Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation. 59 * 12 * 6 * 24 * 2 * 105
−, ÷, +, ×, =
The question asks us to find the correct sequence of mathematical signs to replace the asterisks (*) in the expression 59 * 12 * 6 * 24 * 2 * 105 such that the equation is balanced. This means the expression on the left side, after replacing the signs, must evaluate to 105.
We need to test each given option, substituting the signs in the order provided, and perform the calculations following the order of operations (BODMAS/PEMDAS). The operations are typically performed in this order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
Evaluating Option 1: −, +, −, +, =
Substituting the signs into the equation:
59 − 12 + 6 − 24 + 2 = 105
Let's calculate the left side step-by-step:
- 59 - 12 = 47
- 47 + 6 = 53
- 53 - 24 = 29
- 29 + 2 = 31
So, the equation becomes 31 = 105, which is false. Option 1 is incorrect.
Evaluating Option 2: ×, −, +, ×, =
Substituting the signs into the equation:
59 × 12 − 6 + 24 × 2 = 105
Following the order of operations (Multiplication first):
- 59 \times 12 = 708
- 24 \times 2 = 48
Now substitute these values back:
708 − 6 + 48 = 105
Perform subtraction and addition from left to right:
- 708 - 6 = 702
- 702 + 48 = 750
So, the equation becomes 750 = 105, which is false. Option 2 is incorrect.
Evaluating Option 3: +, ×, +, −, =
Substituting the signs into the equation:
59 + 12 × 6 + 24 − 2 = 105
Following the order of operations (Multiplication first):
- 12 \times 6 = 72
Now substitute this value back:
59 + 72 + 24 − 2 = 105
Perform addition and subtraction from left to right:
- 59 + 72 = 131
- 131 + 24 = 155
- 155 - 2 = 153
So, the equation becomes 153 = 105, which is false. Option 3 is incorrect.
Evaluating Option 4: −, ÷, +, ×, =
Substituting the signs into the equation:
59 − 12 ÷ 6 + 24 × 2 = 105
Following the order of operations (Division and Multiplication first, from left to right):
- 12 \div 6 = 2
- 24 \times 2 = 48
Now substitute these values back:
59 − 2 + 48 = 105
Perform subtraction and addition from left to right:
- 59 - 2 = 57
- 57 + 48 = 105
So, the equation becomes 105 = 105, which is true. Option 4 is correct.
Conclusion
By systematically testing each option and applying the correct order of operations, we found that the signs −, ÷, +, ×, = correctly balance the given equation.
Revision Table: Order of Operations
| Acronym | Meaning | Order |
|---|---|---|
| B / P | Brackets / Parentheses | First |
| O / E | Orders / Exponents (Powers, Square Roots, etc.) | Second |
| D / M | Division and Multiplication | Third (from left to right) |
| A / S | Addition and Subtraction | Fourth (from left to right) |
Additional Information: Equation Balancing Practice
Balancing equations by replacing signs is a common type of problem that tests your understanding of mathematical operations and the order of operations. To improve, practice solving similar problems. Pay close attention to the division operation, especially when it might result in fractions or decimals, although in many competitive exams, the numbers are chosen to give integer results at each step when the correct signs are used.
Understanding the BODMAS/PEMDAS rule is crucial for solving these types of problems accurately. A single mistake in the order can lead to an incorrect result. Always perform multiplication and division before addition and subtraction if they appear in the expression without brackets changing the order.
Similar Questions
Which two numbers and two signs should be interchanged to make the given equation correct?
5 + 44 - 8 × 25 = 203
Select the set in which the numbers are related in the same way as are the numbers of the following set.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits.)
(60, 5, 6)
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A & B means ‘A is the son of B’
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Statements:
All pens are plates.
All plates are trays.
Some trays are boxes.
Conclusions:
I. Some boxes are plates.
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III. Some boxes are pens.
IV. No tray is a plate.
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