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.
Similar Questions
The two expressions on either side of the equal sign will have the same value if two numbers on the left-hand side are interchanged and two signs on the right-hand side are interchanged.
What are those two numbers (not digits) and the two signs?
4 × 3 ÷ 6 + 2 - 8 = 10 + 2 × 3 ÷ 5 - 18
- At a banquet, every 2 people shared a cake, every 6 people shared a bowl of soup, and every 8 people shared a platter of fruit. There were a total of 42 items. How many people were present at the banquet?
If + means ×, × means −, − means ÷, and ÷ means +, what will be the value of the given expression?
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Which two signs need to be interchanged to make the following equation correct?
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Select the figure from among the given options that can replace the question mark (?) in the following series.
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\(72\div9-15+4\times3=?\) If + = \(\times\), - = /, \(\times\) = +, / = -; then,
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Important Questions from Mathematical Operations
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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.)
(6, 13, 78)
(5, 22, 110)
If + means -, - means ×, × means ÷, ÷ means +, then what will come in place of the question mark (?) in the following equation?
28 - 6 ÷ 4 + 14 × 14 = ?
In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its 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.)
X : 649 :: 956 : Y
Which two numbers should be interchanged to make the given equation correct?
75 ÷ 5 + 15 × 4 - 17 × 3 + (60 ÷ 6) × 10 = 100
(Note: Interchange should be done of the entire number and not individual digits of a given number.)
If '+' means minus, '-' means multiplication, '÷' means plus, and 'x' means division, then solve the equation:
15 - 3 + 10 x 5 ÷ 5
