Divide And Write Your Answer In Simplest Form. 5 3 ÷ 3 \frac{5}{3} \div 3 3 5 ​ ÷ 3

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Introduction

In mathematics, division is a fundamental operation that involves sharing a certain quantity into equal parts or groups. When we divide a fraction by a number, we are essentially finding how many times the number fits into the fraction. In this article, we will explore the concept of dividing a fraction by a number and provide a step-by-step guide on how to simplify the result.

Understanding the Concept of Division

Division is the inverse operation of multiplication. When we divide a number by another number, we are essentially asking how many times the second number fits into the first number. In the case of fractions, division involves finding the reciprocal of the second number and multiplying it by the first fraction.

Dividing a Fraction by a Number: A Step-by-Step Guide

To divide a fraction by a number, we can follow these steps:

  1. Find the Reciprocal: The first step is to find the reciprocal of the number by which we are dividing. The reciprocal of a number is obtained by swapping its numerator and denominator.
  2. Multiply the Fraction: Once we have the reciprocal, we multiply it by the original fraction.
  3. Simplify the Result: Finally, we simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD).

Applying the Steps to the Given Problem

Now, let's apply these steps to the given problem: 53÷3\frac{5}{3} \div 3.

Step 1: Find the Reciprocal

The reciprocal of 3 is 13\frac{1}{3}.

Step 2: Multiply the Fraction

We multiply the original fraction 53\frac{5}{3} by the reciprocal 13\frac{1}{3}:

53×13=5×13×3=59\frac{5}{3} \times \frac{1}{3} = \frac{5 \times 1}{3 \times 3} = \frac{5}{9}

Step 3: Simplify the Result

The result 59\frac{5}{9} is already in its simplest form, so we don't need to simplify it further.

Conclusion

In conclusion, dividing a fraction by a number involves finding the reciprocal of the number, multiplying it by the original fraction, and simplifying the result. By following these steps, we can simplify complex division problems involving fractions. In this article, we applied these steps to the given problem 53÷3\frac{5}{3} \div 3 and obtained the result 59\frac{5}{9}.

Frequently Asked Questions

  • What is the reciprocal of a number? The reciprocal of a number is obtained by swapping its numerator and denominator.
  • How do I simplify a fraction? To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
  • What is the difference between division and multiplication? Division is the inverse operation of multiplication. When we divide a number by another number, we are essentially asking how many times the second number fits into the first number.

Final Answer

The final answer to the problem 53÷3\frac{5}{3} \div 3 is 59\boxed{\frac{5}{9}}.

Introduction

Dividing fractions can be a challenging concept for many students. However, with a clear understanding of the steps involved, it can be a straightforward process. In this article, we will address some of the most frequently asked questions about dividing fractions, providing step-by-step explanations and examples to help clarify the concepts.

Q&A: Dividing Fractions

Q1: What is the reciprocal of a number?

A1: The reciprocal of a number is obtained by swapping its numerator and denominator. For example, the reciprocal of 3 is 13\frac{1}{3}, and the reciprocal of 52\frac{5}{2} is 25\frac{2}{5}.

Q2: How do I simplify a fraction?

A2: To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify 68\frac{6}{8}, we can divide both the numerator and denominator by 2, resulting in 34\frac{3}{4}.

Q3: What is the difference between division and multiplication?

A3: Division is the inverse operation of multiplication. When we divide a number by another number, we are essentially asking how many times the second number fits into the first number. For example, 12 ÷ 3 = 4, because 3 fits into 12 four times.

Q4: How do I divide a fraction by a number?

A4: To divide a fraction by a number, we can follow these steps:

  1. Find the reciprocal of the number by which we are dividing.
  2. Multiply the original fraction by the reciprocal.
  3. Simplify the result by dividing both the numerator and denominator by their GCD.

Q5: What is the result of dividing 53\frac{5}{3} by 3?

A5: To divide 53\frac{5}{3} by 3, we can follow the steps outlined above:

  1. Find the reciprocal of 3, which is 13\frac{1}{3}.
  2. Multiply 53\frac{5}{3} by 13\frac{1}{3}, resulting in 59\frac{5}{9}.
  3. Simplify the result, which is already in its simplest form.

Q6: How do I divide a fraction by a fraction?

A6: To divide a fraction by a fraction, we can follow these steps:

  1. Find the reciprocal of the second fraction.
  2. Multiply the first fraction by the reciprocal of the second fraction.
  3. Simplify the result by dividing both the numerator and denominator by their GCD.

Q7: What is the result of dividing 23\frac{2}{3} by 34\frac{3}{4}?

A7: To divide 23\frac{2}{3} by 34\frac{3}{4}, we can follow the steps outlined above:

  1. Find the reciprocal of 34\frac{3}{4}, which is 43\frac{4}{3}.
  2. Multiply 23\frac{2}{3} by 43\frac{4}{3}, resulting in 89\frac{8}{9}.
  3. Simplify the result, which is already in its simplest form.

Conclusion

Dividing fractions can be a challenging concept, but with a clear understanding of the steps involved, it can be a straightforward process. By following the steps outlined in this article, you can simplify complex division problems involving fractions. Remember to find the reciprocal of the number or fraction by which you are dividing, multiply the original fraction by the reciprocal, and simplify the result by dividing both the numerator and denominator by their GCD.

Final Tips

  • Always find the reciprocal of the number or fraction by which you are dividing.
  • Multiply the original fraction by the reciprocal.
  • Simplify the result by dividing both the numerator and denominator by their GCD.
  • Practice, practice, practice! The more you practice dividing fractions, the more comfortable you will become with the process.

Frequently Asked Questions: Dividing Fractions

  • What is the reciprocal of a number? The reciprocal of a number is obtained by swapping its numerator and denominator.
  • How do I simplify a fraction? To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
  • What is the difference between division and multiplication? Division is the inverse operation of multiplication. When we divide a number by another number, we are essentially asking how many times the second number fits into the first number.