What is the Process for Multiplying a Fraction by a Whole Number

When it comes to multiplying a fraction by a whole number, there is a specific process that needs to be followed in order to obtain the correct result. This process involves understanding the concept of fractions and whole numbers, and how they interact with one another mathematically.

To begin with, let’s review what a fraction and a whole number represent. A fraction is a number that represents a part of a whole, and it consists of two parts – a numerator and a denominator. The numerator represents the number of parts we have, while the denominator represents the total number of equal parts that make up the whole. On the other hand, a whole number represents a complete and undivided unit.

Now, when we multiply a fraction by a whole number, we are essentially trying to find a certain number of parts of the original fraction. To do this, we multiply the numerator of the fraction by the whole number, while keeping the denominator the same. Let’s look at an example to illustrate this:

Consider the fraction 1/3 and the whole number 4. To multiply these, we would multiply the numerator (1) by the whole number (4), resulting in 4. Therefore, 1/3 multiplied by 4 is equal to 4/3.

However, it is important to note that the fraction obtained after multiplying a fraction by a whole number may not always be simplified. In the above example, 4/3 is not in its simplest form, as the numerator (4) and the denominator (3) share a common factor of 1. To simplify the fraction, we need to find the greatest common factor (GCF) of the numerator and the denominator, and divide both by that number. In this case, the GCF of 4 and 3 is 1, so dividing both the numerator and denominator by 1 results in the simplified fraction of 4/3.

Now that we understand the general process for multiplying a fraction by a whole number, let’s explore a few more examples to solidify this concept:

1. Multiply 1/2 by 3.
1/2 multiplied by 3 gives us (1 * 3) / 2, which simplifies to 3/2 or 1 1/2.

2. Multiply 2/5 by 6.
2/5 multiplied by 6 gives us (2 * 6) / 5, which simplifies to 12/5 or 2 2/5.

3. Multiply 3/4 by 9.
3/4 multiplied by 9 gives us (3 * 9) / 4, which simplifies to 27/4 or 6 3/4.

As you can see, by following the process of multiplying the numerator of the fraction by the whole number while keeping the denominator the same, we can find the desired result.

In conclusion, the process for multiplying a fraction by a whole number involves multiplying the numerator of the fraction by the whole number, while keeping the denominator the same. This allows us to find a certain number of parts of the original fraction. It is important to simplify the resulting fraction if possible by finding the greatest common factor and dividing both the numerator and denominator by that number. By understanding this process and practicing with various examples, one can confidently solve any multiplication problem involving fractions and whole numbers.