Place parentheses in the following equation to make it true.
6 + 6 ÷ 6 x 6 - 6 = 0
(6 + 6 ÷ 6) x (6 - 6) = 0
To place parentheses in the equation to make it true, we need to follow the order of operations (PEMDAS/BODMAS). According to these rules, we need to perform the calculations inside parentheses first, followed by exponents (powers and square roots), then multiplication and division (from left to right), and finally addition and subtraction (from left to right).
Given the equation:
6 + 6 ÷ 6 x 6 - 6 = 0
Let's add parentheses to ensure the correct order of operations:
(6 + (6 ÷ 6) x 6) - 6 = 0
Now we can solve it step-by-step:
1. Start with the parentheses:
6 ÷ 6 = 1
The equation becomes:
(6 + 1 x 6) - 6 = 0
2. Now perform the multiplication:
1 x 6 = 6
The equation becomes:
(6 + 6) - 6 = 0
3. Continue with the addition:
6 + 6 = 12
The equation becomes:
12 - 6 = 0
4. Finally, perform the subtraction:
12 - 6 = 6
Therefore, the equation:
6 + 6 ÷ 6 x 6 - 6 = 0
becomes true when parenthesized as:
(6 + (6 ÷ 6) x 6) - 6 = 0
To place parentheses in the equation to make it true, we need to follow the order of operations (PEMDAS/BODMAS).
First, let's break down the equation:
6 + 6 ÷ 6 x 6 - 6
According to the order of operations, we need to perform the calculations in the parentheses first, then the division and multiplication from left to right, and finally the addition and subtraction from left to right.
As the equation stands, we don't need parentheses for the addition and subtraction because they are already in the correct order. However, we need to add parentheses to control the order of the division and multiplication.
Option 1:
6 + (6 ÷ 6) x 6 - 6 = 0
In this option, we put parentheses around the division only (6 ÷ 6), which evaluates to 1. The equation becomes:
6 + 1 x 6 - 6 = 0
Next, we perform the multiplication:
6 + 1 x 6 = 6 + 6 = 12
Finally, we perform the subtraction:
12 - 6 = 6
So, with this option, the equation evaluates to 6, not 0.
Option 2:
(6 + 6) ÷ (6 x 6 - 6) = 0
In this option, we put parentheses around the addition (6 + 6) and around the multiplication and subtraction (6 x 6 - 6). The equation becomes:
12 ÷ (36 - 6) = 0
Next, we perform the subtraction inside the parentheses:
12 ÷ 30 = 0.4
So, with this option, the equation evaluates to 0.4, not 0.
Based on the original equation, it is not possible to place parentheses to make it evaluate to 0.