How To Solve 1/8 Divided By 3/4: A Simple Guide
Table of Contents :
To solve the mathematical expression ( \frac{1}{8} \div \frac{3}{4} ), you can follow a simple series of steps that will help you understand the division of fractions. Let's break down the process in an easy-to-follow manner!
Understanding Division of Fractions
When you divide by a fraction, it can be a bit confusing at first. However, the key to solving it is to multiply by the reciprocal of the fraction you are dividing by.
What is a Reciprocal?
The reciprocal of a fraction is simply flipping the numerator and the denominator. For example, the reciprocal of ( \frac{3}{4} ) is ( \frac{4}{3} ).
The Steps to Solve ( \frac{1}{8} \div \frac{3}{4} )
Step 1: Write the Problem
You start with the expression: [ \frac{1}{8} \div \frac{3}{4} ]
Step 2: Multiply by the Reciprocal
Instead of dividing, you will multiply by the reciprocal of ( \frac{3}{4} ): [ \frac{1}{8} \times \frac{4}{3} ]
Step 3: Multiply the Fractions
Now, multiply the numerators and the denominators: [ \text{Numerator: } 1 \times 4 = 4 ] [ \text{Denominator: } 8 \times 3 = 24 ] This gives you: [ \frac{4}{24} ]
Step 4: Simplify the Fraction
To simplify ( \frac{4}{24} ), find the greatest common divisor (GCD) of 4 and 24, which is 4: [ \frac{4 \div 4}{24 \div 4} = \frac{1}{6} ]
Final Result
Thus, the result of ( \frac{1}{8} \div \frac{3}{4} ) is: [ \frac{1}{6} ]
Quick Reference Table
Here’s a quick reference table summarizing the steps to solve any division of fractions:
<table> <tr> <th>Step</th> <th>Description</th> </tr> <tr> <td>1</td> <td>Write the original expression.</td> </tr> <tr> <td>2</td> <td>Multiply by the reciprocal of the second fraction.</td> </tr> <tr> <td>3</td> <td>Multiply the numerators together and the denominators together.</td> </tr> <tr> <td>4</td> <td>Simplify the resulting fraction if possible.</td> </tr> </table>
Important Notes
Remember, when dividing fractions, always multiply by the reciprocal to make the process much easier! 📐✨
Common Mistakes to Avoid
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Forgetting the Reciprocal: Many people forget to flip the second fraction and end up dividing incorrectly. Always take a moment to remind yourself to find the reciprocal first!
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Not Simplifying: After performing the operations, some may forget to simplify the final fraction, which is crucial for clarity and correctness.
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Confusion with Mixed Numbers: If you ever come across mixed numbers, convert them to improper fractions before applying the division process.
Practice Problems
To solidify your understanding, try solving these problems using the steps outlined above:
- ( \frac{2}{3} \div \frac{1}{6} )
- ( \frac{5}{8} \div \frac{3}{5} )
- ( \frac{7}{10} \div \frac{2}{3} )
Solutions
- ( \frac{2}{3} \div \frac{1}{6} = \frac{4}{1} = 4 )
- ( \frac{5}{8} \div \frac{3}{5} = \frac{25}{24} )
- ( \frac{7}{10} \div \frac{2}{3} = \frac{21}{20} )
By practicing with these problems, you can enhance your skills in handling fraction division effortlessly!
Understanding how to solve problems like ( \frac{1}{8} \div \frac{3}{4} ) empowers you to tackle more complex mathematical challenges. With a firm grasp of this division process, fractions will no longer seem daunting, and you'll be ready to approach any division problem with confidence! 🧠💪