/*! 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 95 For exercises 95-97, evaluate. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Problem 95

For exercises 95-97, evaluate. $$ \frac{5}{21}+\frac{2}{21} $$

Short Answer

Expert verified
\frac{1}{3}

Step by step solution

01

Identify the fractions

Both fractions \(\frac{5}{21}\) and \(\frac{2}{21}\) share the same denominator, 21.
02

Add the numerators

Since the denominators are the same, add the numerators together: \(5 + 2 = 7.\)
03

Write the result as a single fraction

Combine the sum of the numerators over the common denominator: \(\frac{7}{21}\).
04

Simplify the fraction

Simplify \(\frac{7}{21}\) by dividing the numerator and the denominator by their greatest common divisor, which is 7: \(\frac{7 \div 7}{21 \div 7} = \frac{1}{3}\).

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.

common denominator
When adding fractions, it's crucial that the fractions you are adding have the same denominator. A common denominator is simply the shared bottom number of the fractions involved.
If the denominators are already the same, like in our example \(\frac{5}{21} + \frac{2}{21}\), you can easily proceed to the next step.
A shared denominator allows the fractions to be directly comparable and combinable.
If you encounter fractions with different denominators, you will first need to find a common denominator. This involves finding the least common multiple (LCM) of the denominators.
sum of numerators
Once you have a common denominator, adding the fractions becomes straightforward. You focus on the numerators, the numbers above the fraction line.
In our example, both fractions \(\frac{5}{21}\) and \(\frac{2}{21}\) share the same denominator, 21.
To add these fractions:
  • Add only the numerators: \(5 + 2 = 7\)
  • Keep the common denominator the same: 21
This gives us the fraction \(\frac{7}{21}\). By combining the numerators, we form a single new fraction that represents the sum of the two original fractions.
simplifying fractions
The final step in working with fractions often involves simplifying the result. A simplified fraction is one where the numerator and the denominator are as small as possible, with no common factors other than 1.
In our example, \(\frac{7}{21}\) can be simplified. To do this, you need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD is 7.
  • Divide the numerator and the denominator by their GCD: \(\frac{7 \div 7}{21 \div 7} = \frac{1}{3}\)
This gives us the simplified fraction \(\frac{1}{3}\).
Simplifying fractions allows for more straightforward results and often makes it easier to understand and use the fraction in further calculations.

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 a fixed length of household copper wire, the relationship of the cross- sectional area, \(x\), and the resistance, \(y\), is an inverse variation. When the cross-sectional area is \(3.14 \times 10^{-6} \mathrm{~m}^{2}\), the resistance is \(5.4 \times 10^{-3} \mathrm{ohm}\). a. Find the constant of proportionality, \(k\). Use scientific notation. Include the units of measurement. b. Write an equation that represents this relationship. c. Find the resistance when the cross-sectional area is \(2.05 \times 10^{-6} \mathrm{~m}^{2}\). Round the mantissa to the nearest tenth.

For exercises 43-58, (a) solve. (b) check. $$ \frac{2}{x}=0 $$

For exercises \(67-82\), use the five steps and a proportion. In 2010 , about \(2,465,940\) Americans died. Find the number of Americans who died without a will. Round to the nearest hundred. (Source: www.cdc.gov, Jan. 11, 2012) Seven out of ten Americans die without a will. (Source: extension.umd.edu)

Explain why the relationship of the number of square feet of carpet that need to be vacuumed, \(x\), and the amount of time it takes to vacuum the carpet, \(y\), is a direct variation.

MRI scans of women with the BRCA1 and BRCA2 genetic mutations that were positive for cancer were wrong five out of six times. (These results are "false positives.") If 1500 women with these mutations had MRI scans that indicated cancer, predict how many of these women did not have cancer. (Source: www.telegraph .co.uk, March 26, 2008)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Logic and Functions

Read Explanation

Statistics

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.