Select The Best Answer For The Question.14. Divide $\frac{7}{24}$ By $\frac{35}{48}$ And Reduce The Quotient To The Lowest Fraction.A. $\frac{245}{1152}$ B. $\frac{4}{10}$ C. $\frac{42}{48}$ D.

by ADMIN 197 views

Understanding the Problem

Dividing fractions can be a challenging task, but with the right approach, it can be simplified. In this article, we will explore how to divide fractions and reduce the quotient to its lowest form. We will use the given problem as an example to illustrate the process.

The Problem

We are given the task of dividing 724\frac{7}{24} by 3548\frac{35}{48} and reducing the quotient to its lowest fraction. We will examine each option and determine which one is the correct answer.

Step 1: Invert and Multiply

To divide fractions, we need to invert the second fraction and multiply. Inverting the second fraction means flipping the numerator and denominator. So, 3548\frac{35}{48} becomes 4835\frac{48}{35}. Now, we multiply the two fractions:

724×4835\frac{7}{24} \times \frac{48}{35}

Step 2: Multiply the Numerators and Denominators

To multiply fractions, we multiply the numerators and denominators separately. So, we get:

7×4824×35\frac{7 \times 48}{24 \times 35}

Step 3: Simplify the Fraction

Now, we simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 7 and 48 is 1, and the GCD of 24 and 35 is 1. So, we get:

7×4824×35=336840\frac{7 \times 48}{24 \times 35} = \frac{336}{840}

Step 4: Reduce the Fraction

To reduce the fraction, we divide both the numerator and denominator by their GCD. The GCD of 336 and 840 is 168. So, we get:

336840=336÷168840÷168=25\frac{336}{840} = \frac{336 \div 168}{840 \div 168} = \frac{2}{5}

The Correct Answer

The correct answer is 25\frac{2}{5}, which is equivalent to 410\frac{4}{10}. Therefore, the correct answer is:

B. 410\frac{4}{10}

Why the Other Options are Incorrect

Let's examine why the other options are incorrect:

  • Option A: 2451152\frac{245}{1152} is not the correct answer because it is not the result of dividing 724\frac{7}{24} by 3548\frac{35}{48}.
  • Option C: 4248\frac{42}{48} is not the correct answer because it is not the result of dividing 724\frac{7}{24} by 3548\frac{35}{48}.
  • Option D: There is no option D, so we can ignore it.

Conclusion

Frequently Asked Questions

Dividing fractions can be a challenging task, but with the right approach, it can be simplified. In this article, we will answer some frequently asked questions about dividing fractions.

Q: What is the rule for dividing fractions?

A: The rule for dividing fractions is to invert the second fraction and multiply. Inverting the second fraction means flipping the numerator and denominator.

Q: How do I invert a fraction?

A: To invert a fraction, you simply flip the numerator and denominator. For example, if you have the fraction ab\frac{a}{b}, the inverted fraction is ba\frac{b}{a}.

Q: What is the difference between dividing fractions and multiplying fractions?

A: Dividing fractions is the same as multiplying fractions by the reciprocal of the second fraction. In other words, dividing ab\frac{a}{b} by cd\frac{c}{d} is the same as multiplying ab\frac{a}{b} by dc\frac{d}{c}.

Q: How do I simplify a fraction after dividing?

A: To simplify a fraction after dividing, you need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: There are several ways to find the GCD of two numbers. One way is to list the factors of each number and find the largest factor that they have in common.

Q: What is the difference between reducing a fraction and simplifying a fraction?

A: Reducing a fraction means dividing both the numerator and denominator by their GCD, while simplifying a fraction means finding the simplest form of the fraction.

Q: How do I reduce a fraction?

A: To reduce a fraction, you need to find the GCD of the numerator and denominator and divide both by the GCD.

Q: What are some common mistakes to avoid when dividing fractions?

A: Some common mistakes to avoid when dividing fractions include:

  • Not inverting the second fraction
  • Not multiplying the fractions
  • Not simplifying the fraction after dividing
  • Not reducing the fraction to its simplest form

Conclusion

Dividing fractions can be a challenging task, but with the right approach, it can be simplified. By following the rules and guidelines outlined in this article, you can become more confident and proficient in dividing fractions. Remember to invert the second fraction, multiply the fractions, simplify the fraction after dividing, and reduce the fraction to its simplest form.