Sure, let's simplify the expression step-by-step using the order of operations rules, which are often remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
The expression we are simplifying is:
[tex]\[ 7 + 2 \cdot 20 - 3 \cdot 9 + 39 \div 3 \][/tex]
### Step-by-step Solution:
1. Multiplication and Division: First, we perform the multiplications and the division from left to right.
- Multiply [tex]\( 2 \cdot 20 \)[/tex]:
[tex]\[
2 \cdot 20 = 40
\][/tex]
- Multiply [tex]\( 3 \cdot 9 \)[/tex]:
[tex]\[
3 \cdot 9 = 27
\][/tex]
- Divide [tex]\( 39 \div 3 \)[/tex]:
[tex]\[
39 \div 3 = 13
\][/tex]
2. Substitute back into the expression: Now, substitute these results back into the original expression:
[tex]\[ 7 + 40 - 27 + 13 \][/tex]
3. Addition and Subtraction from left to right: Finally, perform the addition and subtraction from left to right.
- First, add [tex]\( 7 + 40 \)[/tex]:
[tex]\[
7 + 40 = 47
\][/tex]
- Then, subtract [tex]\( 47 - 27 \)[/tex]:
[tex]\[
47 - 27 = 20
\][/tex]
- Finally, add [tex]\( 20 + 13 \)[/tex]:
[tex]\[
20 + 13 = 33
\][/tex]
The simplified result of the expression [tex]\( 7 + 2 \cdot 20 - 3 \cdot 9 + 39 \div 3 \)[/tex] is:
[tex]\[ 33.0 \][/tex]
