/*! 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 70 Write an equivalent fraction wit... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 70

Write an equivalent fraction with the given denominator. $$\frac{4}{9}=\frac{}{36}$$

Short Answer

Expert verified
The equivalent fraction of \( \frac{4}{9} \) with the denominator 36 is \( \frac{16}{36} \).

Step by step solution

01

Determine the Scale Factor

To find the equivalent fraction, identify how much the given denominator 9 needs to be multiplied to equal the desired denominator 36. Calculate the scale factor which is \( \frac{36}{9} = 4 \).
02

Multiply the Numerator

After identifying the scale factor, then multiply the numerator of the original fraction by this scale factor. Therefore, \( 4 * 4 = 16 \).
03

Write the Equivalent Fraction

The equivalent fraction of \( \frac{4}{9} \) with the denominator 36 is found by replacing the numerator with the result from step 2, leading to \( \frac{16}{36} \).

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.

Denominators
When it comes to fractions, the denominator is the bottom number. It essentially shows how many equal parts the whole is divided into. Understanding denominators is crucial when working with equivalent fractions. Equivalent fractions have different numerators and denominators, but they represent the same quantity or proportion.
To find equivalent fractions, it's often necessary to change the denominator to a desired value, like in the exercise where 9 was changed to 36. Knowing how to adjust the denominator while keeping the fraction's value the same is key to mastering fractions!
Scale Factor
The scale factor is a number we use to ensure our fraction鈥檚 value remains unchanged when adjusting the denominator. To find the scale factor, divide the new denominator by the old one. In the given problem, we needed to change 9 to 36. Thus, our scale factor was calculated as:
  • New denominator: 36
  • Old denominator: 9
  • Scale factor: \( \frac{36}{9} = 4\)
With the scale factor identified as 4, it's applied to both the numerator and denominator. This action guarantees that changing the fraction鈥檚 form doesn't alter its value.
Numerator Transformation
To create an equivalent fraction while maintaining the correct proportion, we transform the numerator using the scale factor. The numerator is the top number in a fraction and tells us how many parts we have. In the example, the original fraction is \(\frac{4}{9}\).
To find the equivalent numerator:
  • Original numerator: 4
  • Scale factor: 4
  • New numerator: \(4 \times 4 = 16\)
The transformation is simple but vital, ensuring the fraction鈥檚 value remains equivalent even as its form changes.
Fraction Multiplication
Multiplying fractions involves multiplying the numerators and denominators separately. This process is fundamental when finding equivalent fractions. By multiplying both parts of the fraction by the same scale factor, we create a new fraction that looks different but has the same value.
For example, in the problem, we used our scale factor on \(\frac{4}{9}\) to get:
  • Numerator: \(4 \times 4 = 16\)
  • Denominator: \(9 \times 4 = 36\)
  • Equivalent fraction: \(\frac{16}{36}\)
This technique ensures we're adjusting our fraction correctly, preserving its original value in a new form.

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 172 to \(177,\) insert \(+,-, \times,\) or \(\div\) into the square so that the statement is true. $$0.064 \square 1.6=0.1024$$

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{3}{10} \frac{7}{25}$$

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$\frac{3}{8}$$

Convert the fraction to a decimal. Place a bar over repeating digits of a repeating decimal. $$\frac{8}{11}$$

The tax per gallon of gasoline in California is \(\$ .466 .\) (Source: Tax Foundation) If you fill your gasoline tank with 12.5 gal of gasoline in California, how much will you pay in taxes?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.