Algebraic Expressions
An algebraic expression is a mathematical phrase that contains numbers, variables, and operations. It represents a quantity or a relationship between quantities. Algebraic expressions are used to describe and solve real-life problems in mathematics and other fields.
Components of an Algebraic Expression
There are several key components of an algebraic expression:
- Variables: These are symbols, usually letters, that represent unknown or changing quantities. Commonly used variables include x, y, and z.
- Constants: These are fixed numerical values.
- Coefficients: These are the numerical factors that are multiplied by the variables.
- Operations: These include addition, subtraction, multiplication, division, and exponentiation.
Examples of Algebraic Expressions
Here are some examples of algebraic expressions:
- 2x + 5
- 3y - 7
- 4a2 - 2ab + 8
- 5x2 + 3xy - 2y2
Key Concepts to Understand
When studying algebraic expressions, it's important to understand the following concepts:
- Like Terms: Terms that have the same variables raised to the same powers. For example, 3x and 7x are like terms.
- Combining Like Terms: The process of simplifying an expression by adding or subtracting like terms.
- Order of Operations: The rules that dictate the sequence in which operations should be performed within an expression (PEMDAS - Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Study Guide
Here are some steps to help you study algebraic expressions:
- Review the basic components of an algebraic expression - variables, constants, coefficients, and operations.
- Practice identifying and simplifying algebraic expressions by combining like terms.
- Understand the order of operations and practice applying it to various expressions.
- Work on solving real-world problems using algebraic expressions.
- Review and practice using exponent rules and distributing to simplify expressions.
By mastering these concepts, you'll be well-prepared to work with algebraic expressions and solve a wide variety of mathematical problems.
.◂Math Worksheets and Study Guides Seventh Grade. Measurement, Perimeter, and Circumference
Study Guide
Measurement, Perimeter, and Circumference 
Worksheet/Answer key
Measurement, Perimeter, and Circumference Worksheet/Answer key
Measurement, Perimeter, and Circumference Worksheet/Answer key
Measurement, Perimeter, and Circumference
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Geometry (NCTM)
Use visualization, spatial reasoning, and geometric modeling to solve problems.
Use geometric models to represent and explain numerical and algebraic relationships.
Measurement (NCTM)
Apply appropriate techniques, tools, and formulas to determine measurements.
Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.
Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.
Connections to the Grade 7 Focal Points (NCTM)
Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.