Problem 64 - Elementary Algebra

Question

. \(10+6 \div 2\)

Step-by-Step Solution

Answer

13

Step 1: Identify the Operations

Look at the given expression, which is 10 + 6 ÷ 2. Identify the operations involved: addition (+) and division (÷).

Step 2: Follow Order of Operations

According to the order of operations (PEMDAS/BODMAS), perform division before addition. So, start by evaluating 6 ÷ 2.

Step 3: Perform the Division

Calculate 6 ÷ 2 and get 3. Now the expression is simplified to 10 + 3.

Step 4: Perform the Addition

Add 10 and 3 together. 10 + 3 equals 13.

Key Concepts

PEMDAS

Understanding the order of operations is crucial when simplifying expressions like the one in the exercise. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

These operations must be solved in this specific order to get the correct result. Here's a quick breakdown:

• Parentheses: Solve anything inside parentheses first
• Exponents: Then calculate exponents (powers and roots, etc.)
• Multiplication and Division: Perform these operations from left to right
• Addition and Subtraction: Finally, tackle these from left to right

In the given exercise, PEMDAS helped prioritise division before addition, ensuring the correct final answer.

Division

Division is one of the fundamental operations in mathematics. It involves splitting a quantity into equal parts. In the exercise, we need to divide 6 by 2.

Mathematically, 6 ÷ 2 can also be written as \(\frac{6}{2}\) . This means we are splitting 6 into 2 equal parts, resulting in 3. Once we compute this, the original expression 10 + 6 ÷ 2 simplifies to 10 + 3.

Always remember to perform division before moving on to other operations like addition, as guided by PEMDAS.

Addition

Addition is the process of finding the total or sum by combining two or more numbers. Once we simplified the expression to 10 + 3, we move onto adding these two numbers.

Now, 10 + 3 means finding the sum of 10 and 3, which gives us 13.

Addition is simpler than division, but it's important to follow the correct order of operations to ensure accurate results. In our example, addition was the final step after performing division.

Simplifying Expressions

Simplifying expressions means breaking them down into their simplest form. This involves performing all the operations in the correct order until you reach the final solution.

In our exercise, we started with the expression 10 + 6 ÷ 2. By following PEMDAS, we identified division should be done first (6 ÷ 2).
This simplified our expression to 10 + 3.

Next, we performed the addition to get the final answer of 13.

The key in simplifying is to take things step by step and follow the correct order of operations. When done correctly, it makes solving complex expressions much easier and less error-prone.