Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation. 7 * 5 * 4 * 2 * 3 * 7
+, −, ÷, −, =
Balancing Mathematical Equations
The question asks us to find the correct sequence of mathematical signs that, when placed sequentially in the blank spaces marked by asterisks (*), will make the equation true.
The given expression is 7 * 5 * 4 * 2 * 3 * 7.
We need to replace the five asterisks with operators from the options and the final number with the result of the calculation, essentially forming an equation of the form:
`$\text{7 \text{[op1]} 5 \text{[op2]} 4 \text{[op3]} 2 \text{[op4]} 3 = 7}$`
Let's examine the options and test them.
Testing Option 2: +, −, ÷, −, =
Substituting the operators from Option 2 into the expression, the equation becomes:
`$\text{7 + 5 - 4 ÷ 2 - 3 = 7}$`
Now, we evaluate the left side of the equation according to the standard order of operations (BODMAS/PEMDAS):
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
Let's evaluate the expression `$\text{7 + 5 - 4 ÷ 2 - 3}$` step by step:
- First, perform the division: `$\text{4 ÷ 2 = 2}$`
The equation is now:
`$\text{7 + 5 - 2 - 3 = 7}$`
- Next, perform addition and subtraction from left to right.
- `$\text{7 + 5 = 12}$`
The equation becomes:
`$\text{12 - 2 - 3 = 7}$`
- Continue with subtraction: `$\text{12 - 2 = 10}$`
The equation becomes:
`$\text{10 - 3 = 7}$`
- Finally, perform the last subtraction: `$\text{10 - 3 = 7}$`
The equation is:
`$\text{7 = 7}$`
The left side of the equation equals the right side. Thus, the equation is balanced with the signs `+`, `−`, `÷`, `−`, and the result `= 7`.
Other options would not balance the equation. For example, Option 1 includes `7 ÷ 5` which does not result in a whole number, making it difficult to reach 7 with subsequent integer operations.
Therefore, the correct combination of mathematical signs is `+`, `−`, `÷`, `−`, which makes the equation `7 + 5 - 4 ÷ 2 - 3 = 7` true.
Revision Table: Order of Operations
| Priority Level | Operation Type | Examples |
|---|---|---|
| 1 | Parentheses/Brackets | ( ), [ ], { } |
| 2 | Exponents/Orders | Powers, Roots |
| 3 | Multiplication and Division | `$\times$`, `$\div$` (from left to right) |
| 4 | Addition and Subtraction | `$+$`, `$-$` (from left to right) |
Additional Information: Solving Equation Balancing Problems
Equation balancing problems require systematic testing of the given options. When testing an option, it is crucial to correctly apply the order of operations (BODMAS/PEMDAS) to evaluate the expression. Perform calculations involving division or multiplication before addition or subtraction. If multiple operations of the same priority level exist (like multiplication and division, or addition and subtraction), solve them from left to right.
Careful calculation is key to accurately determining which sequence of signs balances the equation.
Similar Questions
Read the given statements and conclusions carefully. You have to take the given statements to be true even if they seem to be at variance from commonly known facts. You have to decide which conclusion/s logically follow/s from the given statements.
Statements:
All beaches are sand.
Some deserts are sand.
All mountains are rocky.
Conclusions:
(I) At least some beaches are desert.
(II) At least some sands are rocky.
Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given equation.
256 * 4 * 9 * 3 * 14 = 51
Select the correct combination of mathematical signs to sequentially replace the * signs and balance the given equation.
86 * 54 * 34 * 68 * 2 * 33
Which two signs should be interchanged to make the given equation correct?
60 × 4 + 9 ÷ 3 - 8 = 34
If '+' means 'division', '-' means 'multiplication', '÷' means 'addition' and '× ' means 'subtraction', then what is the value of the following expression?
14 - 4 ÷ 133 + 7 × 17
Which two signs should be interchanged to make the given equation correct?
625 ÷ 25 + 7 × 318 - 112 = 381
Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
5 * 23 * 24 * 4 * 10 * 111
Which of the following interchanges of signs would make the given equation correct?
100 + 100 × 50 - 2 ÷ 3 = 51
Which of the following interchange of numbers and signs would make the given equation correct?
24 × 9 + 6 ÷ 24 - 18 = 22
Select the correct combination of mathematical signs that can sequentially replace the * signs and balance the given equation.
11 * 13 * 238 * 17 * 34 = 123
Important Questions from Logical Puzzle
If ‘A’ denotes ‘addition’, ‘B’ denotes ‘subtraction’, ‘C’ denotes ‘multiplication’ and ‘D’ denotes ‘division’, then what will be the value of the following expression?
6 C (57 B 8) D 7 B 32 A 9
If, 5 + 7 = 47, 3 + 8 = 35, 9 + 2 = 29 then 7 + 4 = ?
Which two signs need to be interchanged to make the following equation correct?
63 ÷ 21 – 7 + 28 × 3 = 144
If ‘–’ stands for ‘÷’, ‘+’ stands for ‘×’, ‘÷’ stands for ‘–’ and ‘×’ stands for ‘+’, then 80 – 20 + 10 ÷ 8 × 10 is equal to:
Which two signs need to be interchanged to make the given equation correct?
3 ÷ 2 - 4 × 5 + 5 = 1
