/*! 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 39 Find three fractions equivalent ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 39

Find three fractions equivalent to each given fraction. \(\frac{12}{54}\)

Short Answer

Expert verified
\(\frac{4}{18}\), \(\frac{6}{27}\), \(\frac{8}{36}\)

Step by step solution

01

- Simplify the Given Fraction

First, simplify the fraction \(\frac{12}{54}\). Find the greatest common divisor (GCD) of 12 and 54. The GCD is 6. Divide both the numerator and the denominator by this GCD to get the simplified fraction. \[ \frac{12 \div 6}{54 \div 6} = \frac{2}{9} \]
02

- Find the First Equivalent Fraction

Multiply both the numerator and the denominator of the simplified fraction \(\frac{2}{9}\) by 2 to get an equivalent fraction. \[ \frac{2 \cdot 2}{9 \cdot 2} = \frac{4}{18} \]
03

- Find the Second Equivalent Fraction

Multiply both the numerator and the denominator of the simplified fraction \(\frac{2}{9}\) by 3 to get another equivalent fraction. \[ \frac{2 \cdot 3}{9 \cdot 3} = \frac{6}{27} \]
04

- Find the Third Equivalent Fraction

Multiply both the numerator and the denominator of the simplified fraction \(\frac{2}{9}\) by 4 to get yet another equivalent fraction. \[ \frac{2 \cdot 4}{9 \cdot 4} = \frac{8}{36} \]

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.

simplifying fractions
Simplifying fractions is a crucial skill in math. It makes calculations easier and solutions clearer. To simplify a fraction, you reduce it to its simplest form by dividing both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). For instance, the fraction \(\frac{12}{54}\) simplifies to \(\frac{2}{9}\) by dividing both 12 and 54 by their GCD, which is 6.

A fraction in its simplest form has no common divisors other than 1 between the numerator and denominator. Simplifying helps when comparing fractions or finding equivalent ones.
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. To find the GCD of two numbers:
  • List the factors of each number.
  • Identify the common factors.
  • Choose the largest factor that both numbers share.

For example, to find the GCD of 12 and 54: The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The common factors are 1, 2, 3, and 6. Hence, their GCD is 6.
Using the GCD, you can simplify fractions efficiently.
multiplying fractions
Multiplying fractions involves multiplying both the numerators and the denominators. To create equivalent fractions, you multiply both parts of a fraction by the same number. This doesn't change the value of the fraction. For example, starting with \(\frac{2}{9}\), you can get:
  • \(\frac{2 \times 2}{9 \times 2} = \frac{4}{18} \)
  • \(\frac{2 \times 3}{9 \times 3} = \frac{6}{27} \)
  • \(\frac{2 \times 4}{9 \times 4} = \frac{8}{36} \)

The value remains the same, but the fractions look different. Multiplying fractions is useful for finding equivalents or adjusting fractions for comparison.

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

Tell which temperature is warmer. \(-5 \frac{1}{2}^{\circ} \mathrm{F}\) or \(-5 \frac{3}{4}^{\circ} \mathrm{F}\)

If the temperature goes up \(1 \frac{1}{4}^{\circ} \mathrm{F}\), it will be \(0^{\circ} \mathrm{F}\). What is the temperature now?

Tell whether segments of the given lengths could be joined to form a triangle. \(3,5,\) and 7

Economics Tell how much change you would get if you paid for each item with a \(\$ 5\) bill. a pack of PlanetQuest cards for \(\$ 2.23\)

If the temperature goes down \(33^{\circ} \mathrm{F}\), it will be \(-10^{\circ} \mathrm{F}\). What is the temperature now?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

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.