Problem 92 - Prealgebra

Question

Simplify. $$24-16+6$$

Step-by-Step Solution

Answer

The simplified expression is 14.

Step 1: Identify the operations

The given expression is \( 24 - 16 + 6 \). This expression involves two operations: subtraction and addition. According to the order of operations (PEMDAS/BODMAS), we should perform the subtraction and addition from left to right.

Step 2: Perform the subtraction

Start with the leftmost operation, which is subtraction in this case. Subtract 16 from 24. \[ 24 - 16 = 8 \] The expression now simplifies to \( 8 + 6 \).

Step 3: Perform the addition

Now, add 6 to the result from the previous step. \[ 8 + 6 = 14 \] This simplifies the entire expression to 14.

Key Concepts

Subtraction

Subtraction is one of the fundamental arithmetic operations. It represents the process of taking one quantity away from another. In our example, the operation is found between 24 and 16. We say we are "subtracting 16 from 24," which means that we are removing 16 from the total of 24.

• Subtraction is represented by the minus sign (-).
• The order of numbers matters: always subtract the second number from the first.

Here, start with 24 and count 16 steps back, or just think of 24, remove 16, and you get 8. Be sure to follow left-to-right operations, especially when combined with other operations like addition.

Addition

Addition is the process of finding the total, or sum, by combining two numbers. After we finished subtracting in the initial expression (24 - 16 + 6), we found the result was 8. Now, we need to add.

• Addition is represented by the plus sign (+).
• It is commutative, which means the order doesn’t matter: 3 + 5 is the same as 5 + 3.

In this example, after subtraction gives 8, we simply add the remaining number, 6. Adding 8 and 6 together, we find that the sum is 14. This completes the calculation of the expression.

Simplifying Expressions

Simplifying expressions involves performing all the operations within a mathematical statement until there are no additional operations left to perform. A simplified expression is much like a tidied-up room: everything is in its place.

• Follow the order of operations: parentheses, exponents, multiplication/division (left-to-right), addition/subtraction (left-to-right).
• Execute each arithmetic operation carefully as you progress through the expression.

For the expression 24 - 16 + 6, the simplification process included handling subtraction first and then addition according to the order of operations. This method led us step-by-step to the final simplified result: 14. Simplification ensures clarity and consistency in solving mathematical expressions.