Problem 21 - Elementary Algebra

Question

For the following problems, use the order of operations to find each value. $$18 \div 2+55$$

Step-by-Step Solution

Answer

Answer: The value of the expression is $$64$$.

Step 1: Check for parentheses and exponents

There are no parentheses or exponents in the given expression, so we can move to the next step.

Step 2: Perform multiplication and division, from left to right

We have one division operation in the expression: $$18 \div 2$$. We will perform this operation: $$18 \div 2 = 9$$.

Step 3: Perform addition and subtraction, from left to right

Now, we have the expression $$9+55$$. We will perform this addition operation: $$9 + 55 = 64$$.

Step 4: Complete the expression

There are no more operations to perform. The value of the expression is $$64$$.

Key Concepts

Division

In mathematics, division is one of the fundamental operations we use to split a number into equal parts. When you see a division sign (÷) in an expression, it means you're going to share something equally. Let's say you have 18 chocolates, and you want to share them equally among 2 friends. In mathematical terms, you would calculate 18 ÷ 2, which simplifies to 9.

This means each friend gets 9 chocolates.

• Start with the total amount: 18 in this case.
• Divide by the number of groups or shares: here, it's 2.
• Calculate the result: 9.

When using division in expressions, always remember that it follows right after any operations inside parentheses or involving exponents, moving from left to right in accordance with the order of operations. In our given expression 18 ÷ 2 + 55, the division is executed first to break down this step clearly.

Addition

Addition is one of the most basic operations in arithmetic. It involves calculating the total of two or more numbers. In our example, after performing the division and getting 9, the next step is to add this result to 55.

Here's how you execute addition for expressions:

• Take the number from the previous result: 9, from the division step.
• Add it to the next number in the sequence: 55.
• Combine both to get the result: 64.

The operation results in the sum of these two numbers, yielding 64 in this case. Addition is calculated after any division or multiplication operations are done. This following of order is crucial for getting the correct results in complex expressions.

Expressions

An expression in mathematics is a combination of numbers and operations, like addition and division, that represents a specific value. Understanding expressions is key to solving many problems in math.

In the expression we used: 18 ÷ 2 + 55, the order of operations, sometimes remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), dictates the sequence in which operations are performed.

• Identify which operations need to be done first, following PEMDAS.
• Calculate each step in the correct order to avoid errors.
• Find the final value by combining all parts of the expression step by step.

When solving expressions, make sure you follow these steps carefully and work through each one methodically to reach the right answer.