Calculate The Product Of 3 11 × 66 \frac{3}{11} \times 66 11 3 ​ × 66 .

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Understanding the Problem

When dealing with multiplication involving fractions and whole numbers, it's essential to understand the concept of multiplying fractions by whole numbers. In this case, we're given the expression 311×66\frac{3}{11} \times 66. Our goal is to calculate the product of this expression.

Breaking Down the Problem

To solve this problem, we need to recall the rule for multiplying fractions by whole numbers. When multiplying a fraction by a whole number, we can simply multiply the numerator of the fraction by the whole number and keep the denominator the same.

Applying the Rule

Let's apply this rule to our given expression. We have 311×66\frac{3}{11} \times 66. To find the product, we'll multiply the numerator (3) by the whole number (66) and keep the denominator (11) the same.

Performing the Multiplication

Now, let's perform the multiplication:

311×66=3×6611\frac{3}{11} \times 66 = \frac{3 \times 66}{11}

Simplifying the Expression

To simplify the expression, we can multiply the numerator (3) by the whole number (66):

3×6611=19811\frac{3 \times 66}{11} = \frac{198}{11}

Reducing the Fraction

Now that we have the expression 19811\frac{198}{11}, we can simplify it further by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 198 and 11 is 11.

Calculating the GCD

To find the GCD of 198 and 11, we can use the Euclidean algorithm or simply list the factors of each number:

Factors of 198: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198 Factors of 11: 1, 11

Dividing the Numerator and Denominator

Now that we have the GCD, we can divide both the numerator and the denominator by 11:

19811=198÷1111÷11=181\frac{198}{11} = \frac{198 \div 11}{11 \div 11} = \frac{18}{1}

Final Answer

Therefore, the product of 311×66\frac{3}{11} \times 66 is 18\boxed{18}.

Conclusion

In this article, we've walked through the process of multiplying a fraction by a whole number. We've applied the rule for multiplying fractions by whole numbers, performed the multiplication, simplified the expression, and reduced the fraction to its simplest form. By following these steps, we've arrived at the final answer of 18\boxed{18}.

Real-World Applications

Multiplying fractions by whole numbers has numerous real-world applications. For example, in cooking, you may need to multiply a recipe by a certain factor to serve a larger group of people. In science, you may need to multiply a measurement by a certain factor to convert it to a different unit. In finance, you may need to multiply a rate by a certain factor to calculate the total amount owed.

Tips and Tricks

When multiplying fractions by whole numbers, it's essential to remember the following tips and tricks:

  • Multiply the numerator by the whole number and keep the denominator the same.
  • Simplify the expression by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their GCD.

By following these tips and tricks, you'll be able to multiply fractions by whole numbers with ease and accuracy.

Common Mistakes

When multiplying fractions by whole numbers, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Forgetting to multiply the numerator by the whole number.
  • Forgetting to simplify the expression by dividing both the numerator and the denominator by their GCD.
  • Reducing the fraction to its simplest form incorrectly.

By being aware of these common mistakes, you'll be able to avoid them and arrive at the correct answer.

Conclusion

In conclusion, multiplying fractions by whole numbers is a fundamental concept in mathematics. By following the steps outlined in this article, you'll be able to multiply fractions by whole numbers with ease and accuracy. Remember to multiply the numerator by the whole number, simplify the expression, and reduce the fraction to its simplest form. With practice and patience, you'll become proficient in multiplying fractions by whole numbers and be able to apply this concept to real-world problems.

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Frequently Asked Questions

Q: What is the rule for multiplying fractions by whole numbers?

A: The rule for multiplying fractions by whole numbers is to multiply the numerator of the fraction by the whole number and keep the denominator the same.

Q: How do I simplify the expression after multiplying a fraction by a whole number?

A: To simplify the expression, divide both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD) and how do I find it?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. You can find the GCD by listing the factors of each number or using the Euclidean algorithm.

Q: Can I reduce a fraction to its simplest form after multiplying it by a whole number?

A: Yes, you can reduce a fraction to its simplest form after multiplying it by a whole number. To do this, divide both the numerator and the denominator by their GCD.

Q: What are some common mistakes to avoid when multiplying fractions by whole numbers?

A: Some common mistakes to avoid when multiplying fractions by whole numbers include:

  • Forgetting to multiply the numerator by the whole number.
  • Forgetting to simplify the expression by dividing both the numerator and the denominator by their GCD.
  • Reducing the fraction to its simplest form incorrectly.

Q: How do I apply the concept of multiplying fractions by whole numbers to real-world problems?

A: You can apply the concept of multiplying fractions by whole numbers to real-world problems in various fields such as cooking, science, and finance. For example, in cooking, you may need to multiply a recipe by a certain factor to serve a larger group of people. In science, you may need to multiply a measurement by a certain factor to convert it to a different unit. In finance, you may need to multiply a rate by a certain factor to calculate the total amount owed.

Q: What are some tips and tricks for multiplying fractions by whole numbers?

A: Some tips and tricks for multiplying fractions by whole numbers include:

  • Multiply the numerator by the whole number and keep the denominator the same.
  • Simplify the expression by dividing both the numerator and the denominator by their GCD.
  • Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their GCD.

Q: Can I use a calculator to multiply fractions by whole numbers?

A: Yes, you can use a calculator to multiply fractions by whole numbers. However, it's essential to understand the concept and be able to apply it manually to ensure accuracy and understanding.

Q: How do I check my work when multiplying fractions by whole numbers?

A: To check your work, multiply the numerator by the whole number and simplify the expression. Then, reduce the fraction to its simplest form by dividing both the numerator and the denominator by their GCD. If the result is correct, you have successfully multiplied the fraction by the whole number.

Conclusion

In conclusion, multiplying fractions by whole numbers is a fundamental concept in mathematics. By following the steps outlined in this article and understanding the frequently asked questions, you'll be able to multiply fractions by whole numbers with ease and accuracy. Remember to multiply the numerator by the whole number, simplify the expression, and reduce the fraction to its simplest form. With practice and patience, you'll become proficient in multiplying fractions by whole numbers and be able to apply this concept to real-world problems.