Which two numbers (not individual digits) should be interchanged to make the given equation correct?
$56+ (11 \times 2) - (52 \div 4) + 16 = 76$
Equation Analysis
The question asks us to identify two numbers in the given equation that need to be swapped to make the equation mathematically correct. The equation provided is:
$$56 + (11 \times 2) - (52 \div 4) + 16 = 76$$
To find the solution, we will first check the value of the equation as it is and then test each option by interchanging the specified numbers.
Original Equation Evaluation
We evaluate the left-hand side (LHS) of the equation using the order of operations (PEMDAS/BODMAS):
- Multiplication and Division (within parentheses):
- $11 \times 2 = 22$
- $52 \div 4 = 13$
- Substitute the results back into the equation: $$56 + 22 - 13 + 16 = 76$$
- Addition and Subtraction (from left to right):
- $56 + 22 = 78$
- $78 - 13 = 65$
- $65 + 16 = 81$
The LHS calculates to 81, which is not equal to the right-hand side (RHS) of 76. This confirms that an interchange is needed.
Testing Number Interchanges
We will now check each option by swapping the mentioned numbers and recalculating the LHS.
| Option Numbers to Interchange | Resulting Equation | LHS Calculation Steps | LHS Result |
|---|---|---|---|
| 11 and 16 | $$56 + (16 \times 2) - (52 \div 4) + 11 = 76$$ | $56 + 32 - 13 + 11 = 88 - 13 + 11 = 75 + 11$ | 86 |
| 56 and 52 | $$52 + (11 \times 2) - (56 \div 4) + 16 = 76$$ | $52 + 22 - 14 + 16 = 74 - 14 + 16 = 60 + 16$ | 76 |
| 2 and 4 | $$56 + (11 \times 4) - (52 \div 2) + 16 = 76$$ | $56 + 44 - 26 + 16 = 100 - 26 + 16 = 74 + 16$ | 90 |
| 52 and 16 | $$56 + (11 \times 2) - (16 \div 4) + 52 = 76$$ | $56 + 22 - 4 + 52 = 78 - 4 + 52 = 74 + 52$ | 126 |
Correct Interchange Identification
The table shows that swapping the numbers 56 and 52 results in the LHS equaling 76, which matches the RHS.
Let's confirm the calculation for this specific interchange:
- Interchange: The numbers 56 and 52 are swapped. The equation becomes: $$52 + (11 \times 2) - (56 \div 4) + 16 = 76$$
- Evaluation using PEMDAS/BODMAS:
- Parentheses/Brackets:
- $11 \times 2 = 22$
- $56 \div 4 = 14$
- Substitute: The equation simplifies to $52 + 22 - 14 + 16$.
- Addition and Subtraction (left to right):
- $52 + 22 = 74$
- $74 - 14 = 60$
- $60 + 16 = 76$
- Parentheses/Brackets:
The calculation confirms that $76 = 76$. Therefore, the correct numbers to interchange are 56 and 52.
Similar Questions
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- Which two signs should be interchanged to make the given equation correct?
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Important Questions from Bodmas Rule
If 2945 ÷ 19 – 11 × 5 = 29 + a, find the value of a.
DIRECTIONS: What should come in place of the question mark (?) in the following question?
3800 - 22 × 1968 ÷ 48 = ? × 7
Solve: {7.88 × 2 + 2.4 × 5 - 242.4 ÷ 4 + [9.2 × 4 - 2.46 of 3 + (36.3 ÷ 3 - 1.42 × 2)]}
What will come in the place of question mark (?) in the given expression?
(420 ÷ 12 × 35 + 452- 152) = ?2
Evaluate: (13 × 8 - √81 × 6 + 1 ) ÷ (√49 + 72 - 18 × 2 + 19)
