Multiply \left(-6 \frac{3}{4}\right)\left(-\frac{5}{54}\right ].

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Introduction

Multiplying mixed numbers and fractions can be a challenging task, but with the right approach, it can be made easier. In this article, we will explore the steps involved in multiplying mixed numbers and fractions, and provide a step-by-step guide on how to do it.

Understanding Mixed Numbers and Fractions

Before we dive into the steps, let's first understand what mixed numbers and fractions are.

  • Mixed Numbers: A mixed number is a combination of a whole number and a fraction. It is written in the form of a + b/c, where a is the whole number and b/c is the fraction.
  • Fractions: A fraction is a way of showing part of a whole. It is written in the form of a/b, where a is the numerator and b is the denominator.

Step 1: Convert the Mixed Number to an Improper Fraction

To multiply a mixed number and a fraction, we need to convert the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than the denominator.

  • To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator.
  • The result is then written as the new numerator over the denominator.

For example, let's convert the mixed number -6 3/4 to an improper fraction.

-6 3/4 = (-6 × 4) + 3 = -24 + 3 = -21/4

Step 2: Multiply the Numerators

Now that we have converted the mixed number to an improper fraction, we can multiply the numerators.

  • To multiply the numerators, we simply multiply the two numerators together.
  • The result is then written as the new numerator.

For example, let's multiply the numerators -21 and -5.

-21 × -5 = 105

Step 3: Multiply the Denominators

Next, we multiply the denominators.

  • To multiply the denominators, we simply multiply the two denominators together.
  • The result is then written as the new denominator.

For example, let's multiply the denominators 4 and 54.

4 × 54 = 216

Step 4: Simplify the Result

Now that we have multiplied the numerators and denominators, we need to simplify the result.

  • To simplify the result, we divide the numerator by the denominator.
  • The result is then written as the new fraction.

For example, let's simplify the result 105/216.

105 ÷ 216 = 0.4852 (approximately)

Conclusion

Multiplying mixed numbers and fractions can be a challenging task, but with the right approach, it can be made easier. By following the steps outlined in this article, you can multiply mixed numbers and fractions with ease.

Example Problem

Let's multiply the mixed number -6 3/4 and the fraction -5/54.

-6 3/4 = (-6 × 4) + 3 = -24 + 3 = -21/4 -5/54

To multiply the numerators, we multiply -21 and -5.

-21 × -5 = 105

To multiply the denominators, we multiply 4 and 54.

4 × 54 = 216

To simplify the result, we divide 105 by 216.

105 ÷ 216 = 0.4852 (approximately)

Therefore, the result of multiplying -6 3/4 and -5/54 is 0.4852 (approximately).

Tips and Tricks

Here are some tips and tricks to help you multiply mixed numbers and fractions:

  • Always convert the mixed number to an improper fraction before multiplying.
  • Multiply the numerators and denominators separately.
  • Simplify the result by dividing the numerator by the denominator.
  • Use a calculator to simplify the result if necessary.

By following these tips and tricks, you can multiply mixed numbers and fractions with ease.

Common Mistakes to Avoid

Here are some common mistakes to avoid when multiplying mixed numbers and fractions:

  • Not converting the mixed number to an improper fraction before multiplying.
  • Multiplying the numerators and denominators together without separating them.
  • Not simplifying the result by dividing the numerator by the denominator.
  • Using the wrong order of operations.

By avoiding these common mistakes, you can ensure that your calculations are accurate and correct.

Conclusion

Introduction

Multiplying mixed numbers and fractions can be a challenging task, but with the right approach, it can be made easier. In this article, we will provide a Q&A guide to help you understand the steps involved in multiplying mixed numbers and fractions.

Q: What is the first step in multiplying a mixed number and a fraction?

A: The first step in multiplying a mixed number and a fraction is to convert the mixed number to an improper fraction. This involves multiplying the whole number by the denominator and adding the numerator.

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

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and add the numerator. For example, to convert the mixed number -6 3/4 to an improper fraction, you would multiply -6 by 4 and add 3, resulting in -21/4.

Q: What is the next step in multiplying a mixed number and a fraction?

A: The next step in multiplying a mixed number and a fraction is to multiply the numerators. This involves multiplying the numerators of the two fractions together.

Q: How do I multiply the numerators?

A: To multiply the numerators, you simply multiply the two numerators together. For example, to multiply the numerators -21 and -5, you would multiply -21 by -5, resulting in 105.

Q: What is the next step in multiplying a mixed number and a fraction?

A: The next step in multiplying a mixed number and a fraction is to multiply the denominators. This involves multiplying the denominators of the two fractions together.

Q: How do I multiply the denominators?

A: To multiply the denominators, you simply multiply the two denominators together. For example, to multiply the denominators 4 and 54, you would multiply 4 by 54, resulting in 216.

Q: What is the final step in multiplying a mixed number and a fraction?

A: The final step in multiplying a mixed number and a fraction is to simplify the result. This involves dividing the numerator by the denominator.

Q: How do I simplify the result?

A: To simplify the result, you divide the numerator by the denominator. For example, to simplify the result 105/216, you would divide 105 by 216, resulting in 0.4852 (approximately).

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

A: Some common mistakes to avoid when multiplying mixed numbers and fractions include not converting the mixed number to an improper fraction before multiplying, multiplying the numerators and denominators together without separating them, not simplifying the result by dividing the numerator by the denominator, and using the wrong order of operations.

Q: How can I practice multiplying mixed numbers and fractions?

A: You can practice multiplying mixed numbers and fractions by working through examples and exercises. You can also use online resources and calculators to help you with your calculations.

Q: What are some real-world applications of multiplying mixed numbers and fractions?

A: Multiplying mixed numbers and fractions has many real-world applications, including calculating percentages, measuring ingredients for recipes, and determining the cost of items.

Conclusion

Multiplying mixed numbers and fractions can be a challenging task, but with the right approach, it can be made easier. By following the steps outlined in this article and practicing with examples and exercises, you can become proficient in multiplying mixed numbers and fractions. Remember to always convert the mixed number to an improper fraction before multiplying, multiply the numerators and denominators separately, simplify the result by dividing the numerator by the denominator, and use a calculator to simplify the result if necessary.