Calculate The Product: 5 6 × 3 4 = 15 24 \frac{5}{6} \times \frac{3}{4} = \frac{15}{24} 6 5 ​ × 4 3 ​ = 24 15 ​

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Introduction

In mathematics, fractions are used to represent a part of a whole. When we multiply fractions, we are essentially finding the product of two or more parts of a whole. In this article, we will explore the concept of multiplying fractions and provide a step-by-step guide on how to calculate the product of two fractions.

What are Fractions?

A fraction is a way of representing a part of a whole. It consists of two parts: the numerator and the denominator. The numerator is the top number, and the denominator is the bottom number. For example, the fraction 3/4 represents 3 parts out of a total of 4 parts.

Multiplying Fractions

When we multiply fractions, we multiply the numerators together and the denominators together. This is represented by the following formula:

a/b × c/d = (a × c) / (b × d)

Example: Calculating the Product of Two Fractions

Let's use the example given in the problem statement: 56×34=1524\frac{5}{6} \times \frac{3}{4} = \frac{15}{24}.

To calculate the product of these two fractions, we multiply the numerators together and the denominators together:

5/6 × 3/4 = (5 × 3) / (6 × 4)

Step 1: Multiply the Numerators

The first step is to multiply the numerators together. In this case, we multiply 5 and 3:

5 × 3 = 15

Step 2: Multiply the Denominators

The next step is to multiply the denominators together. In this case, we multiply 6 and 4:

6 × 4 = 24

Step 3: Write the Product as a Fraction

Now that we have multiplied the numerators and denominators together, we can write the product as a fraction:

15/24

Simplifying the Fraction

In this case, the fraction 15/24 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 15 and 24 is 3.

15 ÷ 3 = 5 24 ÷ 3 = 8

Therefore, the simplified fraction is:

5/8

Conclusion

In this article, we have explored the concept of multiplying fractions and provided a step-by-step guide on how to calculate the product of two fractions. We have used the example given in the problem statement to demonstrate the process of multiplying fractions and simplifying the result.

Common Mistakes to Avoid

When multiplying fractions, it is essential to remember the following common mistakes to avoid:

  • Not multiplying the numerators and denominators together: Make sure to multiply the numerators and denominators together to get the correct product.
  • Not simplifying the fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • Not checking for common factors: Check for common factors between the numerator and the denominator to simplify the fraction.

Real-World Applications

Multiplying fractions has many real-world applications, including:

  • Cooking: When cooking, you may need to multiply fractions to scale up or down a recipe.
  • Science: In science, you may need to multiply fractions to calculate the concentration of a solution.
  • Finance: In finance, you may need to multiply fractions to calculate interest rates or investment returns.

Practice Problems

To practice multiplying fractions, try the following problems:

  • 23×45=??\frac{2}{3} \times \frac{4}{5} = \frac{?}{?}
  • 34×23=??\frac{3}{4} \times \frac{2}{3} = \frac{?}{?}
  • 56×34=??\frac{5}{6} \times \frac{3}{4} = \frac{?}{?}

Conclusion

Introduction

In our previous article, we explored the concept of multiplying fractions and provided a step-by-step guide on how to calculate the product of two fractions. In this article, we will answer some frequently asked questions about multiplying fractions to help you better understand this concept.

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is:

a/b × c/d = (a × c) / (b × d)

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to multiply the numerators together and the denominators together. For example:

3/4 × 5/6 = (3 × 5) / (4 × 6)

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

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

3/4 × 2 = (3 × 2) / 4 = 6/4

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. For example:

15/24 = (15 ÷ 3) / (24 ÷ 3) = 5/8

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

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

3/4 + 5/6 = ?

To add these fractions, you need to find a common denominator, which is 12. Then, you can add the numerators together:

(3 × 3) / 12 + (5 × 2) / 12 = 9/12 + 10/12 = 19/12

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. For example:

-3/4 × 2/3 = (-3 × 2) / (4 × 3) = -6/12 = -1/2

Q: How do I multiply fractions with zero in the numerator or denominator?

A: If a fraction has zero in the numerator or denominator, the result will be zero. For example:

0/4 × 3/2 = 0

Q: Can I multiply a fraction by a fraction with a variable in the numerator or denominator?

A: Yes, you can multiply a fraction by a fraction with a variable in the numerator or denominator. The result will be a fraction with the variable in the numerator or denominator. For example:

x/4 × 3/y = (x × 3) / (4 × y) = 3x/4y

Conclusion

In conclusion, multiplying fractions is a fundamental concept in mathematics that has many real-world applications. By following the step-by-step guide and answering the frequently asked questions in this article, you can become proficient in multiplying fractions and simplify the result. Remember to practice multiplying fractions to become more confident in your math skills.

Practice Problems

To practice multiplying fractions, try the following problems:

  • 23×45=??\frac{2}{3} \times \frac{4}{5} = \frac{?}{?}
  • 34×23=??\frac{3}{4} \times \frac{2}{3} = \frac{?}{?}
  • 56×34=??\frac{5}{6} \times \frac{3}{4} = \frac{?}{?}

Real-World Applications

Multiplying fractions has many real-world applications, including:

  • Cooking: When cooking, you may need to multiply fractions to scale up or down a recipe.
  • Science: In science, you may need to multiply fractions to calculate the concentration of a solution.
  • Finance: In finance, you may need to multiply fractions to calculate interest rates or investment returns.

Common Mistakes to Avoid

When multiplying fractions, it is essential to remember the following common mistakes to avoid:

  • Not multiplying the numerators and denominators together: Make sure to multiply the numerators and denominators together to get the correct product.
  • Not simplifying the fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
  • Not checking for common factors: Check for common factors between the numerator and the denominator to simplify the fraction.