/*! 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 11 Solve proportion. \(\frac{a}{3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 11

Solve proportion. \(\frac{a}{3}=\frac{14}{21}\)

Short Answer

Expert verified
a = 2

Step by step solution

01

- Set up the Equation

Start with the given proportion: \(\frac{a}{3} = \frac{14}{21}\)
02

- Cross Multiply

To solve the proportion, use cross-multiplication: \(a \times 21 = 14 \times 3\)
03

- Simplify and Solve for 'a'

Calculate the right-hand side and divide by 21: \(21a = 42\), then \(a = \frac{42}{21}\)
04

- Simplify the Result

Simplify \(\frac{42}{21}\): \(a = 2\)

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 method used to solve proportions. It involves multiplying the numerator of one fraction by the denominator of the other fraction.

This method can be observed in the following steps:
  • Identify the two fractions in the proportion.
  • Multiply the numerator of the first fraction by the denominator of the second fraction.
  • Multiply the numerator of the second fraction by the denominator of the first fraction.

When dealing with the proportion \(\frac{a}{3} = \frac{14}{21}\), cross multiplication gives us: \[ a \times 21 = 14 \times 3 \] By performing these cross multiplications, we eliminate the fractions, making it straightforward to solve for the unknown variable.
Simplification
Simplification is the process of reducing an equation or expression to its simplest form. This is crucial in solving mathematical problems efficiently.

In our example, after cross multiplication, we get: \[ 21a = 42 \] Now, we need to isolate 'a' by performing opposite operations.

First, divide both sides of the equation by 21: \[ a = \frac{42}{21} \]
This fraction can be further simplified. When you divide 42 by 21, you get: \[ a = 2 \]
Thus, the equation in its simplest form shows that the value of 'a' is 2.
Solving Equations
Solving equations involves finding the value of the unknown variable that makes the equation true.

Starting from our previously simplified equation: \[ 21a = 42 \] We isolate the variable 'a' by using the principles of equality.

Here鈥檚 a quick reminder of the steps used:
  • Perform the same operation on both sides of the equation.
  • Operations might include addition, subtraction, multiplication, or division.
  • In this case, we divide both sides by 21.
This gives us: \[ a = \frac{42}{21} = 2 \]
Double-checking your work is a good habit. Substituting 'a = 2' back into the original proportion: \[ \frac{2}{3} = \frac{14}{21} \] confirms that both sides are equal, validating our solution.

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

In Exercises \(9-14\), is the triangle with sides of the given lengths a right triangle? \(3 \sqrt{3} \mathrm{cm}, 6 \mathrm{cm}, 3 \mathrm{cm}\)

Draw segments \(\overline{A B}, \overline{C D},\) and \(\overline{E F}\) such that \(A B\) is about 2 inches, \(C D\) is about 3 inches, and \(E F\) is about 4 inches. Construct \(\overline{U V}\) so that \(\frac{A B}{C D}=\frac{E F}{U V}\)

State whether the polygons are always, sometimes, or never similar. A right triangle and an acute triangle.

Prove that the ratio of the perimeters of two similar triangles equals the ratio of the lengths of any two corresponding sides.

The sides of a triangle are in the ratio of \(3: 4: 5 .\) If the perimeter is 90 centimeters, find the lengths of each side.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Decision 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.