Multiply $6 \cdot \frac{3}{8}$. Simplify The Answer And Express It As A Mixed Number.A. $2 \frac{1}{4}$ B. 1 C. $\frac{9}{4}$ D. $6 \frac{3}{8}$

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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 and express it as a mixed number.

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 2 3/4 or 3 1/2. Mixed numbers can be used to represent quantities that are part of a whole, such as a pizza that is cut into 8 slices and you have eaten 2 3/4 of it.

Multiplying Mixed Numbers

To multiply mixed numbers, we need to follow a specific order of operations. The first step is to multiply the whole numbers together, and then multiply the fractions together. Finally, we need to add the product of the whole numbers to the product of the fractions.

Step 1: Multiply the Whole Numbers

The first step is to multiply the whole numbers together. In this case, we have 6 and 3/8. To multiply the whole numbers, we simply multiply 6 by 3, which gives us 18.

Step 2: Multiply the Fractions

The next step is to multiply the fractions together. In this case, we have 3/8 and 1 (which can be written as 8/8). To multiply the fractions, we need to multiply the numerators together and the denominators together. This gives us (3 x 8) / (8 x 8) = 24/64.

Step 3: Add the Product of the Whole Numbers to the Product of the Fractions

The final step is to add the product of the whole numbers to the product of the fractions. In this case, we have 18 and 24/64. To add these two numbers, we need to convert the whole number to a fraction with the same denominator as the fraction. This gives us 18 = 144/8. Now we can add the two fractions together: (144/8) + (24/64) = (144 x 8) / (8 x 8) + (24/64) = 1152/64 + 24/64 = 1176/64.

Simplifying the Answer

The final step is to simplify the answer. To simplify the fraction, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 1176 and 64 is 8. Dividing both numbers by 8 gives us 147/8.

Expressing the Answer as a Mixed Number

The final step is to express the answer as a mixed number. To do this, we need to divide the numerator by the denominator and write the remainder as a fraction. In this case, 147 divided by 8 is 18 with a remainder of 3. Therefore, the answer can be expressed as 18 3/8.

Conclusion

Multiplying mixed numbers can be a challenging task, but with the right approach, it can be simplified. By following the steps outlined in this article, you can multiply mixed numbers and express the answer as a mixed number. Remember to multiply the whole numbers together, multiply the fractions together, add the product of the whole numbers to the product of the fractions, simplify the answer, and finally express the answer as a mixed number.

Example Problems

Here are a few example problems to help you practice multiplying mixed numbers:

  • Multiply 2 3/4 and 3 1/2.
  • Multiply 5 1/8 and 2 3/4.
  • Multiply 3 1/2 and 4 1/8.

Answer Key

Here are the answers to the example problems:

  • 2 3/4 x 3 1/2 = 7 11/16
  • 5 1/8 x 2 3/4 = 13 5/32
  • 3 1/2 x 4 1/8 = 14 3/16

Tips and Tricks

Here are a few tips and tricks to help you multiply mixed numbers:

  • Make sure to multiply the whole numbers together first.
  • Multiply the fractions together next.
  • Add the product of the whole numbers to the product of the fractions.
  • Simplify the answer by dividing both the numerator and the denominator by their GCD.
  • Express the answer as a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction.

Introduction

Multiplying mixed numbers can be a challenging task, but with the right approach, it can be simplified. In this article, we will provide a Q&A guide to help you understand the process of multiplying mixed numbers and address some common questions and concerns.

Q: What is the order of operations when multiplying mixed numbers?

A: The order of operations when multiplying mixed numbers is to multiply the whole numbers together, then multiply the fractions together, and finally add the product of the whole numbers to the product of the fractions.

Q: How do I multiply fractions when multiplying mixed numbers?

A: To multiply fractions when multiplying mixed numbers, you need to multiply the numerators together and the denominators together. For example, if you have 3/8 and 1 (which can be written as 8/8), you would multiply the numerators together (3 x 8) and the denominators together (8 x 8) to get 24/64.

Q: How do I add the product of the whole numbers to the product of the fractions?

A: To add the product of the whole numbers to the product of the fractions, you need to convert the whole number to a fraction with the same denominator as the fraction. For example, if you have 18 and 24/64, you would convert 18 to a fraction with the same denominator (18 = 144/8) and then add the two fractions together: (144/8) + (24/64) = (144 x 8) / (8 x 8) + (24/64) = 1152/64 + 24/64 = 1176/64.

Q: How do I simplify the answer when multiplying mixed numbers?

A: To simplify the answer when multiplying mixed numbers, you need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, if you have 1176/64, the GCD of 1176 and 64 is 8. Dividing both numbers by 8 gives you 147/8.

Q: How do I express the answer as a mixed number when multiplying mixed numbers?

A: To express the answer as a mixed number when multiplying mixed numbers, you need to divide the numerator by the denominator and write the remainder as a fraction. For example, if you have 147/8, dividing 147 by 8 gives you 18 with a remainder of 3. Therefore, the answer can be expressed as 18 3/8.

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

A: Some common mistakes to avoid when multiplying mixed numbers include:

  • Not multiplying the whole numbers together first
  • Not multiplying the fractions together
  • Not adding the product of the whole numbers to the product of the fractions
  • Not simplifying the answer by dividing both the numerator and the denominator by their GCD
  • Not expressing the answer as a mixed number by dividing the numerator by the denominator and writing the remainder as a fraction

Q: How can I practice multiplying mixed numbers?

A: You can practice multiplying mixed numbers by working through example problems, such as:

  • Multiply 2 3/4 and 3 1/2.
  • Multiply 5 1/8 and 2 3/4.
  • Multiply 3 1/2 and 4 1/8.

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

A: Multiplying mixed numbers has many real-world applications, such as:

  • Calculating the area of a room or a piece of land
  • Determining the cost of materials for a project
  • Finding the volume of a container or a tank
  • Calculating the amount of time it takes to complete a task

Conclusion

Multiplying mixed numbers can be a challenging task, but with the right approach, it can be simplified. By following the steps outlined in this article and practicing with example problems, you can become more confident and proficient in multiplying mixed numbers. Remember to multiply the whole numbers together, multiply the fractions together, add the product of the whole numbers to the product of the fractions, simplify the answer, and finally express the answer as a mixed number.