/*! 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 35 Simplify. $$ \frac{14}{21} ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 35

Simplify. $$ \frac{14}{21} $$

Short Answer

Expert verified
The simplified form is \( \frac{2}{3} \).

Step by step solution

01

Identify the Greatest Common Divisor (GCD)

To simplify the fraction \( \frac{14}{21} \), first identify the greatest common divisor (GCD) of the numerator (14) and the denominator (21). The GCD of 14 and 21 is 7.
02

Divide the Numerator and Denominator by the GCD

Divide the numerator (14) and the denominator (21) by their GCD (7). This gives: \( \frac{14 梅 7}{21 梅 7} = \frac{2}{3} \).
03

Write Down the Simplified Form

After dividing by the GCD, the simplified form of the fraction \( \frac{14}{21} \) is \( \frac{2}{3} \).

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.

greatest common divisor
Simplifying fractions involves breaking them down to their simplest form. One of the critical steps in this process is identifying the Greatest Common Divisor (GCD). The GCD is the largest number that can divide both the numerator and the denominator without leaving a remainder.
In the given example, the fraction is \( \frac{14}{21} \). To simplify it, we need to find the GCD of 14 and 21. You can do this by listing the factors of each number:
  • Factors of 14: 1, 2, 7, 14
  • Factors of 21: 1, 3, 7, 21
The common factors are 1 and 7. The greatest of these is 7, so the GCD of 14 and 21 is 7. Once we have the GCD, we can use it to simplify the fraction by dividing both the numerator and the denominator by the GCD.
numerator
The numerator is the top number of a fraction. It indicates how many parts of a whole are being considered. In our fraction \( \frac{14}{21} \), the numerator is 14.
When simplifying a fraction, the numerator is divided by the GCD. For example, dividing our numerator 14 by the GCD 7, we get:
\[ 14 \div 7 = 2 \] So, the new numerator for our simplified fraction is 2.
This step is essential for achieving a simplified fraction where both numbers are as small as possible, making it easier to understand and work with.
denominator
The denominator is the bottom number of a fraction. It tells us the total number of equal parts the whole is divided into. For the fraction \( \frac{14}{21} \), the denominator is 21.
Similar to the numerator, the denominator is also divided by the GCD during simplification. In our example, dividing the denominator 21 by the GCD 7, we get:
\[ 21 \div 7 = 3 \] So, the new denominator for our simplified fraction is 3.
This step completes the process of simplifying the fraction, so our final simplified fraction is \( \frac{2}{3} \). Simplifying fractions makes them easier to work with and understand, especially in more complex mathematical problems.

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

Simplify using a calculator. Round your answer to the nearest thousandth. $$ |13.5+8(-4.7)|^{3} $$

Simplify. $$ \frac{7^{2}-(-1)^{5}}{3-2 \cdot 3^{2}+5} $$

Find the area of a rectangle when the length is \(36 \mathrm{ft}\) and the width is 12 ft.

Simplify. $$ 9 t^{4}+7 t-5\left(9 t^{3}-2 t\right) $$

Evaluate using a calculator. $$ (t+4)^{2}-12 \div(19-17)+68, \text { for } t=5 $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Applied 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.