Multiply $5 \frac{1}{3} \cdot 1 \frac{5}{6}$. Simplify The Answer And Write It As A Mixed Number.A. $9 \frac{7}{9}$B. \$5 \frac{5}{18}$[/tex\]C. $9 \frac{14}{18}$D. $\frac{176}{18}$

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Introduction

Multiplying mixed numbers can be a challenging task, but with the right approach, it can be simplified. In this article, we will explore the process of multiplying mixed numbers and provide a step-by-step guide on how to simplify the answer. We will also examine the different options available and determine which one is the correct solution.

What are Mixed Numbers?

A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as 5 1/3 or 2 3/4. Mixed numbers can be used to represent a variety of quantities, including measurements, time, and money.

Multiplying Mixed Numbers

To multiply mixed numbers, we need to follow a specific procedure. Here are the steps:

  1. Convert the mixed numbers to improper fractions: The first step is to convert the mixed numbers to improper fractions. To do this, we multiply the whole number by the denominator and then add the numerator. For example, 5 1/3 can be converted to an improper fraction as follows:

    5 1/3 = (5 × 3) + 1 = 16/3

    Similarly, 1 5/6 can be converted to an improper fraction as follows:

    1 5/6 = (1 × 6) + 5 = 11/6

  2. Multiply the improper fractions: Once we have converted the mixed numbers to improper fractions, we can multiply them together. To do this, we multiply the numerators and denominators separately. For example:

    (16/3) × (11/6) = (16 × 11) / (3 × 6) = 176/18

  3. Simplify the answer: The final step is to simplify the answer by dividing the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 176 and 18 is 2. Therefore, we can simplify the answer as follows:

    176/18 = (176 ÷ 2) / (18 ÷ 2) = 88/9

However, we need to convert this improper fraction back to a mixed number. To do this, we divide the numerator by the denominator and write the remainder as a fraction. In this case:

88 ÷ 9 = 9 with a remainder of 7

Therefore, the mixed number equivalent of 88/9 is 9 7/9.

Conclusion

In conclusion, multiplying mixed numbers requires a step-by-step approach. We need to convert the mixed numbers to improper fractions, multiply them together, and then simplify the answer by dividing the numerator and denominator by their GCD. In this case, the correct answer is 9 7/9.

Comparison of Options

Let's compare the options available:

  • Option A: 9 7/9: This is the correct answer.
  • Option B: 5 5/18: This is not the correct answer.
  • Option C: 9 14/18: This is not the correct answer.
  • Option D: 176/18: This is the improper fraction equivalent of the correct answer, but it is not the mixed number equivalent.

Final Answer

Introduction

Multiplying mixed numbers can be a challenging task, but with the right approach, it can be simplified. In this article, we will explore the process of multiplying mixed numbers and provide a step-by-step guide on how to simplify the answer. We will also examine the different options available and determine which one is the correct solution.

Q&A Guide

Q: What are mixed numbers?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as 5 1/3 or 2 3/4.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, 5 1/3 can be converted to an improper fraction as follows:

5 1/3 = (5 × 3) + 1 = 16/3

Q: How do I multiply two mixed numbers together?

A: To multiply two mixed numbers together, you need to follow these steps:

  1. Convert the mixed numbers to improper fractions.
  2. Multiply the improper fractions together.
  3. Simplify the answer by dividing the numerator and denominator by their greatest common divisor (GCD).

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

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6.

Q: How do I simplify an improper fraction?

A: To simplify an improper fraction, you need to divide the numerator and denominator by their GCD. For example, 88/9 can be simplified as follows:

88 ÷ 9 = 9 with a remainder of 7

Therefore, the mixed number equivalent of 88/9 is 9 7/9.

Q: What is the final answer to the problem 5 1/3 × 1 5/6?

A: The final answer to the problem 5 1/3 × 1 5/6 is 9 7/9.

Q: Why is 9 7/9 the correct answer?

A: 9 7/9 is the correct answer because it is the result of multiplying 5 1/3 and 1 5/6 together and simplifying the answer.

Q: What are the other options available?

A: The other options available are:

  • Option B: 5 5/18: This is not the correct answer.
  • Option C: 9 14/18: This is not the correct answer.
  • Option D: 176/18: This is the improper fraction equivalent of the correct answer, but it is not the mixed number equivalent.

Conclusion

In conclusion, multiplying mixed numbers requires a step-by-step approach. We need to convert the mixed numbers to improper fractions, multiply them together, and then simplify the answer by dividing the numerator and denominator by their GCD. In this case, the correct answer is 9 7/9.

Final Answer

The final answer is Option A: 9 7/9.