what is \((4+5) \times 2 - 3 \div 1\)?
This problem involves evaluating a mathematical expression where the standard arithmetic operators have been replaced with different ones. We need to carefully apply the given substitutions and then follow the order of operations (BODMAS/PEMDAS) to find the correct result.
Symbol Substitutions Explained
The question provides a specific set of rules for substituting the mathematical operators:
- The plus sign (\(+\)) is replaced by the multiplication sign (\(\times\)).
- The minus sign (\(-\)) is replaced by the plus sign (\(+\)).
- The multiplication sign (\(\times\)) is replaced by the division sign (\(\div\)).
- The division sign (\(/\)) is replaced by the minus sign (\(-\)).
Expression Evaluation Step-by-Step
The original expression given is: \((4 + 5) \times 2 - 3 \div 1\)
Let's apply the substitutions rule by rule:
- Substitute '+' with '\(\times\)': The expression becomes \((4 \times 5) \times 2 - 3 \div 1\).
- Substitute '\(\times\)' with '\(\div\)': The expression is now \((4 \times 5) \div 2 - 3 \div 1\).
- Substitute '-' with '+': The expression changes to \((4 \times 5) \div 2 + 3 \div 1\).
- Substitute '/' with '-': The final substituted expression is \((4 \times 5) \div 2 + 3 - 1\).
Now, we evaluate the new expression \((4 \times 5) \div 2 + 3 - 1\) using the standard order of operations (BODMAS/PEMDAS):
- Brackets / Parentheses: First, calculate the operation inside the parentheses.
\(4 \times 5 = 20\)
The expression simplifies to: \(20 \div 2 + 3 - 1\)
- Division: Next, perform the division operation.
\(20 \div 2 = 10\)
The expression becomes: \(10 + 3 - 1\)
- Addition: Then, perform the addition.
\(10 + 3 = 13\)
The expression is now: \(13 - 1\)
- Subtraction: Finally, perform the subtraction.
\(13 - 1 = 12\)
Therefore, the value of the expression after applying the given symbol substitutions is 12.
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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.)
