/*! 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 396 Simplify. $$ \frac{46}{4+4} ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 396

Simplify. $$ \frac{46}{4+4} $$

Short Answer

Expert verified
\( \frac{23}{4} \)

Step by step solution

01

Simplify the denominator

First, add the numbers in the denominator: \[ 4 + 4 = 8 \]
02

Rewrite the fraction with the simplified denominator

Replace the sum in the denominator: \[ \frac{46}{8} \]
03

Simplify the fraction

Divide both the numerator and the denominator by their greatest common divisor (GCD). Here, the GCD of 46 and 8 is 2, so divide both by 2: \[ \frac{46 \div 2}{8 \div 2} = \frac{23}{4} \]

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.

Simplifying Fractions
Simplifying fractions means making the fraction as simple as possible. In most cases, this means converting the fraction into a form where the numerator and denominator are as small as they can be, relatively prime to each other. This is also known as reducing the fraction.
To simplify a fraction, you can follow these steps:
  • Find the greatest common divisor (GCD) of both the numerator and the denominator.
  • Divide both the numerator and the denominator by their GCD.
For example, in the fraction \( \frac{46}{8} \), we found that the GCD of 46 and 8 is 2. Dividing both the numerator and the denominator by 2 gives us the simplified fraction \( \frac{23}{4} \). This process reduces the fraction to its simplest form.
Greatest Common Divisor
The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. Finding the GCD is important for simplifying fractions.
Here's a simple way to find the GCD using the Euclidean algorithm:
  • Divide the larger number by the smaller number.
  • Take the remainder and divide the smaller number by this remainder.
  • Repeat the process until the remainder is zero. The last non-zero remainder is the GCD.
For the fraction \( \frac{46}{8} \), you can use the Euclidean algorithm to find the GCD:
  • 46 divided by 8 is 5 with a remainder of 6.
  • 8 divided by 6 is 1 with a remainder of 2.
  • 6 divided by 2 is 3 with a remainder of 0.
So, the GCD of 46 and 8 is 2. Using the GCD, you can then simplify \( \frac{46}{8} \) to \( \frac{23}{4} \).
Addition in Fractions
In addition to simplifying fractions, it's essential to understand addition in fractions.
To add fractions, follow these steps:
  • Ensure the fractions have a common denominator. If not, find the least common multiple (LCM) of the denominators and convert the fractions.
  • Add the numerators while keeping the denominator the same.
  • Simplify the resulting fraction, if possible.
For example, consider \( \frac{1}{4} + \frac{1}{6} \). First, find the LCM of 4 and 6, which is 12.
Convert both fractions: \( \frac{1}{4} = \frac{3}{12} \) and \( \frac{1}{6} = \frac{2}{12} \).
Add the numerators: \( 3 + 2 = 5 \).
The result is \( \frac{5}{12} \).
Since 5 and 12 have no common divisor other than 1, \( \frac{5}{12} \) is already simplified.
Understanding how to add and simplify fractions is crucial in many areas of math, from basic arithmetic to advanced algebra.

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

What is the difference between the additive inverse and the multiplicative inverse of a number?

Simplify using the distributive property. $$ 7(3 n+9)-(4 n-13) $$

Helen bought a 24-pound turkey for her family's Thanksgiving dinner and wants to know what time to put the turkey in to the oven. She wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey: (a) First, by multiplying \(24 \cdot 20\) to find the total number of minutes and then multiplying the answer by \(\frac{1}{60}\) to convert minutes into hours. (b) Next, by multiplying \(24\left(20 \cdot \frac{1}{60}\right)\). (C) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \((24 \cdot 20) \frac{1}{60}, \quad\) and \(\quad(b),\) where you multiplied \(24\left(20 \cdot \frac{1}{60}\right),\) should be equal?

Convert the units. One stick of butter contains 91.6 grams of fat. Convert this to milligrams.

Convert the units. Crista will serve 20 cups of juice at her son's party. Convert the volume to gallons.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Probability and 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.