Which two signs should be interchanged to make the given equation correct? 17 + 10 × 5 ÷ 9 + 18 = 53
× and ÷
Solving Mathematical Equation by Swapping Signs
The problem asks us to find which pair of mathematical signs needs to be interchanged in the given equation to make it correct. The original equation is:
\(17 + 10 \times 5 \div 9 + 18 = 53\)
Let's evaluate the original equation using the order of operations (BODMAS/PEMDAS):
\(17 + (10 \times 5) \div 9 + 18\)
\(17 + 50 \div 9 + 18\)
\(17 + (50 \div 9) + 18\)
Since \(50 \div 9\) results in a non-integer (\(\approx 5.56\)), the original equation does not result in the integer 53. We need to test each option by swapping the specified signs and re-evaluating the equation.
Testing Options for Sign Interchange
Option 1: Interchanging + and ÷
If we interchange the + and ÷ signs, the equation becomes:
\(17 \div 10 \times 5 + 9 \div 18 = 53\)
Evaluate using order of operations:
\((17 \div 10) \times 5 + (9 \div 18)\)
\(1.7 \times 5 + 0.5\)
\(8.5 + 0.5 = 9\)
This does not equal 53.
Option 2: Interchanging + and ×
If we interchange the + and × signs, the equation becomes:
\(17 \times 10 + 5 \div 9 \times 18 = 53\)
Evaluate using order of operations:
\((17 \times 10) + (5 \div 9) \times 18\)
\(170 + (5/9) \times 18\)
\(170 + (5 \times 18 / 9)\)
\(170 + (90 / 9)\)
\(170 + 10 = 180\)
This does not equal 53.
Option 3: Interchanging + and −
The original equation does not contain a − sign. Therefore, this interchange is not possible with the given equation structure.
Option 4: Interchanging × and ÷
If we interchange the × and ÷ signs, the equation becomes:
\(17 + 10 \div 5 \times 9 + 18 = 53\)
Evaluate using order of operations:
\(17 + (10 \div 5) \times 9 + 18\)
\(17 + 2 \times 9 + 18\)
\(17 + (2 \times 9) + 18\)
\(17 + 18 + 18\)
\(17 + 36 = 53\)
This equals 53. Therefore, interchanging the × and ÷ signs makes the equation correct.
Conclusion
By testing each option and applying the order of operations, we find that interchanging the × and ÷ signs correctly solves the mathematical equation, resulting in 53.
Revision Table: Checking Sign Interchanges
| Interchanged Signs | New Equation | Evaluation | Result | Correct? |
|---|---|---|---|---|
| + and ÷ | \(17 \div 10 \times 5 + 9 \div 18\) | \(1.7 \times 5 + 0.5 = 8.5 + 0.5 = 9\) | 9 | No |
| + and × | \(17 \times 10 + 5 \div 9 \times 18\) | \(170 + (5/9) \times 18 = 170 + 10 = 180\) | 180 | No |
| × and ÷ | \(17 + 10 \div 5 \times 9 + 18\) | \(17 + 2 \times 9 + 18 = 17 + 18 + 18 = 53\) | 53 | Yes |
Additional Information on Order of Operations
When solving mathematical equations involving multiple operations, it is crucial to follow a specific order. This order is commonly known by acronyms like BODMAS or PEMDAS.
- BODMAS: Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In the context of this problem, Division and Multiplication are performed before Addition and Subtraction. If both Division and Multiplication are present, they are performed from left to right as they appear in the equation. Similarly, Addition and Subtraction are performed from left to right.
Understanding the correct order of operations is fundamental to solving such mathematical equation problems accurately.
Similar Questions
Which of the following interchange of numbers and mathematical signs would make the given equation correct?
30 ÷ 6 × 4 + 15 - 35 = 25
Select the correct combination of mathematical signs that can sequentially replace the * signs and make the equation correct.
48 * 12 * 8 * 15 * 3 * 44
By Interchanging the given two numbers which of the following equation will be not correct?
9 and 6
By Interchanging the given two numbers which of the following equation will be correct?
2 and 8
Which two signs should be interchanged to make the given equation correct?
95 * 5 + 19 ÷ 2 − 21 = 36
By interchanging the given two signs and numbers which of the following equation will be not correct?
+ and –, 3 and 5
Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
50 * 25 * 10 * 2 * 175
Which two signs and two numbers should be interchanged in the following equation to make it correct?
10 × 11 + 19 - 323 ÷ 3 = 50
By interchanging the given two signs which of the following equation will be not correct?
+ and ÷
By interchanging the given two signs and numbers which of the following equation will be not correct?
× and +, 7 and 4
I. 7 × 8 + 4 – 6 ÷ 3 = 57
II. 4 × 8 – 9 ÷ 3 + 7 = 3
Important Questions from Logical Puzzle
Seven persons P, Q, R, S, T, U and V like different watches namely W1, W2, W3, W4, W5, W6 and W7 (not necessarily in the same order). P and R do not like odd numbered watch. T likes W5. U does not like W2 or W3 or W6 or W7. P likes prime numbered watch. Q likes W4. S likes W2 or W7. Which of the following statement(s) is/are correct ?
I. S likes W7.
II. R likes W2.
III. U likes W1.
IV. V likes W3.
If ‘+’ means ‘×’, ‘×’ means ‘÷’, ‘÷’ means ‘–’ and ‘–’ means ‘+’, then
16 + 18 × 3 ÷ 6 = ?
In a certain code language, ‘Today is last match’ is written as ‘Sa Te Mo Pt’, ‘Last king like your team’ is written as ‘De Ra Mo Lo Zs’, ‘Our team won today match’ is written as ‘Te Ra Pt Ae We’. What is the code for ‘Our won is Last’ in that code language?
In a certain code language, ‘LETTER’ is written as ‘ZLZYIO’. What is the code for ‘ACTION’ in that code language?
If A denotes ‘+’, B denotes ‘×’, C denotes ‘-’, and D denotes ‘÷’, then what will come in place of ‘?’ in the following equation?
34 A 15 B 3 C 11 B 2 A (51 D 17) = ?
