The question asks us to find the correct equation after interchanging the numbers 12 and 6, and the signs ÷ and +.
Let's analyze each option:
- Option 1: 6 ÷ 4 × 5 - 12 + 3 = 30
- After interchanging 12 and 6, and ÷ and +, the equation becomes: 12 + 4 × 5 - 6 ÷ 3 = 12 + 20 - 2 = 30. This equation is correct.
- Option 2: 9 ÷ 6 × 4 + 12 - 3 = 18
- After interchanging 12 and 6, and ÷ and +, the equation becomes: 9 + 6 × 4 - 12 ÷ 3 = 9 + 24 - 4 = 29. This is incorrect.
- Option 3: 12 ÷ 3 - 8 - 6 + 1 = 15
- After interchanging 12 and 6, and ÷ and +, the equation becomes: 6 + 3 - 8 - 12 + 1 = -10. This is incorrect.
- Option 4: 4 - 6 × 12 ÷ 5 + 7 = 22
- After interchanging 12 and 6, and ÷ and +, the equation becomes: 4 + 6 ÷ 12 × 5 - 7 = 4 + 2.5 -7 = -0.5. This is incorrect.
Therefore, only Option 1 results in a correct equation after the interchanges. The core concept involves carefully substituting the numbers and operators, following the order of operations (PEMDAS/BODMAS) to evaluate each resulting expression. The key to solving this type of problem is methodical substitution and precise calculation, ensuring the correct order of mathematical operations is maintained throughout the process. The order of operations determines the sequence in which calculations are performed, impacting the final result. Accurate application of the order of operations is crucial for obtaining the correct solution. Incorrect application leads to erroneous results. The solution is obtained through careful step-by-step substitution and calculation.
Similar Questions
Which two numbers (not digits) should be interchanged to make the given equation correct?
21 × 8 – 18 + (64 ÷ 2) + 32 = 64
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged. What are those two numbers (not digits) and the two signs?
9 × 1 ÷ 3 + 8 – 7 = 12 ÷ 3 + 2 × 33 – 13
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged.
What are those two numbers (not digits) and the two signs?
4 × 3 ÷ 6 + 2 - 8 = 10 + 2 × 3 ÷ 5 - 18
- 4 is related to 125 following a certain logic. Following the same logic, 8 is related to 729. Which of the following numbers is related to 1728 using the same logic?
(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.) Which two numbers (not digits) and which two signs should be interchanged to yield the value ‘zero’ for the following expression?
13 + 65 ÷ 2 × 8 – 21
If 'A' stands for '+', 'B' stands for '-', 'C' stands for 'x' and 'D' stands for '÷', what will come in place of the question mark in the following equation?
7 C 9 B 35 D 5 A 3 = ?
Which option represents the correct order of the given words as they would appear in an English dictionary?
1. Mimic
2. Million
3. Minaret
4. Millstone
5. Mimicry
What will come in place of the question mark (?) in the following equation if '+' and '÷'are interchanged and 'x' and '-' are interchanged?
3÷4-5×6+2=?
Which two numbers (not digits) and which two signs should be interchanged to make the following equation valid?
55 × 5 ÷ 1 – 3 + 14 = 0
If + means -, - means x, x means ÷, ÷ means +, what will come in place of the question mark (?) in the given equation?
70 × 2 – 4 ÷ 60 + 150 = ?
Important Questions from Mathematical Operations
Which two numbers (not digits) should be interchanged to make the given equation correct?
21 × 8 – 18 + (64 ÷ 2) + 32 = 64
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged. What are those two numbers (not digits) and the two signs?
9 × 1 ÷ 3 + 8 – 7 = 12 ÷ 3 + 2 × 33 – 13
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
