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.
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.)
