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
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
