/*! 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 624 In the following exercises, add.... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 624

In the following exercises, add. $$\frac{15}{32}+\frac{9}{32}$$

Short Answer

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

Step by step solution

01

Identify the Denominators

Both fractions have the same denominator, which is 32. This means they can be added directly.
02

Add the Numerators

Since the denominators are the same, add the numerators: 15 + 9. This gives 24.
03

Write the New Fraction

The fraction formed by adding the numerators is \(\frac{24}{32}\).
04

Simplify the Fraction

Simplify \(\frac{24}{32}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 8: \(\frac{24 \div 8}{32 \div 8} = \frac{3}{4} \).

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, it is crucial to have a common denominator. The denominator is the bottom number of a fraction, representing the total number of equal parts. A common denominator is a shared multiple of the denominators of the fractions being added. In the example \(\frac{15}{32} + \frac{9}{32}\), both fractions already have the same denominator, which is 32. This simplifies the addition process because you can directly add the numerators (top numbers) while keeping the denominator the same. When working with fractions that do not have a common denominator, you'll need to find one, either through multiplying the denominators or finding the least common multiple (LCM).
Simplifying Fractions
Simplifying fractions makes them easier to understand and work with. Simplifying involves reducing the fraction to its simplest form, where the numerator and denominator are as small as possible. This is done by dividing both the numerator and the denominator by their greatest common divisor (GCD). In the example, after combining the fractions \(\frac{15}{32} + \frac{9}{32} = \frac{24}{32}\), we simplified \(\frac{24}{32}\) by dividing both the numerator (24) and denominator (32) by their GCD (8). This resulted in \(\frac{3}{4}\). A simplified fraction is always preferred because it is the most concise and clear representation of the value.
Greatest Common Divisor (GCD)
The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD helps in simplifying fractions. For example, in \(\frac{24}{32}\), we want to find the GCD of 24 and 32. We can find the GCD by listing the factors of each number:
  • Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  • Factors of 32: 1, 2, 4, 8, 16, 32
The common factors are 1, 2, 4, and 8. The greatest one is 8, so the GCD is 8. By dividing both 24 and 32 by 8, we simplify \(\frac{24}{32}\) to \(\frac{3}{4}\). Understanding how to find the GCD is vital for simplifying fractions efficiently.

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

In the following exercises, simplify. $$ \frac{9^{2}-4^{2}}{9-4} $$

In the following exercises, perform the indicated operation. $$ 3 \frac{5}{8}+3 \frac{7}{8} $$

In the following exercises, translate and solve. Three-eighths of \(y\) is 24

In the following exercises, perform the indicated operations and simplify. $$\frac{4}{11} \div \frac{2}{7 d}$$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(\frac{u+v}{w}\) when \(u=-4, v=-8, w=2\)
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Pure Maths

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.