Problem 13 - Elementary Algebra

Question

For the following problems, use the order of operations to find each value. $$(21+4) \div 5 \cdot 2$$

Step-by-Step Solution

Answer

Answer: The value of the expression is 10.

Step 1: Solve within Parentheses/Brackets

According to the order of operations, we need to first solve the expression inside the parentheses: $$(21+4) \div 5 \cdot 2$$ Solve for (21+4): $$25 \div 5 \cdot 2$$

Step 2: Division

Next, we need to perform the division operation: $$25 \div 5 \cdot 2$$ Divide 25 by 5: $$5 \cdot 2$$

Step 3: Multiplication

Finally, perform the multiplication operation: $$5 \cdot 2$$ Multiply 5 by 2: $$10$$ So the value of the given expression is 10.

Key Concepts

Parentheses

Parentheses are used to group parts of a mathematical expression that need to be solved first. This is the first step in the order of operations. Whenever you see parentheses, it's a sign to pause and tackle them before moving on to other calculations.

In our example, the operation inside the parentheses is \(21 + 4\). No matter what other operations are outside, solve this part first. Here, adding these numbers gives us 25.

• The expression becomes: \(25 \div 5 \cdot 2\).
• This result is crucial for the next operations.

Always remember, what is inside parentheses changes the outcome! Without solving these first, the entire calculation would go wrong.

Division

Division comes after parentheses in the order of operations. Once what's inside the parentheses is resolved, move on to division if it is next in line.

In the remaining expression \(25 \div 5 \cdot 2\), division is the next operation. Here, divide 25 by 5 to simplify this part of the expression.

• Performing the division gives you 5.
• The expression now reduces to \(5 \cdot 2\).

Always ensure that division is carried out correctly, as it can significantly influence the final result.

Multiplication

Multiplication follows division when working with order of operations, assuming no addition or subtraction appears in between. It is the last step in our given example.

Back to our simplified expression, after dividing, we are left with \(5 \cdot 2\).
Multiplying these values gives you the final result.

• Multiply 5 by 2, resulting in 10.
• This final step gives you the value of the original expression.

By following these steps in order, you ensure that the expression is calculated correctly according to mathematical rules.