Simplifying Fractions: 4 1/4 - 2 5/6
When working with mixed numbers and fractions, it's essential to understand how to perform basic arithmetic operations, such as subtraction. In this article, we'll explore how to subtract 2 5/6 from 4 1/4 and simplify the result as a fraction.
Converting Mixed Numbers to Improper Fractions
Before we begin the subtraction process, we need to convert both mixed numbers to improper fractions.
4 1/4
To convert 4 1/4 to an improper fraction, we multiply the whole number part (4) by the denominator (4) and then add the numerator (1).
4 × 4 = 16
16 + 1 = 17
So, 4 1/4 is equal to 17/4.
2 5/6
To convert 2 5/6 to an improper fraction, we multiply the whole number part (2) by the denominator (6) and then add the numerator (5).
2 × 6 = 12
12 + 5 = 17
So, 2 5/6 is equal to 17/6.
Subtracting the Fractions
Now that we have both mixed numbers converted to improper fractions, we can perform the subtraction.
17/4 - 17/6
To subtract these fractions, we need to find the least common multiple (LCM) of the denominators, which are 4 and 6. The LCM of 4 and 6 is 12.
We can rewrite both fractions with a denominator of 12:
17/4 = 51/12 17/6 = 34/12
Now, we can subtract the fractions:
51/12 - 34/12 = 17/12
Simplifying the Result
The result of the subtraction is 17/12. This is an improper fraction, and we can simplify it by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 17 and 12 is 1, so the fraction remains the same.
Therefore, 4 1/4 - 2 5/6 = 17/12.
By following these steps, we've successfully simplified the subtraction of mixed numbers and expressed the result as a fraction.
