Which two signs should be interchanged to make the given equation correct? $152 + 8 \times 16 \div 9 - 4 = 309$
Interchanging Signs to Correct the Equation
The problem asks us to find which pair of mathematical signs, when interchanged in the given equation, makes it correct. The equation is:
$$152 + 8 \times 16 \div 9 - 4 = 309$$
To solve this, we need to test each option by swapping the specified signs and then evaluating the equation using the standard order of operations (BODMAS/PEMDAS): Brackets, Orders, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Evaluating the Original Equation
Let's first check the original equation:
$$152 + 8 \times 16 \div 9 - 4$$
- Multiplication first: $8 \times 16 = 128$
- Equation becomes: $152 + 128 \div 9 - 4$
- Division next: $128 \div 9 \approx 14.22$
- Equation becomes: $152 + 14.22 - 4$
- Addition: $152 + 14.22 = 166.22$
- Subtraction: $166.22 - 4 = 162.22$
Since $162.22 \neq 309$, the original equation is incorrect.
Testing the Options
Now, let's test each option:
Option 1: Interchange $\div$ and -
The equation becomes:
$$152 + 8 \times 16 - 9 \div 4 = 309$$
- Multiplication: $8 \times 16 = 128$
- Equation: $152 + 128 - 9 \div 4$
- Division: $9 \div 4 = 2.25$
- Equation: $152 + 128 - 2.25$
- Addition: $152 + 128 = 280$
- Subtraction: $280 - 2.25 = 277.75$
Since $277.75 \neq 309$, this option is incorrect.
Option 2: Interchange $\div$ and +
The equation becomes:
$$152 \div 8 \times 16 + 9 - 4 = 309$$
- Division first: $152 \div 8 = 19$
- Equation becomes: $19 \times 16 + 9 - 4$
- Multiplication next: $19 \times 16 = 304$
- Equation becomes: $304 + 9 - 4$
- Addition: $304 + 9 = 313$
- Subtraction: $313 - 4 = 309$
Since $309 = 309$, this option makes the equation correct.
Option 3: Interchange - and +
The equation becomes:
$$152 - 8 \times 16 \div 9 + 4 = 309$$
- Multiplication: $8 \times 16 = 128$
- Equation: $152 - 128 \div 9 + 4$
- Division: $128 \div 9 \approx 14.22$
- Equation: $152 - 14.22 + 4$
- Subtraction: $152 - 14.22 = 137.78$
- Addition: $137.78 + 4 = 141.78$
Since $141.78 \neq 309$, this option is incorrect.
Option 4: Interchange + and x
The equation becomes:
$$152 \times 8 + 16 \div 9 - 4 = 309$$
- Multiplication first: $152 \times 8 = 1216$
- Equation becomes: $1216 + 16 \div 9 - 4$
- Division next: $16 \div 9 \approx 1.78$
- Equation becomes: $1216 + 1.78 - 4$
- Addition: $1216 + 1.78 = 1217.78$
- Subtraction: $1217.78 - 4 = 1213.78$
Since $1213.78 \neq 309$, this option is incorrect.
Conclusion
By testing all the options, we found that interchanging the division ($\div$) and addition (+) signs results in a correct equation. The steps for Option 2 are:
- Swap '+' and '$\div$': $152 \div 8 \times 16 + 9 - 4 = 309$
- Perform division: $19 \times 16 + 9 - 4 = 309$
- Perform multiplication: $304 + 9 - 4 = 309$
- Perform addition: $313 - 4 = 309$
- Perform subtraction: $309 = 309$
Therefore, the correct signs to interchange are $\div$ and +.
Similar Questions
- Which two signs should be interchanged to make the given equation correct? $67 - 84 \div 12 \times 5 + 31 = 71$
What will come in place of the question mark (?) in the following equation if '+' means 'x', 'x' means '-', '-' means '$\div$' and '$\div$' means '+'?
$18 \div 4 + 3 \times 2 - 2 = ?$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 = ?What will come in the place of the question mark (?) in the following equation, if '+' and '-' are interchanged and 'x' and '÷' are interchanged?
(28 ÷ 4) - (15 x 3) + 48 = ?
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 = ?
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)
