Multiply. Write Your Answer As A Fraction In Simplest Form.$\frac{5}{4} \times \frac{10}{9}$

Introduction

In mathematics, multiplication of fractions is a fundamental operation that involves multiplying two or more fractions together. When multiplying fractions, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately. In this article, we will explore the concept of multiplying fractions, with a focus on the multiplication of two fractions: $\frac{5}{4} \times \frac{10}{9}$.

What is a Fraction?

A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator (the number on top) and the denominator (the number on the bottom). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into. For example, the fraction $\frac{3}{4}$ represents three equal parts out of a total of four parts.

Multiplying Fractions: A Step-by-Step Guide

To multiply fractions, we need to follow a simple step-by-step process:

1. Multiply the Numerators: Multiply the numerators of the two fractions together.
2. Multiply the Denominators: Multiply the denominators of the two fractions together.
3. Simplify the Result: Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Example: Multiplying $\frac{5}{4} \times \frac{10}{9}$

Let's apply the step-by-step process to multiply the fractions $\frac{5}{4} \times \frac{10}{9}$.

Step 1: Multiply the Numerators

Multiply the numerators of the two fractions together: $5 \times 10 = 50$.

Step 2: Multiply the Denominators

Multiply the denominators of the two fractions together: $4 \times 9 = 36$.

Step 3: Simplify the Result

The resulting fraction is $\frac{50}{36}$. To simplify this fraction, we need to find the greatest common divisor (GCD) of 50 and 36. The GCD of 50 and 36 is 2. Therefore, we can simplify the fraction by dividing both the numerator and the denominator by 2:

$\frac{50}{36} = \frac{50 \div 2}{36 \div 2} = \frac{25}{18}$

Conclusion

In conclusion, multiplying fractions involves multiplying the numerators and denominators separately and then simplifying the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). By following this step-by-step process, we can multiply fractions with ease and accuracy.

Common Mistakes to Avoid

When multiplying fractions, it's essential to avoid common mistakes such as:

• Not multiplying the numerators and denominators separately: Make sure to multiply the numerators and denominators separately to avoid errors.
• Not simplifying the resulting fraction: Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
• Not using the correct order of operations: Use the correct order of operations (PEMDAS) when multiplying fractions.

Real-World Applications

Multiplying fractions has numerous real-world applications, including:

• Cooking: When cooking, we often need to multiply fractions to scale up or down a recipe.
• Science: In science, we often need to multiply fractions to calculate concentrations or rates.
• Finance: In finance, we often need to multiply fractions to calculate interest rates or investment returns.

Practice Problems

To practice multiplying fractions, try the following problems:

• $\frac{3}{4} \times \frac{5}{6}$
• $\frac{2}{3} \times \frac{7}{8}$
• $\frac{4}{5} \times \frac{9}{10}$

Conclusion

Introduction

In our previous article, we explored the concept of multiplying fractions, with a focus on the multiplication of two fractions: $\frac{5}{4} \times \frac{10}{9}$. In this article, we will answer some of the most frequently asked questions about multiplying fractions.

Q&A

Q: What is the rule for multiplying fractions?

A: The rule for multiplying fractions is to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately.

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to multiply the numerators and denominators separately and then simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

A: Yes, you can multiply a fraction by a whole number. To do this, simply multiply the numerator of the fraction by the whole number and keep the denominator the same.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

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

A: Multiplying fractions involves multiplying the numerators and denominators separately, while adding fractions involves finding a common denominator and adding the numerators.

Q: Can I multiply a negative fraction by a positive fraction?

A: Yes, you can multiply a negative fraction by a positive fraction. The result will be a negative fraction.

Q: How do I multiply fractions with decimals?

A: To multiply fractions with decimals, you need to convert the decimals to fractions and then multiply the fractions.

Q: Can I multiply a fraction by a percentage?

A: Yes, you can multiply a fraction by a percentage. To do this, simply multiply the numerator of the fraction by the percentage and keep the denominator the same.

Q: How do I multiply fractions with variables?

A: To multiply fractions with variables, you need to multiply the numerators and denominators separately and then simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Q: Can I multiply a fraction by a mixed number?

A: Yes, you can multiply a fraction by a mixed number. To do this, simply multiply the numerator of the fraction by the whole number part of the mixed number and keep the denominator the same.

Common Mistakes to Avoid

When multiplying fractions, it's essential to avoid common mistakes such as:

• Not multiplying the numerators and denominators separately: Make sure to multiply the numerators and denominators separately to avoid errors.
• Not simplifying the resulting fraction: Simplify the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
• Not using the correct order of operations: Use the correct order of operations (PEMDAS) when multiplying fractions.

Real-World Applications

Multiplying fractions has numerous real-world applications, including:

• Cooking: When cooking, we often need to multiply fractions to scale up or down a recipe.
• Science: In science, we often need to multiply fractions to calculate concentrations or rates.
• Finance: In finance, we often need to multiply fractions to calculate interest rates or investment returns.

Practice Problems

To practice multiplying fractions, try the following problems:

• $\frac{3}{4} \times \frac{5}{6}$
• $\frac{2}{3} \times \frac{7}{8}$
• $\frac{4}{5} \times \frac{9}{10}$

Conclusion

In conclusion, multiplying fractions is a fundamental operation in mathematics that involves multiplying the numerators and denominators separately and then simplifying the resulting fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). By following this step-by-step process and avoiding common mistakes, we can multiply fractions with ease and accuracy.