Question

How do you insert parentheses to make \[4.2 - {2^2} \div 9 + 2 = 6\] true?

Answer 1

Hint: To solve this type of problem we will not start with directly putting the parentheses. That will be like a trial-and-error method. We will shift or transpose the numbers one by one that are not entangled with any other number. Like here we will shift 2 and 9 one by one on RHS. Then we will try to put the parentheses.

Complete step-by-step answer:
Given that,
 \[4.2 - {2^2} \div 9 + 2 = 6\]
Now we will shift 2 on RHS,
 \[4.2 - {2^2} \div 9 = 6 - 2\]
On solving the RHS we get,
 \[4.2 - {2^2} \div 9 = 4\]
Now we will shift 9.
 \[4.2 - {2^2} = 4 \times 9\]
On multiplying we get,
 \[4.2 - {2^2} = 36\]
Now it’s the step where we need to insert the parentheses.
Case 1: \[4.\left( {2 - {2^2}} \right)\]
In this we inserted the parentheses. On solving we should get the RHS. Let’s check!
 \[4.\left( {2 - {2^2}} \right) = 4.\left( {2 - 4} \right) \ne 36\] No. this is not the correct place of the parentheses.
Case 2: \[{(4.2 - 2)^2}\]
 In this we inserted the parentheses. On solving we should get the RHS. Let’s check!
 \[{(4.2 - 2)^2} = {\left( {8 - 2} \right)^2} = {6^2} = 36\] Yes . this is the place to insert the parentheses.
So the correct arrangement is \[\left( {{{\left( {4.2 - 2} \right)}^2} \div 9} \right) + 2 = 6\]
So, the correct answer is “ \[\left( {{{\left( {4.2 - 2} \right)}^2} \div 9} \right) + 2 = 6\] ”.

Note: Here note that directly trying to insert the brackets will consume the time. And this will be very confusing. Also note that when we solve problems like this we follow the BODMAS rule. In which we solve the brackets first and then division-multiplication-addition-subtraction consecutively.
Note that the division need not to separate the whole equation like \[\left( {4.2 - {2^2}} \right) \div \left( {9 + 2} \right) = 6\] .we can use the parentheses the way we did in the equation above.