Understanding the Problem
To simplify the expression 888 1/7 + 888 2/7 + 888 3/7 X 888 4/7 + 888 5/7 + 888 6/7, we need to follow the order of operations, which is essential in mathematics.
Step 1: Convert Mixed Numbers to Improper Fractions
- 888 1/7 = (888 * 7 + 1) / 7 = 6217 / 7
- 888 2/7 = (888 * 7 + 2) / 7 = 6218 / 7
- 888 3/7 = (888 * 7 + 3) / 7 = 6219 / 7
- 888 4/7 = (888 * 7 + 4) / 7 = 6220 / 7
- 888 5/7 = (888 * 7 + 5) / 7 = 6221 / 7
- 888 6/7 = (888 * 7 + 6) / 7 = 6222 / 7
Step 2: Apply Order of Operations
- First, perform the multiplication:
- (888 3/7) X (888 4/7) = (6219 / 7) * (6220 / 7) = 38726718 / 49
Step 3: Combine the Terms
- Now, add all the terms together:
- Total = (6217 / 7) + (6218 / 7) + (38726718 / 49) + (6221 / 7) + (6222 / 7)
- To combine these fractions, convert all fractions to have a common denominator (49 in this case).
Final Calculation
- After finding a common denominator and adding all the fractions, simplify to get the final answer.
This process illustrates how to simplify complex expressions by breaking them down into manageable steps while adhering to the order of operations.