Insert parentheses to make this equation correct:
7 - 6 x 7 / 5 + 7 = - 43.4
/ is used for division sign
To insert parentheses in the given equation (7 - 6 x 7 / 5 + 7 = -43.4) to make it correct, we need to follow the order of operations (also known as PEMDAS/BODMAS). Here's the breakdown:
1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)
Based on this, let's consider different possibilities:
Option 1: No Parentheses
Without using parentheses, the equation is solved as:
7 - 6 x 7 / 5 + 7 = -43.4
7 - 42 / 5 + 7 = -43.4
7 - 8.4 + 7 = -43.4
6.6 - 43.4 = -43.4
-36.8 = -43.4
As the result doesn't match, we should try different grouping possibilities.
Option 2: Parentheses around the subtraction
Using parentheses to group the subtraction part, the equation becomes:
7 - (6 x 7) / 5 + 7 = -43.4
7 - 42 / 5 + 7 = -43.4
7 - 8.4 + 7 = -43.4
-1.4 + 7 = -43.4
5.6 = -43.4
The result is incorrect, so this is not the correct solution.
Option 3: Parentheses around the multiplication
Using parentheses to group the multiplication part, the equation turns into:
(7 - 6) x (7 / 5) + 7 = -43.4
1 x 1.4 + 7 = -43.4
1.4 + 7 = -43.4
8.4 = -43.4
This solution is also incorrect.
Option 4: Parentheses around the division
Using parentheses to group the division part, the equation becomes:
7 - 6 x (7 / 5 + 7) = -43.4
7 - 6 x (1.4 + 7) = -43.4
7 - 6 x 8.4 = -43.4
7 - 50.4 = -43.4
-43.4 = -43.4
Finally, using parentheses around the division part gives us the correct solution.
Therefore, the correct equation with parentheses added is:
7 - 6 x (7 / 5 + 7) = -43.4