Multiply And Write Your Answer As A Fraction, Whole Number, Or Mixed Number. 2 1 3 × 1 5 8 = □ 2 \frac{1}{3} \times 1 \frac{5}{8} = \square 2 3 1 ​ × 1 8 5 ​ = □

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Introduction

Multiplying mixed numbers is an essential skill in mathematics, particularly in algebra and geometry. Mixed numbers are a combination of a whole number and a fraction, and they can be multiplied together to obtain a product. In this article, we will explore the process of multiplying mixed numbers, and we will provide a step-by-step guide on how to do it.

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. For example, 2 1/3 is a mixed number, where 2 is the whole number and 1/3 is the fraction.

Why Multiply Mixed Numbers?

Multiplying mixed numbers is an essential skill in mathematics because it allows us to solve problems that involve the multiplication of two or more mixed numbers. For example, if we have two mixed numbers, 2 1/3 and 1 5/8, we can multiply them together to obtain a product.

How to Multiply Mixed Numbers

To multiply mixed numbers, we need to follow a step-by-step process. Here are the steps:

Step 1: Multiply the Whole Numbers

The first step is to multiply the whole numbers together. In the example above, we have 2 1/3 and 1 5/8. We can multiply the whole numbers together by multiplying 2 and 1.

2 × 1 = 2

Step 2: Multiply the Fractions

The next step is to multiply the fractions together. In the example above, we have 1/3 and 5/8. We can multiply the fractions together by multiplying the numerators (1 and 5) and the denominators (3 and 8).

(1 × 5) / (3 × 8) = 5/24

Step 3: Add the Whole Number and the Fraction

The final step is to add the whole number and the fraction together. In the example above, we have 2 and 5/24. We can add the whole number and the fraction together by adding 2 and 5/24.

2 + 5/24 = 2 5/24

Step 4: Simplify the Fraction (if necessary)

The final step is to simplify the fraction (if necessary). In the example above, we have 2 5/24. We can simplify the fraction by dividing the numerator (5) and the denominator (24) by their greatest common divisor (GCD).

GCD(5, 24) = 1

Since the GCD is 1, we cannot simplify the fraction further.

Example: Multiplying Mixed Numbers

Let's use an example to illustrate the process of multiplying mixed numbers. Suppose we have two mixed numbers, 2 1/3 and 1 5/8. We can multiply them together to obtain a product.

2 1/3 × 1 5/8 = ?

To multiply the mixed numbers, we need to follow the steps outlined above.

Step 1: Multiply the Whole Numbers

2 × 1 = 2

Step 2: Multiply the Fractions

(1 × 5) / (3 × 8) = 5/24

Step 3: Add the Whole Number and the Fraction

2 + 5/24 = 2 5/24

Step 4: Simplify the Fraction (if necessary)

GCD(5, 24) = 1

Since the GCD is 1, we cannot simplify the fraction further.

Therefore, the product of 2 1/3 and 1 5/8 is 2 5/24.

Conclusion

Multiplying mixed numbers is an essential skill in mathematics, particularly in algebra and geometry. By following the steps outlined above, we can multiply mixed numbers together to obtain a product. In this article, we have provided a step-by-step guide on how to multiply mixed numbers, and we have used an example to illustrate the process.

Common Mistakes to Avoid

When multiplying mixed numbers, there are several common mistakes to avoid. Here are some of the most common mistakes:

  • Not multiplying the whole numbers together: When multiplying mixed numbers, it is essential to multiply the whole numbers together first.
  • Not multiplying the fractions together: When multiplying mixed numbers, it is essential to multiply the fractions together second.
  • Not adding the whole number and the fraction together: When multiplying mixed numbers, it is essential to add the whole number and the fraction together.
  • Not simplifying the fraction (if necessary): When multiplying mixed numbers, it is essential to simplify the fraction (if necessary).

Practice Problems

To practice multiplying mixed numbers, try the following problems:

  • 3 2/5 × 2 3/4 = ?
  • 4 1/2 × 3 2/3 = ?
  • 2 3/4 × 1 1/2 = ?

Answer Key

Here are the answers to the practice problems:

  • 3 2/5 × 2 3/4 = 7 13/20
  • 4 1/2 × 3 2/3 = 14 5/6
  • 2 3/4 × 1 1/2 = 4 5/8
    Multiplying Mixed Numbers: A Q&A Guide =====================================

Introduction

Multiplying mixed numbers can be a challenging task, but with the right guidance, it can be made easier. In this article, we will provide a Q&A guide on multiplying mixed numbers, covering common questions and answers.

Q: What is a mixed number?

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. For example, 2 1/3 is a mixed number, where 2 is the whole number and 1/3 is the fraction.

Q: Why do I need to multiply mixed numbers?

A: Multiplying mixed numbers is an essential skill in mathematics, particularly in algebra and geometry. It allows us to solve problems that involve the multiplication of two or more mixed numbers.

Q: How do I multiply mixed numbers?

A: To multiply mixed numbers, you need to follow a step-by-step process. Here are the steps:

  1. Multiply the whole numbers together.
  2. Multiply the fractions together.
  3. Add the whole number and the fraction together.
  4. Simplify the fraction (if necessary).

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

A: The order of operations when multiplying mixed numbers is:

  1. Multiply the whole numbers together.
  2. Multiply the fractions together.
  3. Add the whole number and the fraction together.
  4. Simplify the fraction (if necessary).

Q: Can I simplify the fraction before multiplying?

A: No, you cannot simplify the fraction before multiplying. You need to multiply the fractions together first, and then simplify the result.

Q: What if the fractions have different denominators?

A: If the fractions have different denominators, you need to find the least common multiple (LCM) of the denominators and convert both fractions to have the same denominator.

Q: Can I use a calculator to multiply mixed numbers?

A: Yes, you can use a calculator to multiply mixed numbers. However, it is essential to understand the concept of multiplying mixed numbers and to be able to do it manually.

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.
  • Not multiplying the fractions together.
  • Not adding the whole number and the fraction together.
  • Not simplifying the fraction (if necessary).

Q: How can I practice multiplying mixed numbers?

A: You can practice multiplying mixed numbers by trying the following problems:

  • 3 2/5 × 2 3/4 = ?
  • 4 1/2 × 3 2/3 = ?
  • 2 3/4 × 1 1/2 = ?

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

A: Multiplying mixed numbers has several real-world applications, including:

  • Cooking: When measuring ingredients, you may need to multiply mixed numbers to get the correct amount.
  • Building: When building a structure, you may need to multiply mixed numbers to get the correct amount of materials.
  • Science: When conducting experiments, you may need to multiply mixed numbers to get the correct amount of chemicals.

Conclusion

Multiplying mixed numbers can be a challenging task, but with the right guidance, it can be made easier. By following the steps outlined in this article and practicing with examples, you can become proficient in multiplying mixed numbers. Remember to avoid common mistakes and to use real-world applications to make the concept more meaningful.