Problem 62 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(5+3(6-4)\)

Step-by-Step Solution

Answer

11

Step 1: Evaluate the Expression Inside the Parentheses

Look at the expression inside the parentheses: y (6-4)Calculate the term within the parentheses first. 6-4=2

Step 2: Multiply the Result of the Parentheses

Now multiply the term outside the parentheses by the result from Step 1:3(2) = 6

Step 3: Add the Results Together

Finally, add the result from Step 2 to the first number in the equation:5 + 6 = 11

Key Concepts

Parentheses in arithmetic

In arithmetic, parentheses are used to dictate the order in which operations should be carried out. Operations enclosed in parentheses are performed first, before any other operations outside the parentheses. For example, in the expression \(5+3(6-4)\), the subtraction inside the parentheses \(6-4\) is carried out first. This makes it simpler to manage complex expressions by breaking them down into smaller, more manageable parts. Always remember, solve what's inside the parentheses first!

Multiplication

Multiplication is one of the basic operations in arithmetic and involves the repeated addition of a number. When you have parentheses in an expression, like \( 5 + 3(6-4) \), you need to handle the operation inside the parentheses first, and then, if there is any multiplication involved, you perform it next. In our example, after solving the expression inside the parentheses \(6-4 = 2\), you multiply 3 by 2 to get 6. Multiplication often comes with parentheses and should be handled carefully to ensure correct results.

Addition

Addition is the process of combining two or more numbers to get a sum. It is also one of the basic operations in arithmetic. In our initial example \(5 + 3(6-4)\), after handling what is inside the parentheses and performing the multiplication, you finally add the results together. After calculating \(3 \times 2 = 6\), you then add 5 to 6 to get a final result of 11. Addition is typically the last step in a sequence of operations unless there are parentheses altering the usual order.