Simplifying the Expression: 3 1/6 - 2 4/5 as a Fraction
In this article, we will simplify the expression 3 1/6 - 2 4/5 as a fraction. To do this, we need to follow the order of operations (PEMDAS) and convert the mixed numbers to improper fractions.
Step 1: Convert Mixed Numbers to Improper Fractions
First, let's convert the mixed numbers to improper fractions:
- 3 1/6 = 19/6 (multiply the whole number part by the denominator and add the numerator)
- 2 4/5 = 14/5 (multiply the whole number part by the denominator and add the numerator)
Now, we can rewrite the expression as:
19/6 - 14/5
Step 2: Find the Least Common Multiple (LCM)
To subtract these fractions, we need to find the least common multiple (LCM) of 6 and 5, which is 30.
Step 3: Convert Fractions to Have the LCM as the Denominator
Now, let's convert both fractions to have a denominator of 30:
- 19/6 = 95/30 (multiply both numerator and denominator by 5)
- 14/5 = 84/30 (multiply both numerator and denominator by 6)
Step 4: Subtract the Fractions
Now, we can subtract the fractions:
95/30 - 84/30 = 11/30
Final Answer
Therefore, the simplified expression 3 1/6 - 2 4/5 as a fraction is:
11/30
