Calculate The Following: 2 9 × 3 = \frac{2}{9} \times 3 = 9 2 × 3 =

Mar 13, 2025 by ADMIN 70 views

**Multiplication of Fractions: A Step-by-Step Guide**

Introduction

In mathematics, fractions are a way to represent a part of a whole. When we multiply fractions, we are essentially finding the product of two or more fractions. In this article, we will focus on calculating the product of a fraction and a whole number. We will use the example of $\frac{2}{9} \times 3$ to demonstrate the step-by-step process.

Understanding the Problem

The problem we are trying to solve is $\frac{2}{9} \times 3$ . To solve this problem, we need to understand the concept of multiplying fractions by whole numbers. When we multiply a fraction by a whole number, we can simply multiply the numerator of the fraction by the whole number.

Step 1: Multiply the Numerator

The first step in solving the problem is to multiply the numerator of the fraction by the whole number. In this case, the numerator is 2 and the whole number is 3. So, we multiply 2 by 3 to get 6.

Step 2: Keep the Denominator the Same

When we multiply a fraction by a whole number, the denominator of the fraction remains the same. In this case, the denominator is 9, so we keep it the same.

Step 3: Write the Product as a Fraction

Now that we have multiplied the numerator and kept the denominator the same, we can write the product as a fraction. In this case, the product is $\frac{6}{9}$ .

Simplifying the Fraction

The fraction $\frac{6}{9}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 6 and 9 is 3. So, we divide both 6 and 9 by 3 to get $\frac{2}{3}$ .

Conclusion

In conclusion, to calculate the product of a fraction and a whole number, we simply multiply the numerator of the fraction by the whole number and keep the denominator the same. We can then write the product as a fraction and simplify it by dividing both the numerator and the denominator by their GCD.

Real-World Applications

Multiplying fractions by whole numbers has many real-world applications. For example, in cooking, we may need to multiply a recipe by a certain number of people. In this case, we would multiply the ingredients by the number of people to get the correct amount. Similarly, in construction, we may need to multiply the amount of materials needed by the number of buildings being constructed.

Tips and Tricks

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

Always multiply the numerator by the whole number.
Keep the denominator the same.
Write the product as a fraction.
Simplify the fraction by dividing both the numerator and the denominator by their GCD.

Common Mistakes

Here are some common mistakes to avoid when multiplying fractions by whole numbers:

Not multiplying the numerator by the whole number.
Changing the denominator.
Not writing the product as a fraction.
Not simplifying the fraction.

Practice Problems

Here are some practice problems to help you practice multiplying fractions by whole numbers:

$\frac{3}{4} \times 2 =$
$\frac{5}{6} \times 3 =$
$\frac{7}{8} \times 4 =$

Answer Key

Here are the answers to the practice problems:

$\frac{3}{4} \times 2 = \frac{6}{4} = \frac{3}{2}$
$\frac{5}{6} \times 3 = \frac{15}{6} = \frac{5}{2}$
$\frac{7}{8} \times 4 = \frac{28}{8} = \frac{7}{2}$
Multiplication of Fractions: A Q&A Guide =====================================================

Introduction

In our previous article, we discussed the concept of multiplying fractions by whole numbers. We provided a step-by-step guide on how to calculate the product of a fraction and a whole number. In this article, we will answer some frequently asked questions (FAQs) related to multiplying fractions by whole numbers.

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

A: The rule for multiplying fractions by whole numbers is to multiply the numerator of the fraction by the whole number and keep the denominator the same. The product can then be written as a fraction and simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

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

Multiply the numerator of the fraction by the whole number.
Keep the denominator the same.
Write the product as a fraction.
Simplify the fraction by dividing both the numerator and the denominator by their GCD.

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

A: The main difference between multiplying fractions and multiplying whole numbers is that when multiplying fractions, we multiply the numerator by the whole number and keep the denominator the same. When multiplying whole numbers, we simply multiply the two numbers together.

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, convert the decimal to a fraction and then multiply the fraction by the fraction.

Q: How do I simplify a fraction after multiplying it by a whole number?

A: To simplify a fraction after multiplying it by a whole number, divide both the numerator and the denominator by their 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 without leaving a remainder.

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

A: To find the GCD of two numbers, list the factors of each number and find the largest factor that they have in common.

Q: Can I multiply a negative fraction by a whole number?

A: Yes, you can multiply a negative fraction by a whole number. When multiplying a negative fraction by a whole number, the product will be negative.

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

A: To multiply a fraction by a fraction, multiply the numerators together and multiply the denominators together. The product can then be simplified by dividing both the numerator and the denominator by their GCD.

Q: What is the difference between multiplying fractions and dividing fractions?

A: The main difference between multiplying fractions and dividing fractions is that when multiplying fractions, we multiply the numerators together and multiply the denominators together. When dividing fractions, we invert the second fraction and multiply.