Which two numbers should be interchanged to make the given equation correct?
$15-26+13\times22÷5=35$
Solving the Equation by Interchanging Numbers
The problem asks us to identify which pair of numbers needs to be swapped in the equation $15-26+13\times22÷5=35$ to make the statement true. We need to test the given options by replacing the numbers and re-evaluating the equation using the standard order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Evaluating the Original Equation
First, let's check the value of the original equation:
$$15-26+13\times22÷5$$
- Division: $22 \div 5 = 4.4$
- Multiplication: $13 \times 4.4 = 57.2$
- Subtraction: $15 - 26 = -11$
- Addition: $-11 + 57.2 = 46.2$
The original equation evaluates to $46.2$, which is not equal to $35$. So, we need to interchange numbers.
Testing Number Interchange Options
Let's test each option by interchanging the specified numbers:
Option 1: Interchange 22 and 26
The equation becomes: $15-22+13\times26÷5$
- Division: $26 \div 5 = 5.2$
- Multiplication: $13 \times 5.2 = 67.6$
- Subtraction: $15 - 22 = -7$
- Addition: $-7 + 67.6 = 60.6$
This result ($60.6$) is not $35$.
Option 2: Interchange 15 and 13
The equation becomes: $13-26+15\times22÷5$
- Division: $22 \div 5 = 4.4$
- Multiplication: $15 \times 4.4 = 66$
- Subtraction: $13 - 26 = -13$
- Addition: $-13 + 66 = 53$
This result ($53$) is not $35$.
Option 3: Interchange 15 and 22
The equation becomes: $22-26+13\times15÷5$
- Division: $15 \div 5 = 3$
- Multiplication: $13 \times 3 = 39$
- Subtraction: $22 - 26 = -4$
- Addition: $-4 + 39 = 35$
This result ($35$) matches the right side of the equation. Therefore, interchanging $15$ and $22$ makes the equation correct.
Option 4: Interchange 35 and 5
Assuming this means replacing the number $5$ in the calculation with $35$: $15-26+13\times35÷5$
- Division: $35 \div 5 = 7$
- Multiplication: $13 \times 7 = 91$
- Subtraction: $15 - 26 = -11$
- Addition: $-11 + 91 = 80$
This result ($80$) is not $35$.
Conclusion
By testing all the options, we found that interchanging the numbers $15$ and $22$ correctly balances the equation.
$$22-26+13\times15÷5 = 35$$
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.)
