Subtraction of Mixed Numbers: 6 1/5 - 2 3/4
In this article, we will discuss the subtraction of mixed numbers, specifically the problem 6 1/5 - 2 3/4.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 2 1/2 is a mixed number, where 2 is the whole number and 1/2 is the fraction.
Converting Mixed Numbers to Improper Fractions
To subtract mixed numbers, it's essential to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 6 1/5 to an Improper Fraction
To convert 6 1/5 to an improper fraction, we multiply the whole number part (6) by the denominator (5) and then add the numerator (1).
6 × 5 = 30 30 + 1 = 31
So, the improper fraction equivalent to 6 1/5 is 31/5.
Converting 2 3/4 to an Improper Fraction
To convert 2 3/4 to an improper fraction, we follow the same steps.
2 × 4 = 8 8 + 3 = 11
So, the improper fraction equivalent to 2 3/4 is 11/4.
Subtracting the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can subtract them.
31/5 - 11/4
To subtract these fractions, we need to find the least common multiple (LCM) of 5 and 4, which is 20. We then convert both fractions to have a denominator of 20.
31/5 = 124/20 11/4 = 55/20
Now we can subtract the fractions:
124/20 - 55/20 = 69/20
Simplifying the Fraction
Finally, we simplify the fraction 69/20 by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1. Therefore, the result remains 69/20.
The Final Answer
The result of subtracting 2 3/4 from 6 1/5 is 69/20.
