/*! 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 8 Subtract and simplify. $$ \f... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 8

Subtract and simplify. $$ \frac{1}{6}-\frac{1}{8} $$

Short Answer

Expert verified
\( \frac{1}{24} \)

Step by step solution

01

Find a Common Denominator

To subtract the fractions, a common denominator is needed. The denominators are 6 and 8. The least common multiple (LCM) of 6 and 8 is 24.
02

Convert Fractions to Common Denominator

Convert each fraction so they both have the common denominator of 24. For \( \frac{1}{6} \), multiply both the numerator and the denominator by 4: \(\frac{1 \times 4}{6 \times 4} = \frac{4}{24} \). For \( \frac{1}{8} \), multiply both the numerator and the denominator by 3: \(\frac{1 \times 3}{8 \times 3} = \frac{3}{24} \).
03

Subtract the Fractions

Now subtract the fractions with the common denominator: \(\frac{4}{24} - \frac{3}{24} = \frac{4 - 3}{24} = \frac{1}{24} \).
04

Simplify the Result

The fraction \( \frac{1}{24} \) is already in its simplest form.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Common Denominator
Having a common denominator makes it easier to add or subtract fractions. The denominator is the bottom number of a fraction, and to work with fractions together, they need the same denominator. For example, when subtracting \[ \frac{1}{6} - \frac{1}{8} \], you must convert both fractions to have the same denominator before you can do the subtraction. This is because it allows you to directly subtract the numerators (the top numbers) while keeping the same denominator.
Least Common Multiple
The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. To subtract fractions, you need to find the LCM of the denominators to create a common denominator. For the fractions \[ \frac{1}{6} \] and \[ \frac{1}{8} \], the LCM of 6 and 8 is 24 because:
  • 24 is a multiple of 6 and 8
  • It is the smallest such multiple

Once you have the LCM, you can adjust the fractions so they have the same denominator, allowing you to perform the subtraction easily.
Simplification of Fractions
Simplifying fractions means making them as simple as possible. When you get a result like \[ \frac{1}{24} \] from your subtraction, you need to check if it can be simplified. A fraction is simplified if the numerator (top number) and the denominator (bottom number) have no common factors other than 1. In the case of \[ \frac{1}{24} \], it is already simplified because 1 and 24 do not have any common factors other than 1.
It's important to always simplify your final answer, so it is in its simplest form.

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Most popular questions from this chapter

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?

Add and simplify. $$ \frac{15}{24}+\frac{7}{36}+\frac{91}{48} $$

Find the average of \(\frac{4}{5}, \frac{1}{2},\) and \(\frac{1}{10} .\)

Hiking the Appalachian Trail. Ellen camped and hiked for three consecutive days along a section of the Appalachian Trail. The distances she hiked on the three days were \(15 \frac{5}{32} \mathrm{mi}, 20 \frac{3}{16} \mathrm{mi}\), and \(12 \frac{7}{8} \mathrm{mi}\). Find the average of these distances.

Simplify. $$ \frac{4}{6} $$
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