Multiply. Write Your Answer As A Fraction In Simplest Form.$\frac{7}{11} \times \frac{5}{3}$

by ADMIN 93 views

=====================================================

Introduction

When it comes to multiplying fractions, it's essential to understand the concept of simplifying the product. In this article, we will delve into the world of fractions and explore how to multiply two fractions, specifically 711×53\frac{7}{11} \times \frac{5}{3}. We will break down the process step by step, providing a clear understanding of the concept and its application.

Understanding Fractions

A fraction is a way to represent a part of a whole. It consists of two parts: the numerator (the number on top) and the denominator (the number on the bottom). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

For example, in the fraction 711\frac{7}{11}, the numerator is 7, and the denominator is 11. This means we have 7 equal parts out of a total of 11 parts.

Multiplying Fractions

To multiply two fractions, we simply multiply the numerators together and multiply the denominators together. This is a fundamental concept in mathematics, and it's essential to understand it to simplify the product of two fractions.

Let's take the example of 711×53\frac{7}{11} \times \frac{5}{3}. To multiply these fractions, we multiply the numerators (7 and 5) together and multiply the denominators (11 and 3) together.

Step-by-Step Solution

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply 7 and 5 together.

7 × 5 = 35

Step 2: Multiply the Denominators

To multiply the denominators, we simply multiply 11 and 3 together.

11 × 3 = 33

Step 3: Write the Product as a Fraction

Now that we have multiplied the numerators and denominators, we can write the product as a fraction.

7×511×3=3533\frac{7 \times 5}{11 \times 3} = \frac{35}{33}

Simplifying the Product

The product of the two fractions is 3533\frac{35}{33}. However, this fraction can be simplified further. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.

Finding the GCD

To find the GCD of 35 and 33, we can use the Euclidean algorithm or simply list the factors of each number.

Factors of 35: 1, 5, 7, 35 Factors of 33: 1, 3, 11, 33

The greatest common divisor of 35 and 33 is 1. Since the GCD is 1, the fraction 3533\frac{35}{33} is already in its simplest form.

Conclusion

In conclusion, multiplying two fractions involves multiplying the numerators together and multiplying the denominators together. The product of the two fractions can be simplified further by finding the greatest common divisor of the numerator and denominator. In this article, we have explored the concept of multiplying fractions and simplified the product of 711×53\frac{7}{11} \times \frac{5}{3}.

Final Answer

The final answer is 3533\boxed{\frac{35}{33}}.

=====================================================

Introduction

In our previous article, we explored the concept of multiplying fractions and simplified the product of 711×53\frac{7}{11} \times \frac{5}{3}. However, we understand that there may be many questions and doubts that readers may have. In this article, we will address some of the most frequently asked questions on the topic of multiplying fractions and simplifying the product.

Q&A

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators together and multiply the denominators together. This will give you the product of the two fractions.

Q: How do I simplify the product of two fractions?

A: To simplify the product of two fractions, you need to find the greatest common divisor (GCD) of the numerator and denominator. Once you have found the GCD, you can divide both the numerator and denominator by the GCD to simplify the fraction.

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. You can find the GCD by listing the factors of each number or using the Euclidean algorithm.

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

A: There are several ways to find the GCD of two numbers. You can list the factors of each number and find the largest common factor, or you can use the Euclidean algorithm. The Euclidean algorithm involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero.

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

A: Multiplying fractions involves multiplying the numerators together and multiplying the denominators together, while adding fractions involves adding the numerators together and keeping the same denominator.

Q: Can I multiply a fraction by a whole number?

A: Yes, you can multiply a fraction by a whole number. To do this, you simply multiply the numerator of the fraction by the whole number and keep the same denominator.

Q: How do I multiply a fraction by a decimal?

A: To multiply a fraction by a decimal, you need to convert the decimal to a fraction first. Once you have converted the decimal to a fraction, you can multiply the fraction by the fraction.

Q: What is the final answer to the problem 711×53\frac{7}{11} \times \frac{5}{3}?

A: The final answer to the problem 711×53\frac{7}{11} \times \frac{5}{3} is 3533\boxed{\frac{35}{33}}.

Conclusion

In conclusion, multiplying fractions involves multiplying the numerators together and multiplying the denominators together. The product of the two fractions can be simplified further by finding the greatest common divisor of the numerator and denominator. We hope that this Q&A article has addressed some of the most frequently asked questions on the topic of multiplying fractions and simplifying the product.

Final Tips

  • Always multiply the numerators together and multiply the denominators together when multiplying fractions.
  • Find the greatest common divisor of the numerator and denominator to simplify the fraction.
  • Use the Euclidean algorithm or list the factors of each number to find the GCD.
  • Convert decimals to fractions before multiplying fractions.

Additional Resources

  • Khan Academy: Multiplying Fractions
  • Mathway: Multiplying Fractions
  • Wolfram Alpha: Multiplying Fractions

We hope that this article has been helpful in addressing some of the most frequently asked questions on the topic of multiplying fractions and simplifying the product. If you have any further questions or doubts, please don't hesitate to contact us.