A Step-by-Step Guide to Multiplying Mixed Numbers

Multiplying mixed numbers can often be perceived as a daunting task for many students. However, with a step-by-step approach, this process can become much simpler and more manageable. In this article, we will guide you through the process of multiplying mixed numbers, providing clear explanations and examples along the way.

Step 1: Convert the mixed numbers to improper fractions.
To begin, convert each mixed number to an improper fraction. This can be done by multiplying the whole number by the denominator of the fraction, and then adding the result to the numerator. The denominator remains the same. For example, if we have the mixed number 2 ½, it would become 5/2 as an improper fraction.

Step 2: Multiply the numerators.
Once the mixed numbers have been converted to improper fractions, multiply the numerators together. This will give you the new numerator for the product.

Step 3: Multiply the denominators.
Similarly, multiply the denominators of the fractions together. This will give you the new denominator for the product.

Step 4: Simplify the fraction, if necessary.
After obtaining the product with the new numerator and denominator, check if it can be simplified. Simplifying the fraction means dividing both the numerator and the denominator by their greatest common factor (GCF). This will result in a fraction expressed in its simplest form.

Step 5: Convert the product to a mixed number, if desired.
If you prefer to express the product as a mixed number, you can convert it back from an improper fraction. This can be done by dividing the numerator by the denominator. The quotient will be the whole number, and the remainder will become the numerator. The denominator remains the same.

Let’s illustrate the steps with an example:
Suppose we want to multiply 3 ¼ by 2 ⅔.

Step 1: Convert the mixed numbers to improper fractions.
3 ¼ becomes 13/4, and 2 ⅔ becomes 8/3.

Step 2: Multiply the numerators.
13/4 * 8/3 = 104/12.

Step 3: Multiply the denominators.
The denominators, 4 and 3, are multiplied: 4 * 3 = 12.

Step 4: Simplify the fraction, if necessary.
In this case, the resulting fraction, 104/12, can be simplified. The GCF of 104 and 12 is 4. Dividing both the numerator and the denominator by 4 gives us 26/3.

Step 5: Convert the product to a mixed number, if desired.
The fraction 26/3 can be converted back to a mixed number. 26 divided by 3 equals 8 with a remainder of 2. Hence, the final result is 8 2/3.

By following these easy steps, you can master the skill of multiplying mixed numbers. Practicing various examples will enhance your proficiency and confidence in this area of mathematics. Remember to always check your work and simplify the fraction if possible. With time, you will become proficient in multiplying mixed numbers, and this operation will no longer be perceived as daunting but rather as an achievable task.