Multiply the numerator by the whole number

Oct 13, 2025 by thesweetdesigns.com 91 views

Introduction

Multiplication of Fractions and Whole Numbers In mathematics, multiplication is a fundamental operation that involves the combination of two or more numbers to produce a product. When it comes to multiplying fractions and whole numbers, it's essential to understand the rules and procedures to obtain the correct result. In this article, we will focus on multiplying a fraction by a whole number, specifically the problem $\frac{5}{7} \times 28$ . We will break down the steps involved in solving this problem and provide a clear explanation of the process.

Understanding the Problem

The given problem is $\frac{5}{7} \times 28$ . 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 are essentially multiplying the numerator of the fraction by the whole number. The denominator of the fraction remains the same.

Multiplying the Numerator

To multiply the numerator, we simply multiply the whole number by the numerator of the fraction. In this case, we multiply 28 by 5.

Multiplication of 28 and 5 $28 \times 5 = 140$

Multiplying the Fraction

Now that we have multiplied the numerator, we can multiply the fraction by the whole number. To do this, we divide the product of the numerator by the original denominator.

Multiplication of the Fraction $\frac{5}{7} \times 28 = \frac{140}{7}$

Simplifying the Fraction

The fraction $\frac{140}{7}$ can be simplified by dividing the numerator by the denominator.

Simplification of the Fraction $\frac{140}{7} = 20$

Conclusion

In conclusion, multiplying a fraction by a whole number involves multiplying the numerator by the whole number and then dividing the product by the original denominator. In the problem $\frac{5}{7} \times 28$ , we multiplied the numerator by 28 and then divided the product by 7 to obtain the final result of 20.

Real-World Applications

Multiplying fractions by whole numbers has numerous real-world applications. For example, in cooking, you may need to multiply a recipe by a certain factor to produce a larger quantity of food. In this case, you would multiply the ingredients by the factor to obtain the correct amount. Similarly, in construction, you may need to multiply the dimensions of a building by a certain factor to produce a larger structure.

Tips and Tricks

When multiplying fractions by whole numbers, it's essential to follow the correct procedure to avoid errors. Here are some tips and tricks to help you:

Multiply the numerator by the whole number: When multiplying a fraction by a whole number, multiply the numerator by the whole number.
Divide the product by the denominator: After multiplying the numerator, divide the product by the original denominator to obtain the final result.
Simplify the fraction: If the fraction can be simplified, do so to obtain the final result.

Common Mistakes

When multiplying fractions by whole numbers, there are several common mistakes to avoid. Here are some of the most common mistakes:

Multiplying the denominator by the whole number: When multiplying a fraction by a whole number, do not multiply the denominator by the whole number. Instead, multiply the numerator by the whole number and then divide the product by the original denominator.
Not simplifying the fraction: If the fraction can be simplified, do not forget to simplify it to obtain the final result.

Conclusion

In conclusion, multiplying a fraction by a whole number involves multiplying the numerator by the whole number and then dividing the product by the original denominator. By following the correct procedure and avoiding common mistakes, you can obtain the correct result. Remember to simplify the fraction if possible to obtain the final result.

Final Answer

The final answer to the problem $\frac{5}{7} \times 28$ is $\boxed{20}$ .

References

[1] Khan Academy. (n.d.). Multiplying Fractions. Retrieved from <https://www.khanacademy.org/math/algebra/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c

Introduction

In our previous article, we discussed the problem of multiplying a fraction by a whole number, specifically the problem $\frac{5}{7} \times 28$ . We broke down the steps involved in solving this problem and provided a clear explanation of the process. In this article, we will answer some of the most frequently asked questions related to this topic.

Q&A

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

A: When multiplying a fraction by a whole number, you multiply the numerator by the whole number and then divide the product by the original denominator.

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 by the whole number.
Divide the product by the original denominator.

Q: What is the difference between multiplying a fraction by a whole number and multiplying two fractions?

A: When multiplying two fractions, you multiply the numerators and denominators separately. When multiplying a fraction by a whole number, you multiply the numerator by the whole number and then divide the product by the original denominator.

Q: Can I simplify the fraction after multiplying it by a whole number?

A: Yes, you can simplify the fraction after multiplying it by a whole number. If the fraction can be simplified, do so to obtain the final result.

Q: What are some common mistakes to avoid when multiplying fractions by whole numbers?

A: Some common mistakes to avoid when multiplying fractions by whole numbers include:

Multiplying the denominator by the whole number instead of multiplying the numerator.
Not simplifying the fraction after multiplying it by a whole number.

Q: How do I know if a fraction can be simplified?

A: A fraction can be simplified if the numerator and denominator have a common factor. To simplify a fraction, divide the numerator and denominator by the common factor.

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

A: Yes, you can use a calculator to multiply fractions by whole numbers. However, it's always a good idea to check your work by multiplying the numerator by the whole number and then dividing the product by the original denominator.

Real-World Applications

Multiplying fractions by whole numbers has numerous real-world applications. For example:

In cooking, you may need to multiply a recipe by a certain factor to produce a larger quantity of food.
In construction, you may need to multiply the dimensions of a building by a certain factor to produce a larger structure.
In finance, you may need to multiply a rate by a certain factor to produce a new rate.

Tips and Tricks

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

Use a multiplication chart: A multiplication chart can help you quickly multiply the numerator by the whole number.
Check your work: Always check your work by multiplying the numerator by the whole number and then dividing the product by the original denominator.
Simplify the fraction: If the fraction can be simplified, do so to obtain the final result.

Conclusion

Final Answer

The final answer to the problem $\frac{5}{7} \times 28$ is $\boxed{20}$ .

References

[1] Khan Academy. (n.d.). Multiplying Fractions. Retrieved from <https://www.khanacademy.org/math/algebra/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c7/x2f4f7c