Evaluating the Expression: 1/2 - 1/3 x 1/4 + 1/5 / 1/6
When dealing with mathematical expressions that involve multiple operations, it's essential to follow the order of operations to ensure accuracy. In this article, we'll evaluate the expression 1/2 - 1/3 x 1/4 + 1/5 / 1/6 step by step.
Step 1: Follow the Order of Operations
The order of operations is a fundamental concept in mathematics that dictates the sequence of operations when evaluating expressions. The acronym PEMDAS is commonly used to remember the order:
- Parentheses
- Exponents
- Multiplication and Division (from left to right)
- Addition and Subtraction (from left to right)
Step 2: Evaluate the Multiplication
The expression contains a multiplication operation: 1/3 x 1/4. To evaluate this, we multiply the numerators (numbers on top) and multiply the denominators (numbers at the bottom), then simplify the fraction:
1/3 x 1/4 = (1 x 1) / (3 x 4) = 1/12
Step 3: Evaluate the Division
The expression contains a division operation: 1/5 / 1/6. To evaluate this, we invert the second fraction (i.e., flip the numerator and denominator) and then multiply:
1/5 / 1/6 = 1/5 x 6/1 = 6/5
Step 4: Evaluate the Expression
Now that we've evaluated the multiplication and division, we can substitute these values back into the original expression:
1/2 - 1/12 + 6/5
Step 5: Simplify the Expression
To simplify the expression, we'll combine the fractions using a common denominator, which is 60.
1/2 = 30/60 -1/12 = -5/60 6/5 = 72/60
Now, we can add and subtract the fractions:
(30 - 5 + 72) / 60 = 97/60
Conclusion
The final result of the expression 1/2 - 1/3 x 1/4 + 1/5 / 1/6 is 97/60. By following the order of operations and evaluating each operation step by step, we can ensure accuracy and arrive at the correct solution.
