Understanding Whole Numbers and Fractions

Oct 13, 2025 by miodeya.com 2 views

Introduction

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 whole numbers and fractions, it's essential to understand the rules and procedures to arrive at the correct answer. In this article, we will explore the product of 15 and $\frac{5}{12}$ , and we will examine the different options provided to determine the correct answer.

Understanding Whole Numbers and Fractions

Before we dive into the multiplication problem, let's briefly review the concepts of whole numbers and fractions.

Whole Numbers: Whole numbers are positive integers that do not contain any fractional parts. Examples of whole numbers include 1, 2, 3, 4, and so on.
Fractions: Fractions are numbers that represent a part of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). For example, $\frac{1}{2}$ represents one-half of a whole, while $\frac{3}{4}$ represents three-quarters of a whole.

Multiplying Whole Numbers and Fractions

When multiplying a whole number by a fraction, we need to multiply the whole number by the numerator and then divide the result by the denominator. This is based on the rule that a/b * c = (a * c) / b.

Step-by-Step Solution

Now, let's apply this rule to the problem at hand: multiplying 15 by $\frac{5}{12}$ .

Multiply the whole number by the numerator: 15 * 5 = 75
Divide the result by the denominator: 75 ÷ 12 = 6.25

Converting the Result to a Mixed Number

To express the result as a mixed number, we need to separate the whole number part from the fractional part. In this case, the whole number part is 6, and the fractional part is $\frac{1}{4}$ .

Therefore, the product of 15 and $\frac{5}{12}$ is $6 \frac{1}{4}$ .

Conclusion

In conclusion, when multiplying a whole number by a fraction, we need to multiply the whole number by the numerator and then divide the result by the denominator. By applying this rule to the problem at hand, we arrived at the correct answer: $6 \frac{1}{4}$ . This result is consistent with the options provided, and we can confidently select option B as the correct answer.

Final Answer

Q: What is the rule for multiplying a whole number by a fraction?

A: The rule for multiplying a whole number by a fraction is to multiply the whole number by the numerator and then divide the result by the denominator. This is based on the rule that a/b * c = (a * c) / b.

Q: How do I convert the result of a multiplication problem involving a whole number and a fraction to a mixed number?

A: To convert the result to a mixed number, you need to separate the whole number part from the fractional part. For example, if the result is 75 ÷ 12 = 6.25, you can express it as $6 \frac{1}{4}$ .

Q: What if the result of a multiplication problem involving a whole number and a fraction is a decimal?

A: If the result is a decimal, you can convert it to a mixed number by separating the whole number part from the fractional part. For example, if the result is 75 ÷ 12 = 6.25, you can express it as $6 \frac{1}{4}$ .

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

A: Yes, you can multiply a fraction by a whole number using a calculator. Simply enter the fraction and the whole number into the calculator, and it will perform the multiplication and display the result.

Q: What if I need to multiply a whole number by a fraction with a negative sign?

A: If you need to multiply a whole number by a fraction with a negative sign, you can simply multiply the whole number by the numerator and then divide the result by the denominator, just like you would with a positive fraction. The negative sign will be carried over to the result.

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

A: No, you cannot multiply a whole number by a fraction with a zero denominator. This is because division by zero is undefined in mathematics.

Q: What if I need to multiply a whole number by a fraction with a decimal numerator or denominator?

A: If you need to multiply a whole number by a fraction with a decimal numerator or denominator, you can simply multiply the whole number by the numerator and then divide the result by the denominator, just like you would with a fraction with integer numerator and denominator.

Q: Can I use a formula to multiply a whole number by a fraction?

A: Yes, you can use a formula to multiply a whole number by a fraction. The formula is:

a/b * c = (a * c) / b

where a is the numerator, b is the denominator, and c is the whole number.

Q: What if I need to multiply a whole number by a fraction with a variable numerator or denominator?

A: If you need to multiply a whole number by a fraction with a variable numerator or denominator, you can simply multiply the whole number by the numerator and then divide the result by the denominator, just like you would with a fraction with integer numerator and denominator.

Conclusion

In conclusion, multiplying whole numbers and fractions can be a bit tricky, but with the right rules and procedures, you can arrive at the correct answer. By following the steps outlined in this article, you can confidently multiply whole numbers and fractions and convert the results to mixed numbers.