Problem 17 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ 13+3 \cdot 7 $$

Step-by-Step Solution

Answer

The evaluated expression is 34.

Step 1: Identify the operations involved

The expression contains the operations of addition and multiplication. The operators are '+' and '\cdot' respectively. The numbers involved are 13, 3, and 7.

Step 2: Apply the order of operations

According to the order of operations (PEMDAS), we perform multiplication before addition. Hence, we first find the product of 3 and 7.

Step 3: Perform the multiplication

The product of 3 and 7 is 21.

Step 4: Perform the addition

The sum of the result of the multiplication (21) and 13 is 34.

Key Concepts

Understanding PEMDAS

When solving mathematical expressions like \(13 + 3 \cdot 7\), it's important to follow the order of operations. The order of operations can be remembered using the acronym **PEMDAS**.

• **P** stands for Parentheses: Any operations inside parentheses are performed first.
• **E** stands for Exponents: Exponential operations come next.
• **MD** stands for Multiplication and Division: After parentheses and exponents, multiplication and division are performed from left to right.
• **AS** stands for Addition and Subtraction: Finally, addition and subtraction are carried out from left to right.

In our example, since there are no parentheses or exponents, we start with multiplication before addressing addition. Identifying the correct order of operations is essential to arriving at the correct solution.

Mastering Multiplication

In this expression, multiplication is the first operation to tackle after determining the correct order using PEMDAS. The expression involves multiplying 3 by 7. Multiplication is simply repeated addition. For instance, multiplying 3 by 7 means you have seven groups of 3, which equals: \[ 3 \cdot 7 = 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21 \]Hence, before moving forward in our expression, the multiplication results in 21. Mastering this operation is key, especially since it often precedes addition in many expressions following the order of operations rules.

Addition in Action

After solving the multiplication part of the expression \( 13 + 3 \cdot 7 \), the result is 21. Now it's time to perform the addition, which is the final step according to the PEMDAS guideline. Addition is the process of combining two or more numbers to get a sum. In our case, add the result of the multiplication (21) to the number 13. So, we compute: \[ 13 + 21 = 34 \]Each number represents a collection, adding them together gives us a total of 34. Mastery of addition helps simplify and conclude many mathematical problems effectively.