What Is 2 9 × 3 \frac{2}{9} \times 3 9 2 ​ × 3 ?A. 5 9 \frac{5}{9} 9 5 ​ B. 2 27 \frac{2}{27} 27 2 ​ C. 6 27 \frac{6}{27} 27 6 ​ D. 6 9 \frac{6}{9} 9 6 ​

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Introduction

Multiplication of fractions is a fundamental concept in mathematics that requires a clear understanding of the underlying principles. In this article, we will delve into the world of fractions and explore the process of multiplying fractions. We will use a specific example to illustrate the concept and provide a step-by-step guide on how to solve it.

What is 29×3\frac{2}{9} \times 3?

To solve this problem, we need to follow the order of operations, which dictates that we multiply the numerator and the denominator separately. The numerator is 2, and the denominator is 9. When we multiply 2 by 3, we get 6. The denominator remains the same, which is 9.

Step 1: Multiply the Numerator and the Denominator

To multiply the numerator and the denominator, we simply multiply the two numbers together. In this case, we have:

29×3=2×39\frac{2}{9} \times 3 = \frac{2 \times 3}{9}

Step 2: Simplify the Fraction

Now that we have multiplied the numerator and the denominator, we need to simplify the fraction. To do this, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 6 and 9 is 3.

Simplifying the Fraction

To simplify the fraction, we divide both the numerator and the denominator by the GCD. In this case, we have:

69=6÷39÷3=23\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}

However, we are not done yet. We need to check if the simplified fraction is among the answer choices.

Answer Choices

Let's take a look at the answer choices:

A. 59\frac{5}{9} B. 227\frac{2}{27} C. 627\frac{6}{27} D. 69\frac{6}{9}

Comparing the Answer Choices

Now that we have simplified the fraction, we can compare it to the answer choices. We can see that the simplified fraction, 23\frac{2}{3}, is not among the answer choices. However, we can rewrite the fraction as a fraction with a denominator of 27, which is the least common multiple (LCM) of 9 and 3.

Rewriting the Fraction

To rewrite the fraction, we multiply both the numerator and the denominator by 9:

23=2×93×9=1827\frac{2}{3} = \frac{2 \times 9}{3 \times 9} = \frac{18}{27}

Conclusion

In conclusion, the correct answer is 1827\frac{18}{27}, which is equivalent to 69\frac{6}{9}. Therefore, the correct answer is:

The Final Answer is: D. 69\frac{6}{9}

Why is this Important?

Understanding how to multiply fractions is crucial in mathematics, as it allows us to solve a wide range of problems. In this article, we have demonstrated how to multiply fractions using a specific example. We have also shown how to simplify fractions and rewrite them in different forms.

Real-World Applications

Multiplication of fractions has numerous real-world applications. For example, in cooking, we often need to multiply fractions to scale up or down a recipe. In finance, we use fractions to calculate interest rates and investment returns. In science, we use fractions to calculate probabilities and statistics.

Common Mistakes

When multiplying fractions, it is easy to make mistakes. Here are some common mistakes to avoid:

  • Not multiplying the numerator and the denominator separately: This can lead to incorrect answers.
  • Not simplifying the fraction: This can lead to fractions that are not in their simplest form.
  • Not rewriting the fraction in different forms: This can make it difficult to compare fractions.

Conclusion

Introduction

Multiplication of fractions is a fundamental concept in mathematics that requires a clear understanding of the underlying principles. In this article, we will provide a Q&A guide to help you understand how to multiply fractions and address common questions and concerns.

Q: What is the order of operations when multiplying fractions?

A: When multiplying fractions, the order of operations is to multiply the numerator and the denominator separately. This means that you multiply the numerators together and the denominators together.

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly. Once you have found the LCM, you can multiply the numerators and denominators together.

Q: Can I simplify fractions after multiplying them?

A: Yes, you can simplify fractions after multiplying them. To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD is the largest number that both the numerator and the denominator can divide into evenly. Once you have found the GCD, you can divide both the numerator and the denominator by the GCD to simplify the fraction.

Q: How do I rewrite fractions in different forms?

A: To rewrite fractions in different forms, you need to multiply both the numerator and the denominator by the same number. For example, if you want to rewrite a fraction with a denominator of 9 as a fraction with a denominator of 27, you would multiply both the numerator and the denominator by 3.

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

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

  • Not multiplying the numerator and the denominator separately
  • Not simplifying the fraction
  • Not rewriting the fraction in different forms
  • Not using the correct order of operations

Q: How do I apply multiplication of fractions in real-world situations?

A: Multiplication of fractions has numerous real-world applications. For example, in cooking, you may need to multiply fractions to scale up or down a recipe. In finance, you may use fractions to calculate interest rates and investment returns. In science, you may use fractions to calculate probabilities and statistics.

Q: Can I use a calculator to multiply fractions?

A: Yes, you can use a calculator to multiply fractions. However, it is still important to understand the underlying principles of multiplication of fractions to ensure that you are using the calculator correctly.

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

A: To check your work when multiplying fractions, you can use the following steps:

  • Multiply the numerators together
  • Multiply the denominators together
  • Simplify the fraction (if necessary)
  • Rewrite the fraction in different forms (if necessary)

Conclusion

In conclusion, multiplication of fractions is a fundamental concept in mathematics that requires a clear understanding of the underlying principles. By following the order of operations and simplifying fractions, you can solve a wide range of problems. We hope that this Q&A guide has helped you understand how to multiply fractions and address common questions and concerns.

Common Fractions and Their Multiples

Here are some common fractions and their multiples:

  • 12\frac{1}{2}: 12×12=14\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}
  • 13\frac{1}{3}: 13×13=19\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
  • 14\frac{1}{4}: 14×14=116\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}
  • 15\frac{1}{5}: 15×15=125\frac{1}{5} \times \frac{1}{5} = \frac{1}{25}

Practice Problems

Here are some practice problems to help you understand how to multiply fractions:

  • 23×34=?\frac{2}{3} \times \frac{3}{4} = ?
  • 12×23=?\frac{1}{2} \times \frac{2}{3} = ?
  • 34×45=?\frac{3}{4} \times \frac{4}{5} = ?
  • 25×56=?\frac{2}{5} \times \frac{5}{6} = ?

Answer Key

Here are the answers to the practice problems:

  • 23×34=612=12\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}
  • 12×23=26=13\frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3}
  • 34×45=1220=35\frac{3}{4} \times \frac{4}{5} = \frac{12}{20} = \frac{3}{5}
  • 25×56=1030=13\frac{2}{5} \times \frac{5}{6} = \frac{10}{30} = \frac{1}{3}