Which of the mathematical signs should be interchanged in the below equation to make it mathematically correct?
$72 - 12 + 8 \times 6 \div 24 = 30$
Identify Equation and Goal
The given mathematical equation is $72 - 12 + 8 \times 6 \div 24 = 30$. The objective is to find which pair of mathematical signs, when interchanged, makes the equation true.
Test Sign Interchanges
We will test the options by interchanging the specified signs and evaluating the expression using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Option A: Interchange '-' and '$\div$'
Original Equation: $72 - 12 + 8 \times 6 \div 24 = 30$
Interchanging '-' and '$\div$' gives: $72 \div 12 + 8 \times 6 - 24$.
Evaluate the expression:
- Division: $72 \div 12 = 6$
- Multiplication: $8 \times 6 = 48$
- The expression becomes: $6 + 48 - 24$
- Addition: $6 + 48 = 54$
- Subtraction: $54 - 24 = 30$
Since $30 = 30$, this interchange makes the equation mathematically correct.
Conclusion for Option A
Interchanging the subtraction sign ('-') and the division sign ('$\div$') results in a correct equation.
Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their 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.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
