Divide $7 / 24$ By $35 / 48$ And Reduce The Quotient To The Lowest Fraction.A) \$42 / 48$[/tex\] B) $2 / 5$ C) $4 / 10$ D) \$245 / 1152$[/tex\]
Introduction
In mathematics, division is a fundamental operation that allows us to find the quotient of two numbers. When dealing with fractions, division can be a bit more complex, but with the right approach, we can simplify even the most daunting expressions. In this article, we will explore how to divide fractions, with a focus on the specific problem of dividing $7 / 24$ by $35 / 48$ and reducing the quotient to its lowest fraction.
Understanding Division of Fractions
Before we dive into the problem at hand, let's take a step back and understand the basics of dividing fractions. When we divide one fraction by another, we are essentially asking what part of the first fraction is equal to the second fraction. To do this, we can use the following approach:
- Invert the second fraction: This means flipping the second fraction upside down, so that the numerator becomes the denominator and vice versa.
- Multiply the fractions: We then multiply the first fraction by the inverted second fraction.
- Simplify the result: Finally, we simplify the resulting fraction to its lowest terms.
Dividing $7 / 24$ by $35 / 48$
Now that we have a solid understanding of how to divide fractions, let's apply this approach to our problem. We want to divide $7 / 24$ by $35 / 48$.
Step 1: Invert the Second Fraction
To start, we need to invert the second fraction, which means flipping the numerator and denominator. So, $35 / 48$ becomes $48 / 35$.
Step 2: Multiply the Fractions
Next, we multiply the first fraction by the inverted second fraction:
To multiply fractions, we simply multiply the numerators together and the denominators together:
Step 3: Simplify the Result
Now, we simplify the resulting fraction to its lowest terms. To do this, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.
The GCD of 336 and 840 is 168. So, we divide both numbers by 168:
Conclusion
And there you have it! By following the steps outlined above, we have successfully divided $7 / 24$ by $35 / 48$ and reduced the quotient to its lowest fraction: $\frac{2}{5}$.
Comparison of Options
Now that we have the correct answer, let's take a look at the options provided:
- A) $42 / 48$: This is not the correct answer.
- B) $2 / 5$: This is the correct answer!
- C) $4 / 10$: This is not the correct answer.
- D) $245 / 1152$: This is not the correct answer.
Final Thoughts
Dividing fractions can seem intimidating at first, but with the right approach, it's a breeze. By following the steps outlined above, you can simplify even the most complex fraction divisions. Remember to invert the second fraction, multiply the fractions, and simplify the result to its lowest terms. Happy calculating!
Additional Resources
If you're looking for more practice problems or want to learn more about fractions, here are some additional resources:
- Khan Academy: Fractions
- Mathway: Fraction Division
- IXL: Fractions
FAQs
- Q: What is the difference between dividing fractions and multiplying fractions? A: When dividing fractions, we invert the second fraction and multiply the fractions. When multiplying fractions, we simply multiply the numerators together and the denominators together.
- Q: How do I simplify a fraction to its lowest terms?
A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.
Frequently Asked Questions: Dividing Fractions =====================================================
Introduction
Dividing fractions can be a bit tricky, but with the right approach, it's a breeze. In this article, we'll answer some of the most frequently asked questions about dividing fractions, including how to invert fractions, multiply fractions, and simplify results.
Q&A
Q: What is the difference between dividing fractions and multiplying fractions?
A: When dividing fractions, we invert the second fraction and multiply the fractions. When multiplying fractions, we simply multiply the numerators together and the denominators together.
Q: How do I invert a fraction?
A: To invert a fraction, we simply flip the numerator and denominator. For example, if we have the fraction $\frac{3}{4}$, the inverted fraction would be $\frac{4}{3}$.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that divides both the numerator and denominator of a fraction without leaving a remainder. For example, the GCD of 12 and 18 is 6.
Q: How do I simplify a fraction to its lowest terms?
A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD. For example, if we have the fraction $\frac{12}{18}$, the GCD is 6. Dividing both numbers by 6, we get $\frac{2}{3}$.
Q: What is the difference between a proper fraction and an improper fraction?
A: A proper fraction is a fraction where the numerator is less than the denominator. For example, $\frac{1}{2}$ is a proper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $\frac{3}{2}$ is an improper fraction.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as an improper fraction. For example, if we have the mixed number $2\frac{1}{2}$, we can convert it to an improper fraction by multiplying 2 by 2 and adding 1, which gives us $5$.
Q: What is the difference between a fraction and a decimal?
A: A fraction is a way of expressing a part of a whole as a ratio of two numbers. A decimal is a way of expressing a fraction as a number with a point separating the whole number part from the fractional part. For example, the fraction $\frac{1}{2}$ is equivalent to the decimal 0.5.
Q: How do I convert a fraction to a decimal?
A: To convert a fraction to a decimal, divide the numerator by the denominator. For example, if we have the fraction $\frac{1}{2}$, we can convert it to a decimal by dividing 1 by 2, which gives us 0.5.
Conclusion
Dividing fractions can be a bit tricky, but with the right approach, it's a breeze. By understanding the basics of inverting fractions, multiplying fractions, and simplifying results, you can tackle even the most complex fraction divisions. Remember to invert the second fraction, multiply the fractions, and simplify the result to its lowest terms. Happy calculating!
Additional Resources
If you're looking for more practice problems or want to learn more about fractions, here are some additional resources:
- Khan Academy: Fractions
- Mathway: Fraction Division
- IXL: Fractions
Final Thoughts
Dividing fractions is an essential skill that can be applied to a wide range of mathematical problems. By mastering the basics of inverting fractions, multiplying fractions, and simplifying results, you can tackle even the most complex fraction divisions with confidence. Remember to practice regularly and seek help when needed. Happy calculating!