Problem 91 - Prealgebra

Question

Simplify. $$24-14+8$$

Step-by-Step Solution

Answer

The simplified result is 18.

Step 1: Identify the Operations

The expression given is \(24-14+8\). It involves two operations: subtraction and addition.

Step 2: Perform the Subtraction

Subtract \(14\) from \(24\), the result is \(24 - 14 = 10\).

Step 3: Perform the Addition

Now add \(8\) to the result from the previous step, which is \(10\). So, \(10 + 8 = 18\).

Step 4: Write the Simplified Result

After performing the operations, the expression simplifies to \(18\).

Key Concepts

Addition and Subtraction

Addition and subtraction are basic arithmetic operations that we often encounter in math problems. They are crucial in simplifying expressions, especially when dealing with multiple numbers and operations.

When handling expressions, always follow the left-to-right sequence for these operations when there are no parentheses to change the order. It's important to start with subtraction, if it's first in line, and then proceed to addition, as you come across them.

• Addition: This operation involves combining two or more numbers to get a sum. For example, adding 2 and 3 gives you 5.
• Subtraction: This process involves taking one number away from another. For example, subtracting 4 from 10 results in 6.

Remember, in our given problem, you first encountered a subtraction before moving on to addition. Understanding the order to process these operations is pivotal for achieving the correct result.

Prealgebra

Prealgebra serves as a foundation for algebra, focusing on basic arithmetic operations and the manipulation of simple expressions. It introduces students to the kind of thinking required for higher math and aims to build a robust mathematical foundation.

Key elements of prealgebra include:

• Understanding Numbers: Recognizing and working with integers, fractions, and decimals.
• Basic Operations: Mastering addition, subtraction, multiplication, and division.
• Order of Operations: Learning the sequence in which operations should be performed in an expression, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

This exercise is a great example of prealgebra in action. It requires you to know how addition and subtraction work and to perform them correctly to simplify an expression.

Simplification of Expressions

Simplification of expressions involves reducing them to their simplest form while ensuring they retain their original value. This process makes equations easier to understand and solve.

To simplify an expression:

• Identify Operations: Look at the expression to determine which arithmetic operations are necessary.
• Follow the Order of Operations: Ensure calculations are performed in the correct sequence.
• Calculate Step-by-Step: Break down the expression into manageable parts, just like in our example where subtraction was performed before addition.

Through simplification, complex expressions become much more straightforward, making them easier to handle in subsequent math problems. It’s an essential skill that will come in handy at all levels of math.