Problem 36 - Algebra A Combined Function

Question

Translate each phrase to an expression and simplify. Subtract -2 from 3 .

Step-by-Step Solution

Answer

The simplified expression is 5.

Step 1: Identify the Operation

The phrase 'subtract -2 from 3' indicates a subtraction operation.

Step 2: Translate to Mathematical Expression

Translate the phrase into a mathematical expression. Since we subtract -2 from 3, it is written as: \[ 3 - (-2) \]

Step 3: Simplify the Expression

Recall that subtracting a negative number is the same as adding its positive. Therefore, the expression becomes: \[ 3 + 2 \]

Step 4: Calculate the Sum

Add the numbers together: 3 + 2 = 5.

Key Concepts

Understanding Subtraction

Subtraction is one of the four basic operations in mathematics. It involves finding the difference between two numbers by taking one number away from another. In an expression, the symbol used for subtraction is the minus sign (-).
When you see a phrase like 'subtract -2 from 3,' it means you're being asked to take away the value of -2 from the starting value 3. This forms the basis of understanding how subtraction works in algebraic expressions. However, subtraction can become slightly more complex when negative numbers come into play.

Working with Negative Numbers

Negative numbers are numbers that are less than zero and are represented with a minus sign in front of them, such as -2, -3, etc. They can initially seem a bit confusing, especially in subtraction.
When you encounter sentences telling you to subtract a negative number, you're actually performing an operation that will add a positive number instead.

• Subtracting a negative number is the same as adding its opposite positive.
• This rule is important for simplifying expressions.

For example, when you subtract -2 from 3 (3 - (-2)), it becomes 3 + 2 due to this rule.
Interestingly, this is why subtractions with negative numbers can often result in a higher number than you started with.

Simplification of Algebraic Expressions

Simplifying an algebraic expression is a process that involves combining like terms and reducing expressions to their simplest form. The goal is to make the expression easier to work with or solve.
In the expression \(3 - (-2)\), simplification uses the rule of negative numbers to change it to \(3 + 2\).
This gives you a more straightforward equation to solve, helping avoid errors in calculation.

• Simplifying helps in efficiently solving mathematical problems.
• It reduces the complexity of the expression.

Once simplified, you merely need to perform the basic arithmetic to arrive at the solution.

Combining Mathematical Operations

Mathematical operations refer to actions we perform on numbers, such as addition, subtraction, multiplication, and division. These operations follow specific rules and orders, which are vital for correctly solving any problem.
When dealing with several operations in the same expression, the order of operations (often remembered as PEMDAS/BODMAS) dictates which operations to perform first.

• P: Parentheses first.
• E: Exponents (i.e., powers and square roots, etc.)
• M/D: Multiplication and Division (from left to right)
• A/S: Addition and Subtraction (from left to right)

In the expression \(3 + 2\), the operations are straightforward enough, with just one addition to perform.
But understanding how operations work together ensures you can tackle more complex algebraic problems with confidence.