Problem 79 - Algebra 1: Concepts and Skills

Question

NUMERICAL EXPRESSIONS Evaluate the expression. Then simplify the answer. (Lesson 1.3) $$ 49 \div 7+2 $$

Step-by-Step Solution

Answer

The evaluation of the expression 49 ÷ 7 + 2 results in 9.

Step 1: Perform Division

According to the order of operations, division must be performed first. Therefore, let's first divide 49 by 7. This division results in 7.

Step 2: Perform Addition

After having resolved the division operation in the given expression, an addition operation remains. We must now add the result from Step 1 (7) to 2. This results in 9.

Key Concepts

Order of Operations

When evaluating numerical expressions, it's crucial to follow the order of operations. This rule determines which operations should be performed first to ensure consistent results. The order is typically remembered by the acronym PEMDAS:

• Parentheses - calculate anything inside parentheses first.
• Exponents - solve any exponential terms next.
• Multiplication and Division - from left to right.
• Addition and Subtraction - from left to right

It is important to note that multiplication and division are performed from left to right, as they appear in the expression, not necessarily multiplication before division. The same rule applies to addition and subtraction. Following these guidelines helps avoid errors when simplifying expressions.

Division

Division is one of the key arithmetic operations and in the order of operations comes before addition or subtraction. In the expression given, \(49 \div 7 + 2\), division occurs first. So you take \(49\) and divide it by \(7\).

• This division simplifies the expression to \(7\), because \(49 \div 7 = 7\).

Remember, division helps break down a problem into smaller amounts, making it easier to manage other operations that follow.
Understanding division can help clear up confusion when evaluating complex expressions, especially when it's prioritized over other operations.

Addition

After completing multiplication and division, addition comes next according to the order of operations. In our exercise, after simplifying \(49 \div 7\) to \(7\), the expression becomes \(7 + 2\). Addition is straightforward, but it’s vital that it's executed at the right step.

• Simply add \(7\) and \(2\) to get \(9\).

Getting comfortable with basic arithmetic like addition can be helpful, especially when ensuring all operations are performed in the correct order. The result from this addition gives us the solution to the expression, showing how each layer of the problem simplifies step-by-step.