/*! 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 52 Determine whether each pair of f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 52

Determine whether each pair of fractions is equivalent. \(\frac{3}{6}\) and \(\frac{5}{10}\)

Short Answer

Expert verified
The pairs of fractions \(\frac{3}{6}\) and \(\frac{5}{10}\) are equivalent.

Step by step solution

01

Simplify the First Fraction

To determine if two fractions are equivalent, we first simplify each fraction. Let's start with \( \frac{3}{6} \). To simplify, find the greatest common divisor (GCD) of 3 and 6, which is 3. Divide both the numerator and the denominator by 3: \( \frac{3}{6} = \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \).
02

Simplify the Second Fraction

Now we simplify \( \frac{5}{10} \). Find the GCD of 5 and 10, which is 5. Then, divide both the numerator and the denominator by 5: \( \frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \).
03

Compare the Simplified Fractions

Now that we have simplified both fractions, \( \frac{3}{6} = \frac{1}{2} \) and \( \frac{5}{10} = \frac{1}{2} \). Since they are both \( \frac{1}{2} \), the original fractions are equivalent.

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 means making them as simple as possible. The idea is to turn a fraction into its smallest form without changing its value. For example, simplifying \( \frac{3}{6} \) involves reducing it to \( \frac{1}{2} \). This is done by dividing the top number (numerator) and the bottom number (denominator) by the same number.

The number we divide by is called the Greatest Common Divisor (GCD). This is the biggest number that can be evenly divided into both the numerator and the denominator.
  • Example: The GCD of 3 and 6 is 3.
  • So, \( \frac{3}{6} \) simplified is \( \frac{3 \div 3}{6 \div 3} = \frac{1}{2} \).
Simplifying helps in comparing fractions and understanding their equivalence.
Greatest Common Divisor
Understanding the greatest common divisor (GCD) is key to simplifying fractions. The GCD of two numbers is the biggest number that divides both without leaving a remainder. Finding the GCD involves listing the factors of each number, then identifying the largest factor common to both.

For example, to find the GCD of 5 and 10:
  • List the factors of 5: 1, 5
  • List the factors of 10: 1, 2, 5, 10
  • The common factors are 1 and 5.
  • The greatest common factor is 5.
Knowing the GCD helps simplify fractions, making it easier to compare and identify equivalent fractions.
Comparing Fractions
When comparing fractions, it's important to determine if they represent the same value, that is, if they are equivalent. One way to do this is to simplify the fractions and see if the resulting fractions are the same.

Take \( \frac{3}{6} \) and \( \frac{5}{10} \) as examples:
  • Simplify \( \frac{3}{6} \) to \( \frac{1}{2} \).
  • Simplify \( \frac{5}{10} \) to \( \frac{1}{2} \).
Since both simplified fractions are \( \frac{1}{2} \), the original fractions are equivalent.

By simplifying fractions before comparing them, we can quickly and easily determine if they are equal.

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

Use the following numbers: \(\begin{array}{llllllll}8691 & 786 & 1235 & 2235 & 85 & 105 & 22 & 222 & 900 & 1470\end{array}\); List the numbers that are divisible by both 3 and 5.

Write each improper fraction as a mixed number or a whole number. See Example 21. $$\frac{17}{5}$$

Perform the indicated operations. $$ -31 \frac{7}{8}-\left(-26 \frac{5}{12}\right) $$

Write each improper fraction as a mixed number or a whole number. See Example 21. $$\frac{182}{175}$$

Answer true or false for each statement. The sum of two negative fractions is always a negative number.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

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.