Write the resulting fraction

Oct 13, 2025 by wbrum.org 110 views

$Write the resulting fraction$

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Introduction

Multiplying fractions is a fundamental concept in mathematics that helps us solve various problems in different fields, such as science, engineering, and finance. In this article, we will explore the concept of multiplying fractions, provide a step-by-step guide on how to do it, and offer examples to illustrate the process.

What are Fractions?

A fraction is a way to represent a part of a whole. It consists of two numbers: a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into.

Example

For instance, the fraction 3/4 represents 3 equal parts out of a total of 4 parts.

Multiplying Fractions

To multiply fractions, we simply multiply the numerators together and multiply the denominators together. The resulting fraction is then simplified to its simplest form.

Formula

The formula for multiplying fractions is:

(a/b) × (c/d) = (ac)/(bd)

where a, b, c, and d are the numerators and denominators of the fractions.

Step-by-Step Guide

Here's a step-by-step guide on how to multiply fractions:

Multiply the numerators: Multiply the top numbers of the two fractions together.
Multiply the denominators: Multiply the bottom numbers of the two fractions together.
Write the resulting fraction: Write the product of the numerators as the new numerator and the product of the denominators as the new denominator.
Simplify the fraction: Simplify the resulting fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Example

Let's multiply the fractions 9/4 and 2/7 using the step-by-step guide:

Multiply the numerators: 9 × 2 = 18
Multiply the denominators: 4 × 7 = 28
Write the resulting fraction: 18/28
Simplify the fraction: The GCD of 18 and 28 is 2. Divide both the numerator and the denominator by 2 to get the simplified fraction: 9/14

Tips and Tricks

Here are some tips and tricks to help you multiply fractions like a pro:

Use a common denominator: When multiplying fractions, it's often helpful to use a common denominator to make the multiplication process easier.
Simplify before multiplying: Simplify the fractions before multiplying them to avoid unnecessary calculations.
Use a calculator: If you're struggling to multiply fractions by hand, use a calculator to get the answer quickly and accurately.

Real-World Applications

Multiplying fractions has many real-world applications, such as:

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 or the volume of a container.
Finance: In finance, you may need to multiply fractions to calculate interest rates or investment returns.

Conclusion

Multiplying fractions is a fundamental concept in mathematics that helps us solve various problems in different fields. By following the step-by-step guide and tips and tricks outlined in this article, you'll be able to multiply fractions like a pro and apply the concept to real-world situations.

Final Thoughts

Multiplying fractions is a skill that takes practice to develop. With patience and persistence, you'll become proficient in multiplying fractions and be able to tackle complex problems with confidence.

References

For further reading on multiplying fractions, check out the following resources:

Khan Academy: Multiplying Fractions
Mathway: Multiplying Fractions
Wolfram Alpha: Multiplying Fractions

If you're interested in learning more about fractions, check out the following related articles:

Adding and Subtracting Fractions
Dividing Fractions
Simplifying Fractions

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Introduction

Multiplying fractions can be a challenging concept for many students. In this article, we will address some of the most frequently asked questions about multiplying fractions, providing clear and concise answers to help you better understand the concept.

Q&A

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is (a/b) × (c/d) = (ac)/(bd), where a, b, c, and d are the numerators and denominators of the fractions.

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then multiply the numerators and denominators accordingly.

Q: Can I multiply fractions with negative numbers?

A: Yes, you can multiply fractions with negative numbers. When multiplying fractions with negative numbers, the result will also be negative.

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 denominator and divide both numbers by the GCD.

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

A: Multiplying fractions and multiplying decimals are two different operations. Multiplying fractions involves multiplying the numerators and denominators separately, while multiplying decimals involves multiplying the numbers as is.

Q: Can I use a calculator to multiply fractions?

A: Yes, you can use a calculator to multiply fractions. However, it's always a good idea to double-check your answer to ensure it's correct.

Q: How do I multiply fractions with variables?

A: To multiply fractions with variables, you need to multiply the variables separately and then multiply the fractions as usual.

Q: Can I multiply fractions with mixed numbers?

A: Yes, you can multiply fractions with mixed numbers. To do this, you need to convert the mixed numbers to improper fractions and then multiply the fractions as usual.

Q: How do I multiply fractions with exponents?

A: To multiply fractions with exponents, you need to multiply the exponents separately and then multiply the fractions as usual.

Examples

Example 1: Multiplying Fractions with Different Denominators

Multiply the fractions 3/4 and 5/6.

Find the LCM of 4 and 6, which is 12.
Multiply the numerators: 3 × 5 = 15
Multiply the denominators: 4 × 6 = 24
Write the resulting fraction: 15/24
Simplify the fraction: The GCD of 15 and 24 is 3. Divide both the numerator and the denominator by 3 to get the simplified fraction: 5/8

Example 2: Multiplying Fractions with Negative Numbers

Multiply the fractions -3/4 and -2/5.

Multiply the numerators: -3 × -2 = 6
Multiply the denominators: 4 × 5 = 20
Write the resulting fraction: 6/20
Simplify the fraction: The GCD of 6 and 20 is 2. Divide both the numerator and the denominator by 2 to get the simplified fraction: 3/10

Example 3: Multiplying Fractions with Variables

Multiply the fractions 2x/3 and 4y/5.

Multiply the numerators: 2x × 4y = 8xy
Multiply the denominators: 3 × 5 = 15
Write the resulting fraction: 8xy/15