Introduction to Mixed Numbers and Multiplication

Oct 13, 2025 by miodeya.com 103 views

Introduction to Mixed Numbers and Multiplication

In mathematics, mixed numbers are a combination of a whole number and a fraction. They are often used to represent quantities that are not whole, but can be expressed as a sum of a whole number and a fraction. In this article, we will focus on calculating the product of a mixed number and a whole number, specifically ${ $2 \frac{3}{8} \times 4\$}$ .

To begin, let's break down the mixed number ${$2 \frac{3}{8}$. The whole number part is 2, and the fraction part is [\frac{3}{8}$. To multiply a mixed number by a whole number, we can multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number.

Multiplying the Whole Number Part

The whole number part of the mixed number is 2, and the whole number we are multiplying by is 4. To multiply these two whole numbers, we simply multiply them together.

2 × 4 = 8

Multiplying the Fraction Part

The fraction part of the mixed number is [\frac{3}{8}$, and we are multiplying it by the whole number 4. To multiply a fraction by a whole number, we multiply the numerator (the top number) by the whole number, and then keep the denominator (the bottom number) the same.

3 × 4 = 12

So, the fraction part of the mixed number becomes [\frac{12}{8}$.

Simplifying the Fraction

The fraction [\frac{12}{8}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 12 and 8 is 4.

12 ÷ 4 = 3 8 ÷ 4 = 2

So, the simplified fraction is [\frac{3}{2}$.

Combining the Whole Number Part and the Simplified Fraction

Now that we have the product of the whole number part (8) and the simplified fraction [\frac{3}{2}$, we can combine them to get the final answer.

8 + [\frac{3}{2}}$

To add a whole number and a fraction, we need to find a common denominator for the whole number and the fraction. In this case, the common denominator is 2.

8 = ${\frac{16}{2}}$

Now we can add the whole number and the fraction:

${\frac{16}{2}}$ + ${\frac{3}{2}}$ = ${\frac{19}{2}}$

Conclusion

In conclusion, the product of $ $2 \frac{3}{8} \times 4\$}$ is ${\frac{19}{2}$. This can be written as a mixed number **9 \frac{1{2}$.

Final Answer

The final answer is: **9 \frac{1}{2}$.

Frequently Asked Questions

Q: What is the product of [ $2 \frac{3}{8} \times 4}$ ?

A: The product of ${ $2 \frac{3}{8} \times 4}$ is ${\frac{19}{2}$.

Q: How do I multiply a mixed number by a whole number?

A: To multiply a mixed number by a whole number, multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

Step-by-Step Solution

Multiply the whole number part of the mixed number by the whole number: 2 × 4 = 8
Multiply the fraction part of the mixed number by the whole number: 3 × 4 = 12
Simplify the fraction: [\frac{12}{8}}$ = ${\frac{3}{2}}$
Combine the whole number part and the simplified fraction: 8 + ${\frac{3}{2}}$ = ${\frac{19}{2}}$

References

Introduction

In our previous article, we discussed how to calculate the product of a mixed number and a whole number, specifically ${$2 \frac{3}{8} \times 4$. We also provided a step-by-step solution and related topics. In this article, we will answer some frequently asked questions about mixed numbers and multiplication.

Q&A

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is often used to represent quantities that are not whole, but can be expressed as a sum of a whole number and a fraction.

Q: How do I multiply a mixed number by a whole number?

A: To multiply a mixed number by a whole number, multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number.

Q: How do I simplify a fraction?

A: To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the product of [ $2 \frac{3}{8} \times 4}$ ?

A: The product of ${ $2 \frac{3}{8} \times 4}$ is ${\frac{19}{2}$.

Q: How do I add a whole number and a fraction?

A: To add a whole number and a fraction, find a common denominator for the whole number and the fraction. Then, add the numerators and keep the denominator the same.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

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

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator, and then add the numerator. The result is the new numerator, and the denominator remains the same.

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

A: To convert an improper fraction to a mixed number, divide the numerator by the denominator, and then write the remainder as the new numerator. The result is the new whole number part, and the denominator remains the same.

Examples

Example 1: Multiplying a Mixed Number by a Whole Number

[ $2 \frac{3}{8} \times 4}$

To solve this problem, we multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number.

2 × 4 = 8 3 × 4 = 12

So, the product of ${ $2 \frac{3}{8} \times 4}$ is ${\frac{12}{8}$.

Example 2: Simplifying a Fraction

[\frac{12}{8}}$

To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor (GCD).

12 ÷ 4 = 3 8 ÷ 4 = 2

So, the simplified fraction is ${\frac{3}{2}$.

Example 3: Adding a Whole Number and a Fraction

[\frac{3}{2} + 2}$

To solve this problem, we find a common denominator for the whole number and the fraction. Then, we add the numerators and keep the denominator the same.

2 = ${\frac{4}{2}}$

So, the sum of ${\frac{3}{2} + 2}$ is [\frac{7}{2}$.

Conclusion

In conclusion, mixed numbers and multiplication can be a bit tricky, but with practice and patience, you can become proficient in solving these types of problems. Remember to multiply the whole number part of the mixed number by the whole number, and then multiply the fraction part of the mixed number by the whole number. Don't forget to simplify the fraction and add the whole number and the fraction if necessary.

Final Answer

The final answer is: **9 \frac{1}{2}$.