Identifying Pairs of Like Fractions- A Guide to Comparing Numerator-Denominator Combinations

Which of the following pairs of numbers contains like fractions? This question often arises in mathematics, particularly when dealing with fractions that have the same denominator. Understanding like fractions is crucial for various mathematical operations, such as adding, subtracting, multiplying, and dividing fractions. In this article, we will explore the concept of like fractions, their properties, and how to identify them in different pairs of numbers.

Like fractions are fractions that share the same denominator. This means that the bottom numbers (denominators) in the pairs are identical. For example, consider the following pairs of fractions:

1. 1/2 and 3/2
2. 4/5 and 7/5
3. 2/3 and 5/3

All these pairs have the same denominator, which is a key characteristic of like fractions. Unlike unlike fractions, which have different denominators, like fractions can be easily added, subtracted, multiplied, or divided.

To add like fractions, simply add the numerators (top numbers) while keeping the denominator the same. For instance, when adding 1/2 and 3/2, you get:

1/2 + 3/2 = (1 + 3) / 2 = 4/2 = 2

Similarly, to subtract like fractions, subtract the numerators and keep the denominator unchanged. For example:

4/5 – 2/5 = (4 – 2) / 5 = 2/5

Multiplying like fractions is also straightforward. You multiply the numerators and keep the denominator the same. For example:

2/3 5/3 = (2 5) / (3 3) = 10/9

Finally, dividing like fractions involves inverting the second fraction and multiplying it by the first fraction. For example:

1/2 ÷ 3/2 = 1/2 2/3 = (1 2) / (2 3) = 2/6 = 1/3

Identifying like fractions in different pairs of numbers is essential for performing these operations. To determine if a pair of fractions is like, compare their denominators. If they are the same, then the fractions are like. If the denominators are different, the fractions are unlike and cannot be directly added, subtracted, multiplied, or divided.

In conclusion, like fractions are fractions with the same denominator, making them easier to work with in various mathematical operations. By understanding the properties of like fractions and how to identify them, you can simplify your calculations and improve your proficiency in fraction-related problems. So, the next time you encounter the question “which of the following pairs of numbers contains like fractions,” you will be well-equipped to find the answer.