If+means -,$\div$means+ , - means $\times$, and $\times$means $\div$, then, what is $30 - 5 + 10 \div 5$?
Evaluating Mathematical Expressions with Symbol Substitution
This problem requires us to evaluate a given mathematical expression, $30 - 5 + 10 \div 5$, after applying a specific set of rules for symbol substitution. We need to carefully replace the symbols and then follow the standard order of operations (like BODMAS/PEMDAS) to find the correct value.
Symbol Substitution Rules
First, let's understand the substitutions provided:
| Original Symbol | Replaced By |
| + | - |
| $\div$ | + |
| - | $\times$ |
| $\times$ | $\div$ |
Applying the Substitution
The original expression is:
$30 - 5 + 10 \div 5$
Now, let's apply the substitution rules to this expression:
- The subtraction symbol '-' between 30 and 5 is replaced by multiplication '$\times$'.
- The addition symbol '+' between 5 and 10 is replaced by subtraction '-'.
- The division symbol '$\div$' between 10 and 5 is replaced by addition '+'.
After applying these substitutions, the expression becomes:
$30 \times 5 - 10 + 5$
Evaluating the New Expression
We now need to evaluate the new expression $30 \times 5 - 10 + 5$ using the order of operations (BODMAS/PEMDAS):
- Multiplication and Division (from left to right):
- First, perform the multiplication: $30 \times 5 = 150$.
- Addition and Subtraction (from left to right):
- Perform the subtraction: $150 - 10 = 140$.
- The expression becomes: $140 + 5$.
- Perform the addition: $140 + 5 = 145$.
Thus, the final evaluated value of the expression after symbol substitution is 145.
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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.)
