\(6 - 2 \times 4 \div 10 + 5 = 6\)
Solving Equation by Sign Interchange
The goal is to find which pair of signs, when interchanged in the equation \(6 - 2 \times 4 \div 10 + 5 = 6\), makes it correct.
We will use the order of operations (PEMDAS/BODMAS): Division/Multiplication before Addition/Subtraction, evaluated from left to right.
Original Equation Evaluation
The given equation is \(6 - 2 \times 4 \div 10 + 5 = 6\).
- Calculate multiplication: \(2 \times 4 = 8\). Equation becomes \(6 - 8 \div 10 + 5 = 6\).
- Calculate division: \(8 \div 10 = 0.8\). Equation becomes \(6 - 0.8 + 5 = 6\).
- Calculate subtraction: \(6 - 0.8 = 5.2\). Equation becomes \(5.2 + 5 = 6\).
- Calculate addition: \(5.2 + 5 = 10.2\).
The result \(10.2 = 6\) is false. The original equation is incorrect.
Testing Sign Interchange: Option D (\(\div\) and \(\times\))
Interchange the multiplication (\(\times\)) sign and the division (\(\div\)) sign.
The equation transforms to \(6 - 2 \div 4 \times 10 + 5 = 6\).
- Calculate division: \(2 \div 4 = 0.5\). Equation becomes \(6 - 0.5 \times 10 + 5 = 6\).
- Calculate multiplication: \(0.5 \times 10 = 5\). Equation becomes \(6 - 5 + 5 = 6\).
- Calculate subtraction: \(6 - 5 = 1\). Equation becomes \(1 + 5 = 6\).
- Calculate addition: \(1 + 5 = 6\).
The result \(6 = 6\) is true.
Conclusion
Interchanging the division (\(\div\)) and multiplication (\(\times\)) signs correctly solves the equation.
Similar Questions
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If ‘A’ stands for ‘\(\div \)', ‘B’ stands for ‘x', ‘C’ stands for ‘+', ‘D’ stands for ‘-', what will come in the place of the question mark '?' in the following equation?
225 B 15 A 15 C 125 D 225 = ?Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 3 - Operations on 3 such as adding /deleting /multiplying etc. to 3 can be performed, Breaking down 3 into | and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(144, 12, 6)
(210, 15, 7)Select the set in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 3 - Operations on 3 such as adding /deleting /multiplying etc. to 3 can be performed, Breaking down 3 into | and 3 and then performing mathematical operations on | and 3 is not allowed.)
(9, 6, 56)
(7,8, 58)If A means +, B means -, C means x, D means \(\div \), then what will come in place of the question mark (?) in the following equation?
18 D 2 A 4 C 5 B 15 = ?If 'A' stands for '+', 'B' stands for '×', 'C' stands for '+' and 'D' stands for '-', then what will come in place of the question mark (?) in the following equation?
47 D 25 A 5 C 2 B 9 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is same as that on the right side of ::?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituen digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 112 :: 15 : Y
Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 Operations on 13 such as adding/subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
