$551 \div 19 - 16 \times 12 + 121 = 100$
Original Equation Evaluation
The problem asks us to find which two signs in the equation $551 \div 19 - 16 \times 12 + 121 = 100$ need to be interchanged to make it mathematically correct.
First, let's evaluate the original 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).
- Division: Calculate $551 \div 19$. This equals $29$.
- Multiplication: Calculate $16 \times 12$. This equals $192$.
Substitute these results back into the equation:
$29 - 192 + 121$
Now, perform the subtraction and addition from left to right:
- $29 - 192 = -163$
- $-163 + 121 = -42$
The original equation evaluates to $-42$, not the target value of $100$. This confirms that an interchange of signs is necessary.
Signs Interchange Result
We will now test the interchange of the addition sign '+' and the subtraction sign '-'. Based on the options provided, this pair is a potential candidate for correction.
After interchanging '+' and '-':
- The original equation is: $551 \div 19 - 16 \times 12 + 121 = 100$
- The modified equation becomes: $551 \div 19 + 16 \times 12 - 121 = 100$
Let's evaluate this new equation using the order of operations (PEMDAS/BODMAS):
- Division: $551 \div 19 = 29$.
- Multiplication: $16 \times 12 = 192$.
Substitute these results into the modified equation:
$29 + 192 - 121$
Perform the addition and subtraction from left to right:
- $29 + 192 = 221$.
- $221 - 121 = 100$.
This result, $100$, matches the required value on the right side of the equation.
Correct Signs Determined
Therefore, interchanging the addition '+' sign and the subtraction '-' sign is the correct operation needed to make the given equation true.
Similar Questions
Which two numbers (not individual digits) should be interchanged to make the given equation correct?
$56+ (11 \times 2) - (52 \div 4) + 16 = 76$What will come in the place of '?' in the following equation, if '+' and '-' are interchanged and also 'x' and '$\div$' are interchanged?
$13 \div 8-96 \times 6+17=?$Which two numbers (not digits of the numbers), from amongst the given options, should be interchanged to make the given equation correct?
$12 \times 9 + 27 \div 3 - 5 = 60$
- Which two signs should be interchanged to make the given equation correct?
$99 \div 33 - 6 + 48 \times 26 = 40$ 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?
36 B 17 D 59 C 224 A 7 = ?What will come in place of the question mark (?) in the following equation, if ‘+’ and ‘–’ are interchanged and ‘×’ and ‘÷’ are interchanged?
16 ÷ 6 + 12 × 3 – 6 = ?Which two signs should be interchanged to make the given equation correct?
$152 + 8 \times 16 \div 9 - 4 = 309$
What will come in the place of the question mark (?) in the following equation, if '÷' and '-' are interchanged and 'x' and '+' are interchanged?
[(48 - 2) ÷ 23] × 19 + 3 = ?
Which two numbers (not individual digits) should be interchanged to make the given equation correct?
$21 \times 5 - 35 + (42 \div 7) + 28 = 96$Which two signs need to be interchanged to make the following equation correct?
$56 \div 28 - 72 + 18 \times 6 = 60$
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)
