/*! 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 30 Add and simplify. $$ \frac{3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 30

Add and simplify. $$ \frac{3}{8}+\frac{1}{8}+\frac{2}{8} $$

Short Answer

Expert verified
\(\frac{3}{4}\)

Step by step solution

01

Identify Common Denominator

Observe that all fractions in the expression \(\frac{3}{8}+\frac{1}{8}+\frac{2}{8}\) have the same denominator, which is 8.
02

Add the Numerators

Since the denominators are the same, add the numerators directly: \(3 + 1 + 2 = 6\). So, the fraction becomes \(\frac{6}{8}\).
03

Simplify the Fraction

To simplify \(\frac{6}{8}\), find the greatest common divisor (GCD) of 6 and 8. The GCD of 6 and 8 is 2. Divide both the numerator and the denominator by 2: \(\frac{6 \div 2}{8 \div 2} = \frac{3}{4}\).

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
To add fractions, the denominators must be the same. The denominator is the bottom part of a fraction. In the expression \(\frac{3}{8} + \frac{1}{8} + \frac{2}{8}\), the number '8' is the common denominator for all the fractions. Having a common denominator means we can add the fractions directly, without needing to adjust them first. This simplifies the addition process considerably.
Numerator Addition
Once you have a common denominator, you can add the numerators together. The numerators are the top parts of the fractions. In this case: \(3 + 1 + 2 = 6\), resulting in the fraction \(\frac{6}{8}\). Working with a common denominator makes this step straightforward because you only need to focus on the numerators.
Fraction Simplification
After combining the numerators, it's time to simplify the fraction. Simplification means rewriting the fraction in its simplest form, where the numerator and denominator have no common factors, other than 1. For \(\frac{6}{8}\), we need to find the GCD and divide both the numerator and the denominator by it. This will give us the simplest possible fraction equivalent to \(\frac{6}{8}\).
Greatest Common Divisor
The Greatest Common Divisor (GCD) is the largest number that can evenly divide both the numerator and the denominator. For \(\frac{6}{8}\), we need to find the GCD of 6 and 8. We can list the factors of each and identify the largest one they share:
Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8
The GCD is 2, as it鈥檚 the highest number common to both.
We then divide both the numerator and the denominator by 2: \(\frac{6 \: 2}{8 \: 2} = \frac{3}{4}\). Now, \(\frac{3}{4}\) is in its simplest 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

Simplify. $$ \frac{\frac{3}{5}-\frac{1}{2}}{\frac{1}{2}-\frac{2}{5}} $$

A guitarist's band is booked for Friday and Saturday nights at a local club. The guitarist is part of a trio on Friday and part of a quintet on Saturday. Thus, the guitarist is paid one-third of one-half the weekend's pay for Friday and one-fifth of one-half the weekend's pay for Saturday. What fractional part of the band's pay did the guitarist receive for the weekend's work? If the band was paid \(\$ 1200\), how much did the guitarist receive?

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{7}{8} $$

Subtract and simplify. $$ \frac{11}{12}-\frac{2}{12} $$

Simplify. $$ \frac{\frac{7}{9}}{\frac{3}{9}} $$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

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.