How to Compare Negative Fractions
Comparing negative fractions can be a challenging task for many students, especially those who are new to the concept of negative numbers. However, with a clear understanding of the rules and techniques involved, it becomes a straightforward process. In this article, we will discuss the steps and methods to compare negative fractions effectively.
Firstly, it is essential to understand that when comparing negative fractions, the larger the absolute value, the smaller the fraction is. This means that a fraction with a larger numerator and denominator will be smaller than a fraction with a smaller numerator and denominator, even if the numerators are negative.
To compare two negative fractions, follow these steps:
1. Convert the fractions to a common denominator: To compare fractions, they must have the same denominator. Multiply the numerator and denominator of each fraction by the necessary factors to achieve a common denominator.
2. Compare the numerators: Once the fractions have a common denominator, compare the numerators. The fraction with the larger numerator is the smaller fraction, and vice versa.
3. Consider the signs: Remember that negative numbers are less than positive numbers. Therefore, if both fractions have negative numerators, the fraction with the larger absolute value is the smaller fraction. If one fraction has a negative numerator and the other has a positive numerator, the fraction with the negative numerator is the smaller fraction.
Let’s look at some examples to illustrate these steps:
Example 1:
Compare the fractions -3/4 and -5/6.
Step 1: Convert the fractions to a common denominator. The least common denominator (LCD) of 4 and 6 is 12.
-3/4 becomes -9/12
-5/6 becomes -10/12
Step 2: Compare the numerators. -9 is larger than -10, so -3/4 is the smaller fraction.
Example 2:
Compare the fractions -2/3 and 1/4.
Step 1: Convert the fractions to a common denominator. The LCD of 3 and 4 is 12.
-2/3 becomes -8/12
1/4 becomes 3/12
Step 2: Compare the numerators. -8 is smaller than 3, so -2/3 is the smaller fraction.
By following these steps and understanding the rules of comparing negative fractions, you can easily determine the relative sizes of two negative fractions. With practice, you will become more proficient in this skill and be able to compare negative fractions with confidence.
