If ‘+’ means ‘subtraction’, ‘−’ means ‘multiplication’, ‘÷’ means ‘addition’ and ‘×’ means ‘division’, then what is the value of the following expression? 22 − 4 + 72 × 18 ÷ 31
Expression Evaluation: Understanding Symbol Substitution
This problem requires us to evaluate a mathematical expression where the standard arithmetic symbols have been assigned new meanings. We need to follow these steps:
- Identify the given symbol substitutions.
- Rewrite the expression using the original numbers but the new meanings of the symbols.
- Apply the standard order of operations (BODMAS/PEMDAS) to calculate the final value.
Symbol Substitution Rules
The question provides the following specific rules for symbol substitution:
- '+' means subtraction ('-')
- '−' means multiplication ('×')
- '÷' means addition ('+')
- '×' means division ('÷')
Applying Substitutions to the Expression
The original expression is: 22 − 4 + 72 × 18 ÷ 31
Let's substitute the symbols according to the given rules:
- Replace '−' with '×':
22 × 4 - Replace '+' with '-':
... - 72 - Replace '×' with '÷':
... ÷ 18 - Replace '÷' with '+':
... + 31
The new expression becomes: 22 × 4 - 72 ÷ 18 + 31
Calculating the Expression Value using BODMAS/PEMDAS
We will now evaluate the transformed expression 22 × 4 - 72 ÷ 18 + 31 using the order of operations (BODMAS/PEMDAS):
- Division (÷): First, perform the division.
72 ÷ 18 = 4The expression is now:
22 × 4 - 4 + 31 - Multiplication (×): Next, perform the multiplication.
22 × 4 = 88The expression is now:
88 - 4 + 31 - Addition (+) and Subtraction (-): Finally, perform addition and subtraction from left to right.
First, subtraction:
88 - 4 = 84The expression is now:
84 + 31Then, addition:
84 + 31 = 115
Therefore, the value of the expression after applying the symbol substitutions and the order of operations is 115.
Similar Questions
Which two signs should be interchanged to make the given equation correct?
$36+8 \times 184-23\div10 = 90$Which two signs should be interchanged to make the given equation correct?
$152 + 8 \times 16 \div 9 - 4 = 309$
Important Questions from Bodmas Rule
The value of 30 ÷ 6 × 5 of (2 + 3) - 12(3 × 2) is equal to:
solve the following:
523 + 523 × 523 ÷ 523
The value of 96 - 4 of (18 - 13) + 4 × 7 is:
Find the value of 45 - 3 × (4 of 6 + 12 ÷ 3 × 6 - 4 × 5) + 6.
The value of \(\frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7}{8} - \frac{5}{4}} \right)} \right] - \frac{4}{5}\) is:
