/*! 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 58 Perform each operation. $$ \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 58

Perform each operation. $$ \frac{3}{5} \cdot\left(\frac{1}{2}+1.75\right) $$

Short Answer

Expert verified
The result of the operation is \(\frac{27}{20}\) or as a mixed number, \(1\frac{7}{20}\).

Step by step solution

01

Simplify the Addition Inside the Parentheses

First, simplify the expression inside the parentheses by adding the fractions and decimal number: 1. Convert the decimal 1.75 to a fraction. 2. Perform the addition. Convert 1.75 to a fraction:1.75 = \(\frac{7}{4}\)Now add \(\frac{1}{2} + \frac{7}{4}\): Find a common denominator for the fractions, which is 4. Rewrite \(\frac{1}{2}\) as \(\frac{2}{4}\): \(\frac{1}{2} = \frac{2}{4}\) Add the fractions:\(\frac{2}{4} + \frac{7}{4} = \frac{9}{4}\). The expression becomes \(\frac{3}{5} \cdot \frac{9}{4}\).
02

Multiply the Fractions

Now, multiply the fractions: To multiply \(\frac{3}{5} \cdot \frac{9}{4}\), multiply the numerators together and the denominators together:Numerator: \(3 \times 9 = 27\)Denominator: \(5 \times 4 = 20\)The resulting fraction is \(\frac{27}{20}\).
03

Simplify the Resulting Fraction

Check if the fraction \(\frac{27}{20}\) can be simplified. Since 27 and 20 have no common factors other than 1, \(\frac{27}{20}\) is in its simplest form. You can also express \(\frac{27}{20}\) as a mixed number:1. Divide 27 by 20. Quotient is 1 and remainder is 7.2. Hence, \(\frac{27}{20} = 1\frac{7}{20}\).

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.

Fraction Addition
Adding fractions involves combining numerators over a common denominator. When fractions do not share the same denominator, the first step is to find a common denominator. This allows the fractions to be rewritten and easily added. In our exercise, we begin with the addition of \(\frac{1}{2}\) and 1.75.

To combine
  • Convert the decimal 1.75 into a fraction: \(1.75 = \frac{7}{4}\)
  • Rewrite \(\frac{1}{2}\) with a common denominator of 4: \(\frac{1}{2} = \frac{2}{4}\)
  • Add the fractions: \(\frac{2}{4} + \frac{7}{4} = \frac{9}{4}\)
These steps illustrate how to add fractions successfully when they have different denominators. Using a common denominator is crucial for accurate fraction addition.
Fraction Multiplication
Fraction multiplication is simpler than addition because it doesn鈥檛 require a common denominator. You directly multiply the numerators and the denominators. In this example, we multiply \(\frac{3}{5}\) by \(\frac{9}{4}\).

Follow these steps:
  • Multiply the numerators: \(3 \times 9 = 27\)
  • Multiply the denominators: \(5 \times 4 = 20\)
  • Combine the results into a new fraction: \(\frac{27}{20}\)
This method applies to any fraction multiplication, making it a straightforward operation. The result is a fraction, which can often be simplified further.
Mixed Numbers
Mixed numbers combine whole numbers with fractions, offering a different way to express improper fractions. For example, after multiplying and simplifying, we obtained \(\frac{27}{20}\). To convert this into a mixed number:
  • Divide the numerator by the denominator: \(27 \div 20\)
  • This results in a quotient of 1 and a remainder of 7
  • Express as \(1\frac{7}{20}\)
Mixed numbers are convenient for visualizing quantities larger than one whole. They provide a tangible way to understand fractions that have a numerator larger than the denominator.

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

Write eighty-one and twelve hundredths using digits. 81.12

Perform the following operations. \(5.198-0.26 \cdot\left(\frac{14}{250}+0.119\right)\)

Perform each operation and simplify. $$ 1,000 \cdot 1,816.001 $$

Round each decimal to the specified position. 817.42 to the nearest ten.

Perform each operation. $$ \frac{3}{16} \cdot 1.36 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Mechanics 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.