/*! 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 29 Subtract and simplify. $$ \f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 29

Subtract and simplify. $$ \frac{5}{12}-\frac{3}{8} $$

Short Answer

Expert verified
The answer is \( \frac{1}{24} \).

Step by step solution

01

- Find a Common Denominator

Identify the least common denominator (LCD) for the fractions. The denominators are 12 and 8. The least common multiple (LCM) of 12 and 8 is 24.
02

- Convert Fractions to Equivalent Fractions with the LCD

Convert each fraction to an equivalent fraction with 24 as the denominator. \[ \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \ \frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24} \]
03

- Subtract the Numerators

Subtract the numerators of the equivalent fractions:\[ \frac{10}{24} - \frac{9}{24} = \frac{10 - 9}{24} = \frac{1}{24} \]
04

- Simplify the Fraction

Check if the fraction can be simplified further. Since 1 is the greatest common divisor of 1 and 24, the fraction \( \frac{1}{24} \) is already in its simplest form.

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 subtract fractions, they need to have the same denominator. This means making the bottom parts of the fractions equal. To do this, find the least common denominator (LCD). This is the smallest number that both denominators divide into evenly.
The given denominators are 12 and 8, and their least common multiple (LCM) is 24.
Finding a common denominator helps in comparing and calculating fractions more easily.
equivalent fractions
Once you have a common denominator, convert each fraction to an equivalent fraction. This preserves the value of the fractions while giving them the same denominator.
For example:
  • Convert \(\frac{5}{12}\) to \(\frac{10}{24}\) by multiplying both the numerator and the denominator by 2.
  • Convert \(\frac{3}{8}\) to \(\frac{9}{24}\) by multiplying both the numerator and the denominator by 3.
Equivalent fractions make subtraction straightforward since the denominators match.
numerator subtraction
After converting the fractions to have a common denominator, subtract the numerators. This involves only the top numbers of the fractions.
For example, with \(\frac{10}{24} - \frac{9}{24}\), subtract 9 from 10 to get 1.
So, \(\frac{10}{24} - \frac{9}{24} = \frac{1}{24}\).
This step is crucial to simplify the fraction math so that it鈥檚 easier to reach the solution accurately.
simplifying fractions
Finally, check if the resulting fraction can be simplified. Simplifying fractions means reducing them to their simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).
In our example, \(\frac{1}{24}\) is already simplified because the GCD of 1 and 24 is 1.
Simplifying helps to get the most concise form of the fraction, making it easier to understand and compare.

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

Estimate each of the following as \(0, \frac{1}{2},\) or 1 . $$ \frac{7}{15} $$

Simplify. $$ \frac{1}{2}-\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{3} $$

Simplify. $$ \frac{\frac{5}{18}}{1 \frac{2}{3}} $$

Simplify. $$ 10^{2}-\left[3 \cdot 2^{4} \div(10-2)+5 \cdot 2\right] \quad[1.9 \mathrm{~d}] $$

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

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Pure 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.