To determine which operation should be carried out first in the expression
[tex]\[ (3 + 2 \cdot 5) - 2^2 + 24 \div 4, \][/tex]
we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Let's break down the steps:
1. Parentheses: We perform the operations inside the parentheses first. Here, inside the parentheses, we have [tex]\(2 \cdot 5\)[/tex].
[tex]\[ 3 + 2 \cdot 5 = 3 + 10 = 13 \][/tex]
So the expression now is:
[tex]\[ 13 - 2^2 + 24 \div 4 \][/tex]
2. Exponents: Next, we evaluate the exponent [tex]\(2^2\)[/tex].
[tex]\[ 2^2 = 4 \][/tex]
Now the expression becomes:
[tex]\[ 13 - 4 + 24 \div 4 \][/tex]
3. Multiplication and Division: We perform any multiplication or division from left to right. Here, we have the division [tex]\(24 \div 4\)[/tex].
[tex]\[ 24 \div 4 = 6 \][/tex]
Updating our expression, we get:
[tex]\[ 13 - 4 + 6 \][/tex]
4. Addition and Subtraction: Finally, we perform addition and subtraction from left to right.
[tex]\[ 13 - 4 = 9 \][/tex]
[tex]\[ 9 + 6 = 15 \][/tex]
Now, let’s summarize the steps:
1. The first operation inside the parentheses was [tex]\(2 \cdot 5\)[/tex].
2. Then, we evaluated the exponent [tex]\(2^2\)[/tex].
3. We then performed the division [tex]\(24 \div 4\)[/tex].
4. Finally, we completed the arithmetic operations with subtraction and addition left to right.
Therefore, the first operation performed in evaluating this expression is multiplication. The correct option is not divide but multiply.
