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Sagot :
To simplify the given expression, we will follow the BODMAS/PEMDAS rules, which stand for:
- Brackets/Parentheses
- Orders (i.e., powers and square roots, etc.)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
The given equation is:
[tex]\[ 90 + \{10 + 15 \times 3 - (20 + 30 - 45 + 5)\} \][/tex]
Let's solve this step-by-step.
### Step 1: Solve the innermost bracket
First, we handle the innermost expressions within the brackets:
[tex]\[ (20 + 30 - 45 + 5) \][/tex]
This can be calculated as:
[tex]\[ 20 + 30 = 50 \][/tex]
[tex]\[ 50 - 45 = 5 \][/tex]
[tex]\[ 5 + 5 = 10 \][/tex]
Therefore,
[tex]\[ (20 + 30 - 45 + 5) = 10 \][/tex]
### Step 2: Substitute the result back into the expression
Now substitute the evaluated expression back:
[tex]\[ 90 + \{10 + 15 \times 3 - 10\} \][/tex]
### Step 3: Perform the multiplication
Next, solve the multiplication:
[tex]\[ 15 \times 3 = 45 \][/tex]
Substitute this back into the expression:
[tex]\[ 90 + \{10 + 45 - 10\} \][/tex]
### Step 4: Handle the addition and subtraction inside the curly brackets
Now add and subtract within the brackets:
[tex]\[ 10 + 45 = 55 \][/tex]
[tex]\[ 55 - 10 = 45 \][/tex]
So we have:
[tex]\[ 90 + 45 \][/tex]
### Step 5: Perform the final addition
Finally, add the remaining numbers:
[tex]\[ 90 + 45 = 135 \][/tex]
### Conclusion
The simplified result of the expression is:
[tex]\[ \boxed{135} \][/tex]
- Brackets/Parentheses
- Orders (i.e., powers and square roots, etc.)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)
The given equation is:
[tex]\[ 90 + \{10 + 15 \times 3 - (20 + 30 - 45 + 5)\} \][/tex]
Let's solve this step-by-step.
### Step 1: Solve the innermost bracket
First, we handle the innermost expressions within the brackets:
[tex]\[ (20 + 30 - 45 + 5) \][/tex]
This can be calculated as:
[tex]\[ 20 + 30 = 50 \][/tex]
[tex]\[ 50 - 45 = 5 \][/tex]
[tex]\[ 5 + 5 = 10 \][/tex]
Therefore,
[tex]\[ (20 + 30 - 45 + 5) = 10 \][/tex]
### Step 2: Substitute the result back into the expression
Now substitute the evaluated expression back:
[tex]\[ 90 + \{10 + 15 \times 3 - 10\} \][/tex]
### Step 3: Perform the multiplication
Next, solve the multiplication:
[tex]\[ 15 \times 3 = 45 \][/tex]
Substitute this back into the expression:
[tex]\[ 90 + \{10 + 45 - 10\} \][/tex]
### Step 4: Handle the addition and subtraction inside the curly brackets
Now add and subtract within the brackets:
[tex]\[ 10 + 45 = 55 \][/tex]
[tex]\[ 55 - 10 = 45 \][/tex]
So we have:
[tex]\[ 90 + 45 \][/tex]
### Step 5: Perform the final addition
Finally, add the remaining numbers:
[tex]\[ 90 + 45 = 135 \][/tex]
### Conclusion
The simplified result of the expression is:
[tex]\[ \boxed{135} \][/tex]
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