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
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
