/*! 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 Determine whether the proportion... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 8

Determine whether the proportion is true or not true. $$\frac{3}{4}=\frac{54}{72}$$

Short Answer

Expert verified
The proportion \(\frac{3}{4}=\frac{54}{72}\) is true.

Step by step solution

01

Understand Cross Multiplication

Cross multiplication is a method used to compare two proportions. If A:B :: C:D, then cross multiplication states that A*D should be equal to B*C. If they are equal, then the proportions are true, otherwise they are not true.
02

Apply Cross Multiplication

Plug in the numbers from the proportion into the cross multiplication method. That means, check if \(3*72\) equals \(4*54\).
03

Evaluate and Compare

Perform the multiplication on both sides to see if the two products are equal. \(3*72=216\) and \(4*54=216\).

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.

Cross Multiplication
Cross multiplication is a powerful tool used to check if two fractions form a true proportion. It works by cross-multiplying the terms of the fractions. For instance, in a proportion like \(\frac{a}{b} = \frac{c}{d}\), you multiply across the equals sign: \(a \times d\) and \(b \times c\).
  • If both products are equal, then the two fractions are indeed a proportion of each other.
  • If they are not equal, the fractions do not form a proportion.
This method is not only simple but also very effective for dealing with equations involving fractions. In the given example, you can verify the equality of \(\frac{3}{4}\) and \(\frac{54}{72}\) by checking if \(3 \times 72 = 4 \times 54\). Since both calculations yield 216, we can confirm that these fractions are proportional.
Fraction Comparison
Comparing fractions can often seem tricky, but with a few methods up your sleeve, it gets much easier. The goal is to determine which fraction is larger, smaller, or if they are equal.
  • Common Denominator Method: Convert both fractions to have the same denominator and then compare the numerators. This helps visualize which fraction numerically has more parts.
  • Cross Multiplication: As seen before, this can also be used to compare fractions. Instead of solving for precision, you're checking which product is greater.
In our example, you don鈥檛 need to convert to a common denominator or use cross multiplication for size comparison. Instead, after cross multiplicative verification, we know they are equivalent. Hence, \(\frac{3}{4}\) is equal to \(\frac{54}{72}\) in size as well.
Equivalent Fractions
Fractions that may look different can in fact represent the same portion or ratio of a whole. These are known as equivalent fractions. Visually and numerically, they are identical, even if the numbers are different. Two fractions are equivalent if the result of multiplying across the fractions remains the same after cross-multiplication.
  • To create equivalent fractions, multiply or divide the numerator and the denominator by the same non-zero number.
  • Check your resulting fractions by reducing both to see if they simplify to the same simplest form.
In the given exercise, \(\frac{3}{4}\) and \(\frac{54}{72}\) are equivalent because both fractions simplify to \(\frac{3}{4}\) when reduced fully. What seems complicated becomes clear as both the cross-multiplication check and simplification affirm their equivalence.

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

Solve. Use the basic percent equation. 18 is \(240 \%\) of what?

During the 2010 baseball season, Johan Santana gave up 66 earned runs and pitched 199 innings for the New York Mets. To calculate Johan Santana's ERA, let \(x=\) the number of earned runs for every nine innings pitched. Then write a proportion and solve it for \(x\). $$\begin{aligned}\frac{66 \text { earned runs }}{199 \text { innings }} &=\frac{x}{9 \text { innings }} \\ 66 \cdot 9 &=199 \cdot x \\\594 &=199 x \\\\\frac{594}{199} &=\frac{199 x}{199} \\\2.98 & \approx x\end{aligned}$$ Roger Clemens's first year with the Boston Red Sox was \(1984 .\) During that season, he pitched 133.1 innings and gave up 64 earned runs. Calculate Clemens's ERA for 1984

During the 2010 baseball season, Johan Santana gave up 66 earned runs and pitched 199 innings for the New York Mets. To calculate Johan Santana's ERA, let \(x=\) the number of earned runs for every nine innings pitched. Then write a proportion and solve it for \(x\). $$\begin{aligned}\frac{66 \text { earned runs }}{199 \text { innings }} &=\frac{x}{9 \text { innings }} \\ 66 \cdot 9 &=199 \cdot x \\\594 &=199 x \\\\\frac{594}{199} &=\frac{199 x}{199} \\\2.98 & \approx x\end{aligned}$$ In \(1987,\) Nolan Ryan had the lowest ERA of any pitcher in the major leagues. That year, he gave up 65 earned runs and pitched 211.2 innings for the Houston Astros. Calculate Ryan's ERA for 1987 .

Solve. Use the proportion method. What is \(250 \%\) of \(18 ?\)

Solve. Use the proportion method. 14 is \(175 \%\) of what?
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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.