A. ${ 5 \frac{2}{5} \times 1 \frac{3}{4} =\$} \begin{tabular}{|l|l|}\hline Estimate & Solve \\hline\end{tabular}

Mar 13, 2025 by ADMIN 113 views

**Multiplication of Mixed Numbers: A Step-by-Step Guide**

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. When we multiply mixed numbers, it can be a bit challenging, but with the right approach, we can simplify the process and arrive at the correct answer. In this article, we will explore the multiplication of mixed numbers, focusing on the problem $5 \frac{2}{5} \times 1 \frac{3}{4}$ .

Understanding Mixed Numbers

Before we dive into the multiplication process, let's take a closer look at mixed numbers. A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$ , where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $5 \frac{2}{5}$ is a mixed number, where $5$ is the whole number, $2$ is the numerator, and $5$ is the denominator.

Estimating the Product

To estimate the product of two mixed numbers, we can multiply the whole numbers and then add the fractions. Let's start by estimating the product of $5 \frac{2}{5}$ and $1 \frac{3}{4}$ .

Multiply the whole numbers: $5 \times 1 = 5$
Add the fractions: $\frac{2}{5} + \frac{3}{4} = \frac{8}{20} + \frac{15}{20} = \frac{23}{20}$

Now, let's add the whole number and the fraction: $5 + \frac{23}{20} = 5 \frac{23}{20}$

Solving the Problem

To solve the problem $5 \frac{2}{5} \times 1 \frac{3}{4}$ , we need to multiply the two mixed numbers. To do this, we can follow these steps:

Multiply the whole numbers: $5 \times 1 = 5$
Multiply the fractions: $\frac{2}{5} \times \frac{3}{4} = \frac{6}{20} = \frac{3}{10}$
Add the whole number and the fraction: $5 + \frac{3}{10} = 5 \frac{3}{10}$

Now, let's multiply the two mixed numbers: $5 \frac{2}{5} \times 1 \frac{3}{4} = 5 \frac{3}{10}$

Conclusion

In this article, we explored the multiplication of mixed numbers, focusing on the problem $5 \frac{2}{5} \times 1 \frac{3}{4}$ . We learned how to estimate the product by multiplying the whole numbers and adding the fractions, and then we solved the problem by following a step-by-step process. By understanding mixed numbers and following these steps, we can simplify the process of multiplying mixed numbers and arrive at the correct answer.

Tips and Tricks

When multiplying mixed numbers, it's essential to multiply the whole numbers and the fractions separately.
When adding fractions, make sure to find the least common denominator (LCD) to add the fractions correctly.
When multiplying fractions, multiply the numerators and the denominators separately.

Common Mistakes

Failing to multiply the whole numbers and the fractions separately.
Not finding the LCD when adding fractions.
Not multiplying the numerators and the denominators separately when multiplying fractions.

Real-World Applications

Multiplication of mixed numbers has many real-world applications, such as:

Calculating the area of a rectangle with mixed number dimensions.
Finding the volume of a rectangular prism with mixed number dimensions.
Calculating the cost of a mixed number quantity of items.

Practice Problems

$3 \frac{1}{2} \times 2 \frac{3}{4} = ?$
$4 \frac{2}{3} \times 1 \frac{1}{2} = ?$
$2 \frac{1}{4} \times 3 \frac{2}{3} = ?$

Conclusion

Q: What is the multiplication of mixed numbers?

A: The multiplication of mixed numbers is a mathematical operation that involves multiplying two or more mixed numbers together. A mixed number is a combination of a whole number and a fraction, written in the form $a \frac{b}{c}$ , where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I multiply mixed numbers?

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

Multiply the whole numbers: Multiply the whole numbers together.
Multiply the fractions: Multiply the numerators and the denominators of the fractions together.
Add the whole number and the fraction: Add the whole number and the fraction together.

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

A: When multiplying mixed numbers, the order of operations is:

Multiply the whole numbers
Multiply the fractions
Add the whole number and the fraction

Q: How do I handle fractions with different denominators when multiplying mixed numbers?

A: When multiplying fractions with different denominators, you need to find the least common denominator (LCD) of the two fractions. The LCD is the smallest number that both fractions can divide into evenly.

Q: What is the least common denominator (LCD)?

A: The least common denominator (LCD) is the smallest number that both fractions can divide into evenly. To find the LCD, you need to list the multiples of each denominator and find the smallest number that appears in both lists.

Q: How do I find the LCD of two fractions?

A: To find the LCD of two fractions, you need to list the multiples of each denominator and find the smallest number that appears in both lists. For example, if the denominators are 4 and 6, the multiples of 4 are 4, 8, 12, 16, ... and the multiples of 6 are 6, 12, 18, 24, ... The smallest number that appears in both lists is 12, so the LCD is 12.

Q: What is the difference between multiplying mixed numbers and multiplying fractions?

A: Multiplying mixed numbers involves multiplying the whole numbers and the fractions together, while multiplying fractions involves multiplying the numerators and the denominators of the fractions together.

Q: Can I multiply mixed numbers with fractions?

A: Yes, you can multiply mixed numbers with fractions. To do this, you need to multiply the whole number and the fraction together, and then multiply the fractions together.

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

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

Failing to multiply the whole numbers and the fractions separately
Not finding the LCD when adding fractions
Not multiplying the numerators and the denominators separately when multiplying fractions

Q: How can I practice multiplying mixed numbers?

A: You can practice multiplying mixed numbers by working through examples and exercises. You can also use online resources and math games to help you practice and build your skills.

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 rectangle with mixed number dimensions
Finding the volume of a rectangular prism with mixed number dimensions
Calculating the cost of a mixed number quantity of items

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

A: Yes, you can use a calculator to multiply mixed numbers. However, it's always a good idea to double-check your work and make sure that the calculator is giving you the correct answer.