/*! 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 3 For exercises \(3-6\), evaluate ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 3

For exercises \(3-6\), evaluate or simplify. $$ \frac{3}{20} \cdot \frac{2}{15} $$

Short Answer

Expert verified
\( \frac{1}{50} \)

Step by step solution

01

- Multiply the Numerators

Multiply the numerators of both fractions together. This means you take the top numbers of the fractions and multiply them: ewline ewline \(\frac{3}{20} \times \frac{2}{15} = \frac{3 \times 2}{20 \times 15}\)
02

- Multiply the Denominators

Next, multiply the denominators of both fractions together. This means you take the bottom numbers of the fractions and multiply them: ewline ewline \(\frac{3 \times 2}{20 \times 15} = \frac{6}{300}\)
03

- Simplify the Fraction

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by that number. The GCD of 6 and 300 is 6: ewline ewline \(\frac{6}{300} \rightarrow \frac{6 \rightarrow 1}{300 \rightarrow 50} = \frac{1}{50}\)

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.

Numerator and Denominator
Fractions consist of two parts: the numerator and the denominator. The numerator is the top number and represents how many parts you have. The denominator is the bottom number and shows the total number of equal parts in a whole.
For example, in the fraction \(\frac{3}{20}\), 3 is the numerator and 20 is the denominator. Understanding this structure is crucial as it lays the foundation for fraction operations.
In the multiplication process, you multiply the numerators with each other and the denominators with each other. This maintains the ratio represented by the fractions.
Simplifying Fractions
Simplifying fractions means reducing them to their simplest form. This process involves expressing a fraction in such a way that the numerator and denominator are as small as possible while still representing the same value. Simplification makes fractions easier to understand and work with.
The steps to simplify a fraction are:
  • Identify the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
  • Rewrite the fraction using the results from the division.
For example, if you have \(\frac{6}{300}\), you first find the GCD of 6 and 300, which is 6. Then, divide both the numerator and denominator by 6 to get \(\frac{1}{50}\). This fraction is now simplified because 1 and 50 have no common divisors other than 1.
Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that can evenly divide both the numerator and the denominator of a fraction. Finding the GCD is essential for simplifying fractions.
To find the GCD of two numbers, you can use several methods, one of the most common being the Euclidean algorithm:
  • Divide the larger number by the smaller number.
  • Take the remainder and divide the smaller number by this remainder.
  • Repeat the process until the remainder is 0. The last non-zero remainder is the GCD.
For example, to find the GCD of 6 and 300:
  • 300 梅 6 = 50 with no remainder.
  • Here, 6 is the GCD as it perfectly divides both 6 and 300.
Understanding and using the GCD allows you to simplify fractions effectively and ensures your solutions are as clear as possible.

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

For exercises 43-58, (a) solve. (b) check. $$ \frac{d+1}{3}=\frac{d-3}{6} $$

For exercises 79-82, (a) clear the fractions and solve. (b) check. $$ \frac{5}{6} h+8=12 $$

For exercises 37-38, \(T=\frac{R}{A}\) represents the relationship of the asset turnover ratio, \(T\); the sales revenue of a company, \(R\); and the total revenues of a company, \(A\). Is the relationship of the given variables a direct variation or an inverse variation? $$ R \text { is constant; the relationship of } A \text { and } T \text {. } $$

The relationship of the diameter of a circle, \(x\), and the circumference of the circle, \(y\), is a direct variation. The diameter of a circle is \(20 \mathrm{~cm}\), and the circumference is \(62.8 \mathrm{~cm}\). a. Find the constant of proportionality, \(k\). b. Write an equation that represents this relationship. c. Find the circumference of a circle with a diameter of \(40 \mathrm{~cm}\).

For exercises \(67-82\), use the five steps and a proportion. About five of 100 pregnant women have pre-eclampsia, a condition that results in high blood pressure. About 300,000 pregnant women per year in the United States have pre-eclampsia. Find the number of pregnant women in the United States used to create this ratio. (Source: www.nytimes.com, March 17, 2009)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

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.