}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 8

Simplify. $$\left(3-1 \frac{3}{4}\right)^{2}$$

Short Answer

Expert verified
\(\frac{25}{16}\)

Step by step solution

01

Convert Mixed Number to Improper Fraction

First, convert the mixed number into an improper fraction. The given mixed number is 1\(\frac{3}{4}\). To convert it, multiply the whole number 1 by the denominator 4, and then add the numerator 3: \( 1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4} \)
02

Subtract Fractions

Subtract the improper fraction from 3. Rewrite 3 as a fraction with the same denominator to perform the subtraction: \( 3 = \frac{3 \times 4}{4} = \frac{12}{4} \).Next, subtract: \( \frac{12}{4} - \frac{7}{4} = \frac{12 - 7}{4} = \frac{5}{4} \)
03

Square the Result

Square the result of the subtraction. \( \frac{5}{4} \rightarrow \left(\frac{5}{4}\right)^2 = \frac{5^2}{4^2} = \frac{25}{16} \)

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.

Converting Mixed Numbers to Improper Fractions
A mixed number consists of a whole number and a fraction. Before performing operations, it's often easier to convert mixed numbers into improper fractions. Here鈥檚 how to do it:
  • Multiply the whole number by the denominator of the fraction.
  • Add the numerator to this product.
  • Place this sum over the original denominator.

For example, to convert the mixed number 1\frac{3}{4} to an improper fraction:
\begin{itemize}
  • Multiply the whole number by the denominator: 1 times 4 = 4 //
  • Add the numerator: 4 + 3 = 7 //
  • Place the sum over the original denominator: \(\frac{7}{4}\) //
    • Now you have the improper fraction!
    This method applies to any mixed number you encounter.
    Subtracting Fractions
    To subtract fractions, they must have a common denominator. This makes the subtraction process straightforward.
    For our example, we need to subtract \frac{7}{4} from 3. First, we convert the whole number into a fraction with the same denominator:
    \begin{itemize}
  • Rewrite 3 as a fraction with denominator 4: \(\frac{3 \times 4}{4} = \frac{12}{4}\) //
  • Now subtract: \(\frac{12}{4} - \frac{7}{4} = \frac{12 - 7}{4} = \frac{5}{4}\) //

    • It鈥檚 that simple! Working with common denominators makes the subtraction of fractions straightforward and ensures accuracy. If the denominators aren't the same, you'll need to find a common denominator before proceeding.
    Squaring Fractions
    Squaring a fraction is a key concept in algebra. It involves raising both the numerator and the denominator of the fraction to the power of two. Here鈥檚 how to do it:
    • Take the numerator and raise it to the power of two.
    • Take the denominator and do the same.

    For our example, we squared \(\frac{5}{4}\):
    \begin{itemize}
  • Square the numerator: \(5^2 = 25\) //
  • Square the denominator: \(4^2 = 16\) //
  • Place the squared numerator over the squared denominator: \(\frac{25}{16}\) //

    • By following these steps, you ensure your squared results are accurate. This method applies to any fraction and is especially helpful in algebraic functions and equations.

    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

    Simplify the expression. $$\frac{14 x y z}{7 z}$$

    Convert the improper fraction to a mixed number. $$\frac{51}{10}$$

    Convert the improper fraction to a mixed number. $$\frac{67}{12}$$

    For a recent year, the population of the United States was reported to be \(296,000,000\). During the same year, the population of California was \(36,458,000\). a. Round the U.S. population to the nearest hundred million. b. Round the population of California to the nearest million. c. Using the results from parts (a) and (b), write a simplified fraction showing the portion of the U.S. population represented by California.

    Convert the mixed number to an improper fraction. $$6 \frac{3}{4}$$
    See all solutions

    Recommended explanations on Math Textbooks

    Applied Mathematics

    Read Explanation

    Logic and Functions

    Read Explanation

    Pure Maths

    Read Explanation

    Geometry

    Read Explanation

    Probability and Statistics

    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.