/*! 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 61 For exercises \(23-74\), evaluat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 61

For exercises \(23-74\), evaluate. $$ \frac{3}{10}+\frac{5}{10} $$

Short Answer

Expert verified
\frac{4}{5}

Step by step solution

01

Identify Common Denominator

Both fractions \(\frac{3}{10}\) and \(\frac{5}{10}\) have the same denominator which is 10.
02

Add the Numerators

Since the denominators are the same, add the numerators directly: \(\frac{3+5}{10}\)
03

Simplify the Fraction

Perform the addition in the numerator: \(\frac{8}{10}\). This can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2: \(\frac{8梅2}{10梅2}=\frac{4}{5}\)

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 dealing with the addition of fractions, the first step is to ensure they have a common denominator. The denominator is the number at the bottom of the fraction. It represents how many total parts the whole is divided into.
If fractions have the same denominator, they can be easily added or subtracted. For example, in our exercise \( \frac{3}{10} \) and \( \frac{5}{10} \) both have the denominator 10.
This means we can add them directly. Always look for a common denominator when working with fractions for seamless addition or subtraction.
Numerator
The numerator is the number at the top of the fraction. It shows how many parts we have out of the whole represented by the denominator. In our case, we have two numerators: 3 and 5 from the fractions \( \frac{3}{10} \) and \( \frac{5}{10} \) respectively.
When the denominators are the same, you simply add the numerators together. Here we get: \[ \frac{3 + 5}{10} = \frac{8}{10} \].
Therefore, understanding numerators helps in correctly adding the parts represented by each individual fraction.
Simplifying Fractions
After adding fractions, the next step is often simplifying the result. Simplifying a fraction means making it as simple as possible without changing its value. This can involve dividing the numerator and the denominator by the same number.
As in our problem, we obtained \( \frac{8}{10} \). To simplify, we look for the greatest common divisor (GCD) of 8 and 10, which is 2. Then, we divide both the numerator and the denominator by their GCD: \[ \frac{8 \div 2}{10 \div 2} = \frac{4}{5} \]
This results in the simplest form of the fraction.
Greatest Common Divisor
The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. This is crucial when simplifying fractions.
Finding the GCD starts with identifying all the common divisors of both numbers. For 8 and 10, the divisors are:
  • 8: 1, 2, 4, 8
  • 10: 1, 2, 5, 10
Here, the largest common divisor is 2. We then use it to simplify the fraction by dividing both the numerator and the denominator by this number: \[ \frac{8\div 2}{10\div 2} = \frac{4}{5} \].
Knowing how to find the GCD makes working with fractions much easier and conversion cleaner.

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

$$ \text { Find } 2.5 \% \text { of } 30 \text {. } $$

$$ \text { Round } 461 \text { to the nearest ten. } $$

For exercises \(85-108\), write \(>\) or \(<\) between the numbers to make a true statement. $$ \frac{3}{11} \quad \frac{2}{7} $$

For exercises 115-118, evaluate. On a scientific calculator, use the fraction key. For graphing calculators, use the Frac command to rewrite the decimal answer as a fraction. $$ \frac{5}{34}-\frac{8}{21} $$

For exercises 115-118, evaluate. On a scientific calculator, use the fraction key. For graphing calculators, use the Frac command to rewrite the decimal answer as a fraction. $$ \frac{5}{34} \div \frac{8}{21} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.