Use Any Method To Multiply.Calculate $3 \times \frac{5}{8}$.

Introduction

Multiplication is a fundamental operation in mathematics that involves the repeated addition of a number. In this article, we will explore the method of multiplying a whole number by a fraction. We will use the given problem $3 \times \frac{5}{8}$ as an example to demonstrate the steps involved in multiplying a whole number by a fraction.

Understanding the Problem

The problem $3 \times \frac{5}{8}$ involves multiplying a whole number (3) by a fraction ($\frac{5}{8}$). To solve this problem, we need to understand the concept of multiplying fractions and whole numbers.

Multiplying Fractions and Whole Numbers

When multiplying a fraction by a whole number, we can multiply the numerator of the fraction by the whole number and keep the denominator the same. This is because the denominator represents the number of equal parts that the numerator is divided into.

Step-by-Step Solution

To solve the problem $3 \times \frac{5}{8}$, we can follow these steps:

Step 1: Multiply the Numerator by the Whole Number

The first step is to multiply the numerator (5) by the whole number (3).

5 × 3 = 15

Step 2: Keep the Denominator the Same

The denominator (8) remains the same.

Step 3: Write the Result as a Fraction

The result of multiplying the numerator by the whole number is 15. Since the denominator remains the same, we can write the result as a fraction: $\frac{15}{8}$.

Simplifying the Result

The fraction $\frac{15}{8}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 15 and 8 is 1, so the fraction cannot be simplified further.

Conclusion

In conclusion, multiplying a whole number by a fraction involves multiplying the numerator by the whole number and keeping the denominator the same. The result is a fraction that can be simplified by dividing both the numerator and the denominator by their greatest common divisor.

Real-World Applications

Multiplying fractions and whole numbers has many real-world applications. For example, in cooking, you may need to multiply a recipe by a fraction to make a larger or smaller batch of food. In science, you may need to multiply a measurement by a fraction to convert it to a different unit.

Practice Problems

Here are some practice problems to help you reinforce your understanding of multiplying fractions and whole numbers:

• $4 \times \frac{3}{5}$
• $2 \times \frac{7}{9}$
• $6 \times \frac{4}{7}$

Answer Key

• $4 \times \frac{3}{5} = \frac{12}{5}$
• $2 \times \frac{7}{9} = \frac{14}{9}$
• $6 \times \frac{4}{7} = \frac{24}{7}$

Common Mistakes

When multiplying fractions and whole numbers, it's easy to make mistakes. Here are some common mistakes to avoid:

• Forgetting to multiply the numerator by the whole number
• Keeping the denominator the same when it should be changed
• Not simplifying the result by dividing both the numerator and the denominator by their greatest common divisor

Tips and Tricks

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

• Use a multiplication chart to help you multiply the numerator by the whole number
• Keep the denominator the same until the end of the problem
• Simplify the result by dividing both the numerator and the denominator by their greatest common divisor

Conclusion

Introduction

In our previous article, we explored the method of multiplying a whole number by a fraction. We used the problem $3 \times \frac{5}{8}$ as an example to demonstrate the steps involved in multiplying a whole number by a fraction. In this article, we will answer some frequently asked questions (FAQs) about multiplying fractions and whole numbers.

Q&A

Q: What is the rule for multiplying fractions and whole numbers?

A: The rule for multiplying fractions and whole numbers is to multiply the numerator of the fraction by the whole number and keep the denominator the same.

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

A: To multiply a fraction by a whole number, follow these steps:

1. Multiply the numerator of the fraction by the whole number.
2. Keep the denominator the same.
3. Write the result as a fraction.

Q: Can I simplify the result of multiplying a fraction by a whole number?

A: Yes, you can simplify the result of multiplying a fraction by a whole number by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides both the numerator and the denominator of a fraction.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the following methods:

1. List the factors of each number and find the greatest common factor.
2. Use the Euclidean algorithm to find the GCD.
3. Use a calculator or online tool to find the GCD.

Q: Can I multiply a fraction by a fraction?

A: Yes, you can multiply a fraction by a fraction by multiplying the numerators and denominators separately.

Q: How do I multiply a fraction by a fraction?

A: To multiply a fraction by a fraction, follow these steps:

1. Multiply the numerators of the two fractions.
2. Multiply the denominators of the two fractions.
3. Write the result as a fraction.

Q: Can I simplify the result of multiplying two fractions?

A: Yes, you can simplify the result of multiplying two fractions by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

A: The main difference between multiplying fractions and whole numbers and multiplying fractions by fractions is that when multiplying fractions and whole numbers, you multiply the numerator by the whole number and keep the denominator the same. When multiplying fractions by fractions, you multiply the numerators and denominators separately.

Q: Can I use a calculator to multiply fractions and whole numbers?

A: Yes, you can use a calculator to multiply fractions and whole numbers. However, it's always a good idea to understand the concept and method of multiplying fractions and whole numbers to ensure accuracy.

Conclusion

In conclusion, multiplying fractions and whole numbers is a fundamental operation in mathematics that involves multiplying the numerator by the whole number and keeping the denominator the same. The result is a fraction that can be simplified by dividing both the numerator and the denominator by their greatest common divisor. We hope this Q&A article has helped you understand the concept and method of multiplying fractions and whole numbers.

Practice Problems

Here are some practice problems to help you reinforce your understanding of multiplying fractions and whole numbers:

• $4 \times \frac{3}{5}$
• $2 \times \frac{7}{9}$
• $6 \times \frac{4}{7}$
• $\frac{3}{4} \times \frac{5}{6}$
• $\frac{2}{3} \times \frac{4}{5}$

Answer Key

• $4 \times \frac{3}{5} = \frac{12}{5}$
• $2 \times \frac{7}{9} = \frac{14}{9}$
• $6 \times \frac{4}{7} = \frac{24}{7}$
• $\frac{3}{4} \times \frac{5}{6} = \frac{15}{24}$
• $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$