$14 - 7 \times 30 \div 10 + 4 = 54$
$- and \div$
Equation Correction: Operator Interchange
The problem requires finding which two signs in the equation
14 - 7 \times 30 \div 10 + 4 = 54$
need to be swapped to make it correct. We will test the options by applying the standard order of operations (BODMAS/PEMDAS).
Order of Operations (BODMAS/PEMDAS)
Remember the order: 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 using BODMAS:
- Equation:
14 - 7 \times 30 \div 10 + 4$ - Multiplication first:
7 \times 30 = 210$. - Equation becomes:
14 - 210 \div 10 + 4$ - Next, division:
210 \div 10 = 21$. - Equation becomes:
14 - 21 + 4$ - Next, subtraction (left to right):
14 - 21 = -7$. - Equation becomes:
-7 + 4$ - Finally, addition:
-7 + 4 = -3$.
The result is
-3$, not
54$. The original equation is incorrect.
Testing Sign Interchange: Minus and Division
According to Option C, we should interchange the subtraction ('-') and division ('÷') signs.
- The equation becomes:
14 \div 7 \times 30 - 10 + 4$ - Division first:
14 \div 7 = 2$. - Equation becomes:
2 \times 30 - 10 + 4$ - Next, multiplication:
2 \times 30 = 60$. - Equation becomes:
60 - 10 + 4$ - Next, subtraction (left to right):
60 - 10 = 50$. - Equation becomes:
50 + 4$ - Finally, addition:
50 + 4 = 54$.
This result,
54$, matches the right side of the original equation. Therefore, interchanging '-' and '÷' corrects the equation.
Similar Questions
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5If 'x' means 'addition', '-' means 'division', '/' means 'subtraction' and '+' means 'multiplication', then which of the equation is correct?
If '+' stands for multiplication, '-' stands for addition, 'x' stands for division, then what is the value of 128 + 9 - 16 x 4 = ?
If 'x' means addition, '-' means division, '÷' means subtraction and '+' means multiplication, then which of the equations is correct?
If 4 x 5 x 2 = 524, 3 x 7 x 2 = 723, and 6 x 8 x 7 = 876, then 9 x 4 x 5 = ?
If '+' means '=', '-' means 'x', '*' means '+' and 'x' means '-', then 36x12+4+6-2-3= ?
Some equations have been solved on the basis of a certain pattern. Find the correct answer for the unsolved equation on that basis.
8x7x6=765, 5x3x2=421, 9x6x4=?
Which of the following interchanges of numbers (not digits) would make the given equation correct?
In a certain code language, '+' represents 'x', '-' represents '+', 'x' represents '=' and '=' represents '-'. What is the answer to the following question?
15 - 5 + 25 + 10 = ?If 19 + 2 x 2 + 3 = 369 and 23 + 2 x 6 + 2 = 565, then what is the value of 7 x 3 + 11 + 3 = ?
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
