An expression is a combination of numbers, variables, and operations. It can include addition, subtraction, multiplication, division, and exponentiation. Expressions are used to represent mathematical relationships and can be used to calculate values.

**Numeric Expressions:**These are expressions that contain only numbers and operations. For example, 5 + 3 * 2.**Variable Expressions:**These are expressions that contain variables, numbers, and operations. For example, 2x + 3y.**Algebraic Expressions:**These are expressions that contain variables, numbers, and operations, including exponents. For example, 3x^{2}- 2x + 5.

Expressions are made up of the following components:

**Numbers:**These are numerical values such as 1, 2, 3.14, etc.**Variables:**These are symbols that represent unknown or changing values, such as x, y, a, b, etc.**Operations:**These are mathematical operations such as addition (+), subtraction (-), multiplication (*), division (/), and exponentiation (^).

When working with expressions, it's important to understand the following key concepts:

**Order of Operations:**Expressions should be evaluated using the order of operations - parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).**Like Terms:**Terms in an expression that have the same variable raised to the same power are called like terms. Like terms can be combined using the properties of addition and subtraction.

Here are some examples of expressions:

- 3x + 2y - 5
- 4(x + 3) - 2y
- 2a
^{2}- 3a + 7

When studying expressions, it's important to practice simplifying, evaluating, and solving expressions. Here are some steps to follow:

- Identify the components of the expression - numbers, variables, and operations.
- Apply the order of operations to simplify the expression.
- Combine like terms if applicable.
- If the expression includes variables, substitute specific values for the variables and evaluate the expression.

Practice working with different types of expressions and solving problems involving expressions to strengthen your understanding of the topic.

Remember to seek help from your teacher or tutor if you encounter any challenges!

Good luck with your studies!

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Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.