How to Compare 3 Fractions with Different Denominators
Comparing fractions with different denominators can sometimes be a challenging task, especially for students who are just learning the basics of fractions. However, with the right approach, it becomes a manageable and even enjoyable process. In this article, we will discuss several methods to compare three fractions with different denominators, helping you to understand the concept better and apply it effectively.
One of the most common methods to compare fractions with different denominators is by finding a common denominator. This involves multiplying the denominators of the fractions and then converting each fraction to an equivalent fraction with the new denominator. Once all the fractions have the same denominator, you can easily compare their numerators to determine which fraction is greater or smaller.
Here’s a step-by-step guide on how to compare three fractions with different denominators using the common denominator method:
1. Identify the denominators of the three fractions.
2. Find the least common multiple (LCM) of the denominators.
3. Convert each fraction to an equivalent fraction with the LCM as the new denominator.
4. Compare the numerators of the equivalent fractions to determine which fraction is greater or smaller.
For example, let’s compare the fractions 1/3, 2/5, and 3/7:
1. The denominators are 3, 5, and 7.
2. The LCM of 3, 5, and 7 is 105.
3. Convert each fraction to an equivalent fraction with a denominator of 105:
– 1/3 = 35/105
– 2/5 = 42/105
– 3/7 = 45/105
4. Compare the numerators: 35, 42, and 45. Since 45 is the largest, 3/7 is the greatest fraction among the three.
Another method to compare fractions with different denominators is by cross-multiplying. This involves multiplying the numerator of one fraction by the denominator of the other fraction and vice versa. By comparing the products, you can determine which fraction is greater or smaller.
Here’s a step-by-step guide on how to compare three fractions with different denominators using the cross-multiplication method:
1. Identify the numerators and denominators of the three fractions.
2. Cross-multiply the numerators and denominators of each pair of fractions.
3. Compare the products to determine which fraction is greater or smaller.
For the same example fractions (1/3, 2/5, and 3/7), let’s compare them using the cross-multiplication method:
1. The numerators are 1, 2, and 3, and the denominators are 3, 5, and 7.
2. Cross-multiply the numerators and denominators:
– 1/3 vs. 2/5: (1 5) = 5 and (2 3) = 6. Since 6 is greater than 5, 2/5 is greater than 1/3.
– 2/5 vs. 3/7: (2 7) = 14 and (3 5) = 15. Since 15 is greater than 14, 3/7 is greater than 2/5.
3. Compare the results: 2/5 > 1/3 and 3/7 > 2/5. Therefore, 3/7 is the greatest fraction among the three.
In conclusion, comparing three fractions with different denominators can be done using the common denominator method or the cross-multiplication method. Both methods have their advantages and can be applied depending on the context and the level of understanding. By mastering these techniques, you’ll be able to compare fractions with confidence and ease.
