Which two signs should be interchanged to make the below equation mathematically correct?
$40+14÷35-30×15=1$
Solving the Equation by Interchanging Signs
The problem requires finding which pair of signs to interchange in the equation $40+14÷35-30×15=1$ to make it mathematically correct.
We will test the option that involves interchanging the addition '+' sign and the multiplication '×' sign, as indicated by the correct answer.
Testing Sign Interchange Option
The given equation is:
$40 + 14 ÷ 35 - 30 × 15 = 1$
The option suggests interchanging '+' and '×'. Let's apply this change:
- Replace '+' with '×'.
- Replace '×' with '+'.
The equation becomes:
$40 × 14 ÷ 35 - 30 + 15 = 1$
Evaluating the Modified Equation
We use the order of operations (BODMAS/PEMDAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction) to solve the modified equation:
- Multiplication: $40 × 14 = 560$
- The equation is now: $560 ÷ 35 - 30 + 15 = 1$
- Division: $560 ÷ 35 = 16$
- The equation is now: $16 - 30 + 15 = 1$
- Subtraction (from left to right): $16 - 30 = -14$
- The equation is now: $-14 + 15 = 1$
- Addition: $-14 + 15 = 1$
The result is $1 = 1$, which is mathematically correct.
Therefore, interchanging the '+' and '×' signs makes the equation correct.
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.)
