/*! 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 20 Determine whether each proportio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 20

Determine whether each proportion is true or false. $$ \frac{0.7}{0.4}=\frac{0.3}{0.1} $$

Short Answer

Expert verified
The proportion is false, as 1.75 does not equal 3.

Step by step solution

01

Understand the Proportion

We need to determine if the given proportion \(\frac{0.7}{0.4} = \frac{0.3}{0.1}\) is true or false by checking if the two ratios are equivalent.
02

Simplify the Right-Hand Side

Calculate the right-hand side of the equation: \(\frac{0.3}{0.1}\). To do this, divide 0.3 by 0.1 to get 3. So, \(\frac{0.3}{0.1} = 3\).
03

Simplify the Left-Hand Side

Calculate the left-hand side of the equation: \(\frac{0.7}{0.4}\). To do this, divide 0.7 by 0.4 to get 1.75. So, \(\frac{0.7}{0.4} = 1.75\).
04

Compare the Two Sides

Now, compare the simplified outcomes from both sides: 1.75 (left side) and 3 (right side). Since these two values are not equal, the proportion is false.

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.

Understanding Ratios
A ratio is a way to compare two quantities by dividing one quantity by the other. Ratios are very helpful in understanding how one part relates to another or to a whole. They can be expressed in various forms such as fractions, decimals, or with a colon, like 3:4. In the context of the given problem, we have a ratio on both sides of the equation:
  • Left-hand side: \(\frac{0.7}{0.4}\)
  • Right-hand side: \(\frac{0.3}{0.1}\)
Both these expressions can be compared by transforming them into the same form, often fractions or decimals, to determine their equivalence. This makes the concept of ratios a foundational skill for solving problems involving proportions.
Learning About Equivalent Fractions
Equivalent fractions are fractions that represent the same portion of a whole, even if the numerators and denominators differ. For example, \(\frac{1}{2}\) is equivalent to \(\frac{2}{4}\) because they reduce to the same value when simplified.
In our problem, determining whether the two fractions in the proportion are equivalent involves comparing their simplified values:
  • Simplify \(\frac{0.7}{0.4}\) to get 1.75
  • Simplify \(\frac{0.3}{0.1}\) to get 3
Since 1.75 and 3 are not the same, these fractions are not equivalent. Thus, they do not represent the same part of a whole, confirming that the given proportion is false.
Simplification of Fractions in Proportions
Simplifying fractions involves reducing them to their simplest form, meaning the numerator and denominator have no common factors other than 1. This process helps in easily comparing two fractions. In proportions, simplification assists in checking whether both sides of the equation are equivalent.
Using our example:
  • For \(\frac{0.3}{0.1}\), dividing both the numerator and denominator by 0.1 gives us 3.
  • For \(\frac{0.7}{0.4}\), dividing both by 0.4 gives us 1.75.
By simplifying each side to a single number, we can easily see they are different, leading to the conclusion that the proportional relationship is incorrect. Understanding simplification, therefore, plays a crucial role in solving and verifying proportions accurately.

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

Without using a calculator, explain how you know that \(\sqrt{27}\) is not approximately 3.296 .

Insert \(<\) or \(>\) to form a true statement. $$ 8.01 \quad 8.1 $$

Solve. A local package express deliveryman is traveling the city expressway at \(45 \mathrm{mph}\) when he is forced to slow down due to traffic ahead. His truck slows at the rate of 3 mph every 5 seconds. Find his speed 8 seconds after braking.

Describe a situation in which writing a proportion might solve a problem related to driving a car.

Two out of every 5 men blame their poor eating habits on too much fast food. In a room of 40 men, how many would you expect to blame their not eating well on fast food?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.