If + means -, $\div$ means +, - means $\times$, and $\times$ means $\div$ then,
what is $18 \div 6 - 2 + 8$?
Understanding Operator Substitution
This problem involves changing the standard meaning of mathematical operators. We need to replace the given operators with new ones and then solve the expression using the standard order of operations (PEMDAS/BODMAS).
Operator Substitution Rules
The question provides the following substitutions:
- '+' means '-'
- '$\div$' means '+'
- '-' means '$\times$'
- '$\times$' means '$\div$'
Applying the Substitution
The original expression is: $18 \div 6 - 2 + 8$
Let's substitute each operator based on the rules:
- Replace '$\div$' with '+'.
- Replace '-' with '$\times$'.
- Replace '+' with '-'.
The expression transforms into:
$18 + 6 \times 2 - 8$
Solving the Transformed Expression
Now, we solve the new expression $18 + 6 \times 2 - 8$ using the order of operations (PEMDAS/BODMAS):
- Parentheses/Brackets: None in this expression.
- Exponents/Orders: None in this expression.
- Multiplication and Division (from left to right): We have multiplication $6 \times 2$.
Calculate $6 \times 2 = 12$.
The expression becomes: $18 + 12 - 8$.
- Addition and Subtraction (from left to right):
First, perform the addition: $18 + 12 = 30$.
The expression becomes: $30 - 8$.
Finally, perform the subtraction: $30 - 8 = 22$.
Final Result
After applying the operator substitutions and following the order of operations, the value of the expression $18 \div 6 - 2 + 8$ is 22.
Similar Questions
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What will come in place of the question mark (?) in the following equation?
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Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?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?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
