$14 - 7 \times 30 \div 10 + 4 = 54$
$- and \div$
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
- Which two signs should be interchanged to make the following equation CORRECT?
$[(15 \div 3) - (4 \times 2)] + [4 - 6] = 5 \times 10$ - If "+" means "$\div$", "-" means "+", "$\times$" means "-" and "$\div$" means "$\times$", which of the following options is CORRECT?
- If 5 @ 2 = 17 and 6 @ 3 = 27, what is 7 @ 4?
- If 9 @ 1 = 82 and 6 @ 2 = 38, what is the value of 7 @ 3?
- You are given a mathematical expression with basic operations. However, the symbols used are not their usual meaning.
You must follow these symbol substitution rules:
'+' means '-'
'-' means 'x'
'x' means '÷'
'÷' means '+'
$120 \div 6 \times 3 - 10 + 4 = ?$ - If $\times$ stands for addition, $\div$ stands for subtraction, + stands for multiplication, and - stands for division, then $12 \times 6 \div 3 - 2 + 5 = ?$
- Which two signs need to be interchanged?
$22 - 4 \times 2 \div 2 + 6 = 20$ - Which interchanges of numbers and signs will make the equation correct? $8 \times 3 + 4 = 28$
- Select the CORRECT sequence of mathematical signs to sequentially replace the A and B to balance the given equation.
15 A 5 B 4 = 35 By interchanging the given two signs which of the following equation will NOT be correct?
$+$ and $\div$
I. $27 \div 3 - 18 \times 3 + 9 = 24$
II. $12 \div 8 \times 12 + 16 - 7 = 19$
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.)
