Problem 57 - Elementary Algebra

Question

\(6+15 \div 3\)

Step-by-Step Solution

Answer

The result of 6 + 15 ÷ 3 is 11.

Step 1: Identify the Order of Operations

Recall the order of operations using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step 2: Division First

According to PEMDAS, perform the division operation first. Calculate: If there are parentheses, handle those first, but in this case, there are none. So, calculate: Note the division of 15 by 3.

Step 3: Perform the Division

Calculate To divide 15 by 3: 15 15 15 3 = 5.

Step 4: Perform the Addition

Now, add the result of the division to 6: 6 +5 = 11. So, the final result: 6 + 5 = 11.

Key Concepts

Understanding PEMDAS

Let's dive deeper into the order of operations using the acronym PEMDAS. PEMDAS helps us remember the correct sequence of operations to solve a mathematical expression accurately. PEMDAS stands for:

P: Parentheses

E: Exponents

M: Multiplication

D: Division

A: Addition

S: Subtraction

It is important to note that multiplication and division, as well as addition and subtraction, should be performed from left to right, based on their occurrence in the expression. In our exercise, the expression is 6 + 15 ÷ 3. There are no parentheses or exponents, so we start by handling the division before moving to addition. This ensures that we follow the correct order to get the right answer.

Performing Division

Now that we know we need to follow PEMDAS, let's focus on the division part of the expression. Division is one of the crucial operations you'll encounter in many mathematical problems. In our given problem, we have 15 ÷ 3.

To perform this operation correctly:

First, take the dividend, which is the number that is being divided. Here, it's 15.

Next, take the divisor, which is the number you are dividing by. Here, it's 3.

Now, divide 15 by 3, which results in 5. This means that 15 ÷ 3 = 5.

By handling the division first, we simplify our original problem to 6 + 5.

Performing Addition

Once the division is completed, the next step is to perform the addition. Addition is one of the most basic arithmetic operations. It involves combining numbers to get their total sum.

In our simplified problem, we now have 6 + 5.

To solve this:

Simply add 6 and 5 together.

You get 11 as a result.

So, 6 + 5 = 11. This means the final answer to the original expression 6 + 15 ÷ 3 is 11.

By breaking down the problem using PEMDAS, we ensure each operation is performed in the correct order, leading us to the correct answer.