Multiply the Numerator and the Whole Number

Oct 13, 2025 by thesweetdesigns.com 7 views

Introduction

In mathematics, multiplying a whole number by a fraction can be a bit tricky, but with the right approach, it can be a breeze. In this article, we will explore the concept of multiplying a whole number by a fraction and provide a step-by-step guide on how to do it. We will also apply this concept to a specific problem, which is to find the product of 15 and $$\frac{5}{12}$$.

What is Multiplication?

Multiplication is a mathematical operation that involves adding a number a certain number of times. For example, 3 × 4 means adding 3 together 4 times: 3 + 3 + 3 + 3 = 12. In the case of multiplying a whole number by a fraction, we need to add the fraction a certain number of times, where the number of times is determined by the whole number.

Multiplying a Whole Number by a Fraction: A Step-by-Step Guide

To multiply a whole number by a fraction, we need to follow these steps:

Multiply the Numerator and the Whole Number: Multiply the numerator of the fraction by the whole number.
Keep the Denominator the Same: Keep the denominator of the fraction the same.
Simplify the Result: Simplify the result by dividing the numerator and the denominator by their greatest common divisor (GCD).

Applying the Steps to the Problem

Now, let's apply these steps to the problem of finding the product of 15 and $$\frac{5}{12}$$.

Step 1: Multiply the Numerator and the Whole Number

To multiply the numerator and the whole number, we need to multiply 5 (the numerator) by 15 (the whole number).

5 × 15 = 75

Step 2: Keep the Denominator the Same

The denominator of the fraction is 12, so we keep it the same.

Step 3: Simplify the Result

To simplify the result, we need to divide the numerator and the denominator by their GCD. The GCD of 75 and 12 is 3.

75 ÷ 3 = 25 12 ÷ 3 = 4

So, the simplified result is $$\frac{25}{4}$$.

Converting the Result to a Mixed Number

To convert the result to a mixed number, we need to divide the numerator by the denominator.

25 ÷ 4 = 6 with a remainder of 1

So, the result is $$6 \frac{1}{4}$$.

Conclusion

In conclusion, multiplying a whole number by a fraction involves multiplying the numerator and the whole number, keeping the denominator the same, and simplifying the result. By following these steps, we can find the product of 15 and $$\frac{5}{12}$$, which is $$6 \frac{1}{4}$$.

Answer

The correct answer is:

B. $$6 \frac{1}{4}$$

Final Thoughts

$Multiplying a whole number by a fraction can be a bit tricky, but with the right approach, it can be a breeze. By following the steps outlined in this article, you can find the product of any whole number and fraction. Remember to multiply the numerator and the whole number, keep the denominator the same, and simplify the result. With practice, you will become more comfortable with this concept and be able to apply it to more complex problems.<br/> **Multiplying a Whole Number by a Fraction: A Q&A Guide**$

Introduction

In our previous article, we explored the concept of multiplying a whole number by a fraction and provided a step-by-step guide on how to do it. In this article, we will answer some frequently asked questions (FAQs) related to multiplying a whole number by a fraction.

Q&A

Q: What is the product of 12 and $$\frac{3}{4}$$?

A: To find the product, we need to multiply the numerator and the whole number, keep the denominator the same, and simplify the result.

12 × 3 = 36 Keep the denominator the same: $$\frac{36}{4}$$ Simplify the result: 36 ÷ 4 = 9

So, the product is 9.

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

A: To multiply a whole number by a fraction with a negative sign, we need to follow the same steps as before, but we need to remember that a negative sign is just a placeholder. When we multiply a negative number by a positive number, the result is negative.

For example, to find the product of -15 and $$\frac{2}{3}$$, we need to multiply the numerator and the whole number, keep the denominator the same, and simplify the result.

-15 × 2 = -30 Keep the denominator the same: $$\frac{-30}{3}$$ Simplify the result: -30 ÷ 3 = -10

So, the product is -10.

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

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

For example, to find the product of 15 and 0.5, we need to convert 0.5 to a fraction.

0.5 = $$\frac{1}{2}$$

Now, we can multiply the whole number by the fraction.

15 × $$\frac{1}{2}$$ = $$\frac{15}{2}$$

So, the product is $$\frac{15}{2}$$.

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

A: To multiply a whole number by a fraction with a variable, we need to follow the same steps as before, but we need to remember that the variable is just a placeholder. When we multiply a variable by a number, we need to multiply the variable by the number.

For example, to find the product of 12 and $$\frac{x}{4}$$, we need to multiply the numerator and the whole number, keep the denominator the same, and simplify the result.

12 × x = 12x Keep the denominator the same: $$\frac{12x}{4}$$ Simplify the result: 12x ÷ 4 = 3x

So, the product is 3x.

Conclusion

In conclusion, multiplying a whole number by a fraction can be a bit tricky, but with the right approach, it can be a breeze. By following the steps outlined in this article, you can answer any question related to multiplying a whole number by a fraction. Remember to multiply the numerator and the whole number, keep the denominator the same, and simplify the result. With practice, you will become more comfortable with this concept and be able to apply it to more complex problems.

Final Thoughts

Multiplying a whole number by a fraction is an essential concept in mathematics, and it has many real-world applications. By mastering this concept, you can solve problems in various fields, such as science, engineering, and finance. So, keep practicing, and you will become a pro at multiplying whole numbers by fractions in no time!