Comparing Fractions: 6 1/8 and 2 3/7
In this article, we will compare two mixed fractions: 6 1/8 and 2 3/7. We will learn how to compare these fractions and determine which one is larger.
Understanding Mixed Fractions
Before we start comparing, let's quickly review what mixed fractions are. A mixed fraction is a combination of a whole number and a fraction. For example, 6 1/8 is a mixed fraction where 6 is the whole number and 1/8 is the fraction part.
Converting to Improper Fractions
To compare these mixed fractions, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator. Here's how we can convert 6 1/8 and 2 3/7 to improper fractions:
6 1/8
To convert 6 1/8 to an improper fraction, we multiply the whole number part (6) by the denominator (8) and then add the numerator (1).
6 × 8 = 48 48 + 1 = 49
So, 6 1/8 is equivalent to 49/8.
2 3/7
To convert 2 3/7 to an improper fraction, we multiply the whole number part (2) by the denominator (7) and then add the numerator (3).
2 × 7 = 14 14 + 3 = 17
So, 2 3/7 is equivalent to 17/7.
Comparing the Fractions
Now that we have converted both mixed fractions to improper fractions, we can compare them:
49/8 vs 17/7
To compare these fractions, we need to find the least common multiple (LCM) of the denominators, which are 8 and 7. The LCM of 8 and 7 is 56. So, we can convert both fractions to have a denominator of 56:
49/8 = 196/56 17/7 = 136/56
Now, we can compare the numerators:
196 > 136
Since 196 is greater than 136, we can conclude that 6 1/8 is greater than 2 3/7.
Conclusion
In conclusion, we have successfully compared two mixed fractions, 6 1/8 and 2 3/7, by converting them to improper fractions and then comparing their numerators. We found that 6 1/8 is greater than 2 3/7.
