Solving the Expression 22/7 × 49/2 × 49/2: Techniques and Methods
When dealing with mathematical expressions that include fractions, it is often necessary to understand and apply various techniques to simplify and solve them. This article will explore the problem of solving the expression 22/7 × 49/2 × 49/2, using both decimal conversion and the common denominator method. The goal is to reach the correct solution, with emphasis on the steps and methods used.
Introduction
Mathematical expressions involving fractions can be complex, but understanding the basic principles can help simplify the process of solving them.
1. Decimal Conversion Method
This method involves converting fractions to decimal form, multiplying them, and then arriving at the final solution.
Step 1: Convert the Fraction 22/7 to Decimal
22/7 3.142857142857143
Step 2: Multiply 3.142857142857143 by 49/2
3.142857142857143 × 49/2 77.14285714285714
Step 3: Multiply the Result by 49/2
77.14285714285714 × 49/2 1894.75
Therefore, the solution using the decimal conversion method is 1894.75.
2. Common Denominator Method
This method involves finding a common denominator and then converting and multiplying fractions accordingly.
Step 1: Simplify the Fraction 22/7
22/7 3 1/7
Step 2: Express 49/2 in a Simpler Form
49/2 24 1/2
Step 3: Perform the Multiplication
3 1/7 × 24 1/2 77
The exact multiplication is:
Step 4: Calculate the Final Result
22/7 × 49/2 × 49/2 77 / 1 × 49/2 3773 / 2 1886 1/2 or 1886.5
3. Expanding the Expression
To expand the expression, follow the steps for combining and simplifying the fractions.
Step 1: Cancel Common Terms
11 × 7 × 49/2 77 × 49/2
Step 2: Simplify Further
77 × 50 - 77 3850 - 77
Step 3: Final Solution
(3850 - 77) / 2 3773 / 2 1886 1/2
Conclusion
Both methods lead to the same final solution, 1886 1/2 or 1886.5, confirming the accuracy of the result. Understanding the steps and methods of solving the expression using decimal conversion and common denominator techniques can be beneficial in various mathematical contexts.