How do you multiply a number by a fraction? Multiplying a number by a fraction is a fundamental skill in mathematics that is essential for various calculations and problem-solving. Whether you are a student learning the basics or an adult dealing with real-life situations, understanding how to multiply a number by a fraction can help you make more informed decisions and solve problems more efficiently.
In this article, we will explore the step-by-step process of multiplying a number by a fraction, including examples and explanations to help you grasp the concept. By the end of this article, you will be able to multiply any number by a fraction with ease.
First, let’s start with the basic principle of multiplying a number by a fraction. When you multiply a number by a fraction, you are essentially finding a part of that number. For instance, if you multiply 4 by 1/2, you are finding half of 4. The result will be 2, as 4 divided by 2 equals 2.
To multiply a number by a fraction, follow these steps:
1. Multiply the numerator (the top number) of the fraction by the number you want to multiply.
2. Keep the denominator (the bottom number) of the fraction unchanged.
3. Simplify the resulting fraction, if possible.
Let’s look at an example to illustrate this process:
Example: Multiply 3 by 2/3.
1. Multiply the numerator (2) by the number (3): 2 3 = 6.
2. Keep the denominator (3) unchanged.
3. The resulting fraction is 6/3.
Now, let’s simplify the fraction:
1. Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3 in this case.
2. 6 ÷ 3 = 2, and 3 ÷ 3 = 1.
The simplified fraction is 2/1, which is equivalent to the whole number 2.
In some cases, you may need to multiply a number by a mixed number (a whole number and a fraction combined). To do this, follow these steps:
1. Convert the mixed number to an improper fraction.
2. Multiply the numerator of the improper fraction by the number you want to multiply.
3. Keep the denominator unchanged.
4. Simplify the resulting fraction, if possible.
Let’s look at an example to demonstrate this process:
Example: Multiply 5 by 3 1/4.
1. Convert the mixed number to an improper fraction: 3 1/4 = (3 4 + 1) / 4 = 13/4.
2. Multiply the numerator (13) by the number (5): 13 5 = 65.
3. Keep the denominator (4) unchanged.
4. The resulting fraction is 65/4.
Now, let’s simplify the fraction:
1. Divide both the numerator and the denominator by their GCD, which is 1 in this case.
2. 65 ÷ 1 = 65, and 4 ÷ 1 = 4.
The simplified fraction is 65/4, which cannot be further reduced.
In conclusion, multiplying a number by a fraction is a straightforward process that involves multiplying the numerator by the number and keeping the denominator unchanged. By following the steps outlined in this article, you can multiply any number by a fraction with ease. Whether you are a student or an adult, understanding this concept will help you solve problems and make informed decisions in various aspects of life.
