Select the correct set of symbols which will fit in the given equation?
-, +, ×
Solving the Equation Puzzle with Symbols
The question asks us to find the correct set of mathematical symbols to place between the numbers 8, 0, 3, and 9 so that the equation equals 35.
The equation is:
\( 8 \_ 0 \_ 3 \_ 9 = 35 \)We are given four options with different combinations of symbols.
Analyzing the Correct Symbol Combination
We need to test the given options to see which set of symbols correctly completes the equation to equal 35. Let's consider the option that provides the symbols \( -, +, \times \) in that order.
Placing these symbols between the numbers, the equation becomes:
\( 8 - 0 + 3 \times 9 = 35 \)Applying the Order of Operations (BODMAS/PEMDAS)
To correctly evaluate the expression \( 8 - 0 + 3 \times 9 \), we must follow the mathematical order of operations. This is often remembered using acronyms like BODMAS or PEMDAS.
- B/P: Brackets or Parentheses
- O/E: Orders or Exponents (like powers and square roots)
- D/M: Division and Multiplication (done from left to right)
- A/S: Addition and Subtraction (done from left to right)
In the expression \( 8 - 0 + 3 \times 9 \), we have subtraction, addition, and multiplication. According to the order of operations, multiplication must be performed before addition and subtraction.
Step-by-Step Calculation:
Step 1: Perform the multiplication operation first.
\( 3 \times 9 = 27 \)Now substitute this result back into the equation:
\( 8 - 0 + 27 \)Step 2: Now we have subtraction and addition. These operations have the same priority, so we perform them from left to right.
First, perform the subtraction:
\( 8 - 0 = 8 \)Substitute this result back:
\( 8 + 27 \)Finally, perform the addition:
\( 8 + 27 = 35 \)Verifying the Equation Result
The result of evaluating \( 8 - 0 + 3 \times 9 \) following the correct order of operations is 35.
\( 8 - 0 + 3 \times 9 = 35 \) \( 8 - 0 + 27 = 35 \) \( 8 + 27 = 35 \) \( 35 = 35 \)Since the calculated result matches the right side of the equation (35), the set of symbols \( -, +, \times \) is indeed the correct one that fits in the given equation.
You can test the other options using the same method and order of operations to confirm that they do not result in 35.
Revision Table: Checking Options
| Option | Symbols | Equation | Calculation | Result |
|---|---|---|---|---|
| 1 | \( +, -, \times \) | \( 8 + 0 - 3 \times 9 \) | \( 8 + 0 - 27 = 8 - 27 \) | \( -19 \) |
| 2 | \( -, +, \times \) | \( 8 - 0 + 3 \times 9 \) | \( 8 - 0 + 27 = 8 + 27 \) | \( 35 \) |
| 3 | \( \times, \times, \times \) | \( 8 \times 0 \times 3 \times 9 \) | \( 0 \times 3 \times 9 = 0 \times 9 \) | \( 0 \) |
| 4 | \( \times, +, \times \) | \( 8 \times 0 + 3 \times 9 \) | \( 0 + 27 \) | \( 27 \) |
The table shows that only option 2 yields the correct result of 35.
Additional Information: Importance of Order of Operations
The order of operations is a fundamental concept in mathematics. It provides a clear set of rules to follow when evaluating expressions with multiple operations, ensuring consistency and accuracy.
Without a standard order, expressions could be interpreted and calculated in different ways, leading to various possible answers for the same problem. For example, without the rule that multiplication comes before addition, \( 8 - 0 + 3 \times 9 \) could potentially be calculated as \( (8 - 0 + 3) \times 9 = 11 \times 9 = 99 \), which is incorrect.
Always remember to apply BODMAS or PEMDAS to solve mathematical expressions correctly.
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