Which two signs and two numbers should be interchanged to make the given equation correct? 17 + 11 – 12 × 36 ÷ 6 = 80
× and - ; 6 and 12
Solving Mathematical Operations by Interchanging Signs and Numbers
The problem asks us to identify which interchange of two mathematical signs and two numbers will make the given equation correct. The original equation is:
\(17 + 11 – 12 × 36 ÷ 6 = 80\)
We need to test the options provided by performing the suggested interchanges and then evaluating the resulting equation using the BODMAS or PEMDAS rule (order of operations).
Testing the Interchange: × and - ; 6 and 12
Let's test the interchange specified in one of the options, where the multiplication sign (\(\times\)) is swapped with the subtraction sign (\(-\)), and the number 6 is swapped with the number 12. The original equation is:
\(17 + 11 – 12 × 36 ÷ 6 = 80\)
After interchanging ‘×’ with ‘–’ and ‘6’ with ‘12’, the equation becomes:
\(17 + 11 \times 6 – 36 ÷ 12\)
Now, we evaluate this new equation following the BODMAS/PEMDAS rule:
- Brackets (or Parentheses)
- Orders (or Exponents)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's apply the rules to the modified equation: \(17 + 11 \times 6 – 36 ÷ 12\)
Step 1: Division
Perform the division operation: \(36 ÷ 12 = 3\)
The equation becomes: \(17 + 11 \times 6 – 3\)
Step 2: Multiplication
Perform the multiplication operation: \(11 \times 6 = 66\)
The equation becomes: \(17 + 66 – 3\)
Step 3: Addition
Perform the addition operation: \(17 + 66 = 83\)
The equation becomes: \(83 – 3\)
Step 4: Subtraction
Perform the subtraction operation: \(83 – 3 = 80\)
The result of the modified equation is 80, which is equal to the right side of the original equation. Therefore, this interchange makes the equation correct.
Let's summarise the operations in a table format:
| Operation | Calculation | Equation Status |
|---|---|---|
| Original Equation | \(17 + 11 – 12 × 36 ÷ 6\) | |
| Interchange × \(\leftrightarrow\) – ; 6 \(\leftrightarrow\) 12 | \(17 + 11 \times 6 – 36 ÷ 12\) | |
| Division (\(36 \div 12\)) | \(17 + 11 \times 6 – 3\) | |
| Multiplication (\(11 \times 6\)) | \(17 + 66 – 3\) | |
| Addition (\(17 + 66\)) | \(83 – 3\) | |
| Subtraction (\(83 – 3\)) | \(80\) | Equation Correct |
Revision Table: BODMAS/PEMDAS Rules
| Order | Rule (BODMAS) | Rule (PEMDAS) | Description |
|---|---|---|---|
| 1 | Brackets (B) | Parentheses (P) | Operations inside brackets first. |
| 2 | Orders (O) | Exponents (E) | Powers, roots, etc. |
| 3 | Division (D) and Multiplication (M) | Multiplication (M) and Division (D) | Perform from left to right as they appear. |
| 4 | Addition (A) and Subtraction (S) | Addition (A) and Subtraction (S) | Perform from left to right as they appear. |
Additional Information: Solving Mathematical Equations
When solving mathematical equations that involve multiple operations, following the correct order of operations is crucial. BODMAS (or PEMDAS) provides a standard sequence to ensure consistent and accurate results. Interchanging signs and numbers requires careful application of these rules to the modified equation.
In problems like this, it is often necessary to test each given option systematically unless a pattern is quickly identified. For each option, you replace the specified signs and numbers in the original equation and then evaluate the new expression using the order of operations.
The key steps are:
- Understand the original equation.
- Identify the proposed interchanges (signs and numbers).
- Rewrite the equation with the interchanges applied.
- Solve the new equation step-by-step using BODMAS/PEMDAS.
- Check if the result matches the required value (in this case, 80).
Similar Questions
In a certain code language, ‘+' represents '×', '-’represents ‘+', '×’ represents '÷’ and '÷’ represents '-'. What is the answer to the following question?
75 - 5 + 25 ÷ 125 = ?If 6 @ 4 @ 7 = 101 and 2 @ 5 @ 11 = 150, then what is the value of A in A @ 8 @ 9 = 289?
If 12 (20) 16 and 21 (35) 28, then what is value of A in 48 (80) A ?
The two given expressions on both the side of the ‘=’ sign will have the same value if two numbers from either side or both side are interchanged. Select the correct numbers to be interchanged from the given options.
4 + 6 × 7 – 27 ÷ 3 = 7 × 8 – 4 + 39 ÷ 3If 11\(25 = 18, 12\)20 = 16 then what is the value of 4$50 = ?
If (2)# * 4 = 2 and (4)# * 4 = 16, then what is the value of A in (6)# * A = 18?
If "α" denotes "subtracted from", "β" denotes "multiplied by", "θ" denotes "added to" and "δ" denotes "divided by", then 10 θ 8 β 4 δ 8 α 9 = ?
In the following question, correct the equation by interchanging two signs.
4 × 3 - 6 ÷ 2 + 7 = 8Which two signs should be interchanged to make the following equation correct?
18 + 24 – 6 × 6 ÷ 3 = 39In a certain code language, ' + ' represents ' × ', ' - ' represents ' + ', ' × ' represents '÷' and '÷' represents ' - '. What is the answer to the following question?
50 + 5 - 700 × 28 = ?
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) = ?
