Which two numbers (not digits of the numbers), from amongst the given options, should be interchanged to make the given equation correct? $12 \times 9 + 27 \div 3 - 5 = 60$
Understanding the Equation Correction Problem
The problem asks us to find which pair of numbers, when swapped within the given equation, makes the equation true. The equation is: $12 \times 9 + 27 \div 3 - 5 = 60$
We need to follow 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) to evaluate the expression.
Evaluating the Original Equation
First, let's calculate the value of the original equation as it is:
- Multiplication: $12 \times 9 = 108$
- Division: $27 \div 3 = 9$
- The equation becomes: $108 + 9 - 5$
- Addition: $108 + 9 = 117$
- Subtraction: $117 - 5 = 112$
The original equation evaluates to $112$, not $60$. So, we need to interchange numbers.
Checking Number Interchange Options
Let's test each option by swapping the specified numbers and re-evaluating the equation.
Option 1: Interchange 27 and 9
The equation becomes: $12 \times 27 + 9 \div 3 - 5 = 60$
- Multiplication: $12 \times 27 = 324$
- Division: $9 \div 3 = 3$
- The equation becomes: $324 + 3 - 5$
- Addition: $324 + 3 = 327$
- Subtraction: $327 - 5 = 322$
This does not equal $60$.
Option 2: Interchange 12 and 3
The equation becomes: $3 \times 9 + 27 \div 12 - 5 = 60$
- Multiplication: $3 \times 9 = 27$
- Division: $27 \div 12 = 2.25$
- The equation becomes: $27 + 2.25 - 5$
- Addition: $27 + 2.25 = 29.25$
- Subtraction: $29.25 - 5 = 24.25$
This does not equal $60$.
Option 3: Interchange 12 and 5
The equation becomes: $5 \times 9 + 27 \div 3 - 12 = 60$
- Multiplication: $5 \times 9 = 45$
- Division: $27 \div 3 = 9$
- The equation becomes: $45 + 9 - 12$
- Addition: $45 + 9 = 54$
- Subtraction: $54 - 12 = 42$
This does not equal $60$.
Option 4: Interchange 5 and 9
The equation becomes: $12 \times 5 + 27 \div 3 - 9 = 60$
- Multiplication: $12 \times 5 = 60$
- Division: $27 \div 3 = 9$
- The equation becomes: $60 + 9 - 9$
- Addition: $60 + 9 = 69$
- Subtraction: $69 - 9 = 60$
This equals $60$. Therefore, interchanging 5 and 9 makes the equation correct.
Conclusion
By testing all the given options, we found that swapping the numbers 5 and 9 in the original equation $12 \times 9 + 27 \div 3 - 5 = 60$ results in a correct equation ($12 \times 5 + 27 \div 3 - 9 = 60$).
Similar Questions
Which two numbers (not individual digits) should be interchanged to make the given equation correct?
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Important Questions from Bodmas Rule
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
What will come in place of the question mark ‘?’ in the following question?
(44 of 15) – [(450 × 240 ÷ 60 – 40) ÷ 80 × 25 + 50] – 10 = ?Simplify: 92 - 18 ( 9 + 36 ÷ 3 × 12 - 27 × 3) + 51
Simplify the following expression.
\(\rm \frac{3}{5}\ of\ \left\{\left(48\div\overline{36\div9}\times\frac{1}{6}\right)+\frac{1}{3}\right\}=?\)
