Which two numbers(not digits) and two signs should be interchanged to make the given equation correct? 100 $\times$ 5 - 110 $\div$ 2 + 12 = 210
5 and 2; + and -
The problem requires us to find which two numbers and two signs need to be interchanged in the given equation to make it mathematically correct.
Equation Analysis
The given equation is:
$100 $\times$ 5 - 110 $\div$ 2 + 12 = 210$
We must follow the order of operations (BODMAS/PEMDAS): Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Original Equation Evaluation
Let's evaluate the original equation:
- Division: $110 \div 2 = 55$
- Multiplication: $100 \times 5 = 500$
- The equation becomes: $500 - 55 + 12$
- Subtraction: $500 - 55 = 445$
- Addition: $445 + 12 = 457$
The result is 457, which is not equal to the right side (210). Therefore, the original equation is incorrect.
Testing Interchange Option A
The proposed correct answer involves interchanging numbers 5 and 2, and signs + and -.
Let's apply these interchanges to the original equation:
- Original: $100 $\times$ 5 - 110 $\div$ 2 + 12 = 210$
- Interchange 5 with 2 and 2 with 5.
- Interchange - with + and + with -.
- New Equation: $100 $\times$ 2 + 110 $\div$ 5 - 12 = 210$
New Equation Evaluation
Now, let's evaluate the modified equation using BODMAS/PEMDAS:
- Division: $110 \div 5 = 22$
- Multiplication: $100 \times 2 = 200$
- The equation becomes: $200 + 22 - 12$
- Addition: $200 + 22 = 222$
- Subtraction: $222 - 12 = 210$
The result is 210, which correctly matches the right side of the equation.
Conclusion
Interchanging the numbers 5 and 2, and the signs + and - makes the equation correct.
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
