what is 8+ (3-2)* 4/1?
Understanding the Symbol Substitution Rule
This problem involves a mathematical expression where the standard arithmetic operators (+, -, *, /) have been assigned new meanings. We need to decode these new rules and then solve the given expression.
The given rules are:
- Addition (\(+\)) is replaced by Subtraction (\(-\))
- Subtraction (\(-\)) is replaced by Multiplication (\(*\))
- Multiplication (\(*\)) is replaced by Division (\(/\))
- Division (\(/\)) is replaced by Addition (\(+\))
The original mathematical expression is: \(8 + (3 - 2) * 4 / 1\)
Applying the Symbol Replacements
Let's apply the given substitution rules to the original expression step-by-step:
- Replace \(+\) with \(-\): The expression becomes \(8 - (3 - 2) * 4 / 1\).
- Replace \(-\) inside the parenthesis with \(*\): The expression becomes \(8 - (3 * 2) * 4 / 1\).
- Replace the first \(*\) with \(/\): The expression becomes \(8 - (3 * 2) / 4 / 1\).
- Replace the \(/\) with \(+\): The expression becomes \(8 - (3 * 2) / 4 + 1\).
So, the transformed expression we need to evaluate is:
\(8 - (3 * 2) / 4 + 1\)
Evaluating the Transformed Expression
Now, we need to solve the new expression \(8 - (3 * 2) / 4 + 1\) using the standard order of operations (often remembered by acronyms like BODMAS or PEMDAS).
The order of operations is: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- Parentheses: First, calculate the expression inside the parentheses.
\(3 \times 2 = 6\) The expression is now: \(8 - 6 / 4 + 1\). - Division: Next, perform the division.
\(\frac{6}{4} = 1.5\) The expression is now: \(8 - 1.5 + 1\). - Subtraction: Perform subtraction from left to right.
\(8 - 1.5 = 6.5\) The expression is now: \(6.5 + 1\). - Addition: Finally, perform the addition.
\(6.5 + 1 = 7.5\)
Therefore, the value of the expression after applying the symbol substitutions and following the order of operations is 7.5.
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?
24 – 4 + 18 × 3 ÷ 7
Which two signs need to be interchanged to make the following equation correct?
{(78 + 70) − (6 × 2))} ÷ 2 = 10Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
(87 * 63) * 6 * 1 * 5
Select the figure from among the given options that can replace the question mark (?) in the following series.
- If += -, - *, *= /, / = +; then,
what is 6+ (4*2)-3/1? - If 'Alpha' means addition, 'Beta' means subtraction, 'Gamma' means multiplication, and 'Delta' means division, then what is the
value of \(100 \ \text{Delta} \ 5 \ \text{Beta} \ 10 \ \text{Alpha} \ 2 \ \text{Gamma} \ 3\)? - What will come in place of the question mark (?) in the following equation?
\(72\div9-15+4\times3=?\) - If + = \(\times\), - = +, \(\times\) = \(\div\), / = -; then,
what is \((4+5) \times 2 - 3 \div 1\)?
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
