Mastering Fraction Multiplication- A Step-by-Step Guide to Multiplying Mixed Numbers

How to Multiply Fractions with a Mixed Number

Multiplying fractions with a mixed number can be a challenging task, especially for those who are new to the concept. However, with a clear understanding of the process and some practice, you can easily master this skill. In this article, we will guide you through the steps to multiply fractions with a mixed number, ensuring that you can confidently solve such problems in no time.

Understanding Mixed Numbers

Before we dive into the multiplication process, it’s essential to have a solid grasp of what a mixed number is. A mixed number consists of a whole number and a fraction. For example, 2 1/3 is a mixed number, where 2 is the whole number and 1/3 is the fraction.

Converting Mixed Numbers to Improper Fractions

To multiply a fraction with a mixed number, you first need to convert the mixed number into an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, follow these steps:

1. Multiply the whole number by the denominator of the fraction.
2. Add the result to the numerator of the fraction.
3. Write the sum as the numerator of the improper fraction, keeping the denominator the same.

For example, let’s convert the mixed number 2 1/3 to an improper fraction:

1. Multiply the whole number (2) by the denominator (3): 2 3 = 6.
2. Add the result (6) to the numerator (1): 6 + 1 = 7.
3. Write the sum (7) as the numerator of the improper fraction, keeping the denominator (3) the same: 7/3.

Now that we have the mixed number as an improper fraction, we can proceed to multiply it with another fraction.

Multiplying Fractions with an Improper Fraction

To multiply fractions with an improper fraction, simply multiply the numerators together and the denominators together. Let’s take the example of multiplying the fraction 3/4 with the improper fraction 7/3:

1. Multiply the numerators: 3 7 = 21.
2. Multiply the denominators: 4 3 = 12.
3. Write the product of the numerators (21) over the product of the denominators (12): 21/12.

Now, we have the product of the fractions. However, we can simplify the result by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. In this case, the GCD of 21 and 12 is 3:

1. Divide the numerator (21) by the GCD (3): 21 ÷ 3 = 7.
2. Divide the denominator (12) by the GCD (3): 12 ÷ 3 = 4.

The simplified fraction is 7/4, which can be written as a mixed number if desired:

1. Divide the numerator (7) by the denominator (4): 7 ÷ 4 = 1 with a remainder of 3.
2. Write the whole number (1) and the remainder (3) as the numerator of the fraction: 1 3/4.

So, the product of 3/4 and 7/3 is 1 3/4.

Conclusion

Multiplying fractions with a mixed number may seem daunting at first, but by following these steps and practicing, you can become proficient in this skill. Remember to convert the mixed number to an improper fraction, multiply the numerators and denominators, and simplify the result if necessary. With time and practice, you’ll be able to solve these problems with ease.