Today, we're going to break down one of the most fundamental concepts in math: algebraic expressions. Think of them as the building blocks of algebra. We'll learn what they are, what their parts are called, and how to work with them.

What Is an Algebraic Expression?

An algebraic expression is a mathematical phrase that contains numbers, variables, and operation symbols. Unlike an equation, it does not have an equals sign. It's a way of representing a quantity without knowing the exact value of the variable.

• Example: $4x+7$

  • This expression says "seven more than four times a number." We don't know what the number is, so we use the variable x to represent it.

The Parts of an Expression

To truly understand expressions, you need to know their vocabulary. Let's look at an example and define each part.

Example Expression: $5x^2+2x-10$

• Terms: The parts of the expression that are separated by addition or subtraction signs.

  • In our example, the terms are 5x2, 2x, and −10.

• Variable: A letter that represents an unknown number.

  • In our example, the variable is x.

• Coefficient: The number multiplied by the variable in a term.

  • In our example, the coefficients are 5 and 2.

• Constant: A term that is a number on its own, without a variable. Its value does not change.

  • In our example, the constant term is −10.

• Exponent: A small number written to the upper right of a base number or variable, indicating how many times to multiply the base by itself.

  • In our example, the exponent is 2.

Step-by-Step: Working with Expressions

There are two main things we do with expressions: evaluating and simplifying.

Step 1: Evaluating an Expression

Evaluating an expression means finding its numerical value when you're given a specific number for the variable. You simply substitute the number for the variable and then use the order of operations (PEMDAS) to solve.

• Example: Evaluate $3y+4$ when $y=5$.

  • Step 1: Substitute. Replace the y with 5. The expression becomes $3(5)+4$.

  • Step 2: Simplify using PEMDAS.

    • First, do the multiplication: $3\times 5=15$.

    • The expression is now $15+4$.

    • Next, do the addition: $15+4=19$.

  • Final Answer: The value of the expression is 19.

Step 2: Simplifying an Expression

Simplifying an expression means making it as easy as possible by combining like terms. Like terms have the same variable raised to the same power.

• Example: Simplify $6x+8-2x+1$.

  • Step 1: Identify the like terms.

    • The variable terms are 6x and −2x.

    • The constant terms are 8 and 1.

  • Step 2: Combine the like terms.

    • Combine the variable terms: $6x-2x=4x$.

    • Combine the constant terms: $8+1=9$.

  • Final Answer: The simplified expression is $4x+9$.

Putting It All Together: Word Problems

Algebraic expressions are especially useful for representing real-world situations.

• Example: Mark has 3 bags of apples. Each bag has the same number of apples. He also has 5 loose apples. Write an algebraic expression to represent the total number of apples Mark has.

  • Step 1: Define the variable. Let a be the number of apples in each bag.

  • Step 2: Write the expression for the bags. Since he has 3 bags with a apples in each, this can be written as 3a.

  • Step 3: Add the loose apples. He has 5 loose apples, so you add 5 to the expression.

  • Final Answer: The expression is $3a+5$.

QUIZ 

+ Biography United States Presidents  by https://www.ducksters.com/

- What is This president most known for?

- How did he die?

- Fun Facts about this president

+ USALEARNS by https://www.usalearns.org

Complete the sentences with Who, Which and Where

Tema 1

• US PRESIDENTS 1-16 QUIZ Cuestionario
• TOO, TOO MANY, TOO MUCH, NOT ENOUGH Cuestionario
• Who, Which, That - Relative Clause