# Using Variables to Represent Measurements

Student View (Opens in new window) ## Instructor Overview

Students write an expression for the length of a train, using variables to represent the lengths of the different types of cars.

# Key Concepts

• A numerical expression consists of a number or numbers connected by the arithmetic operations of addition, subtraction, multiplication, division, and exponentiation.
• An algebraic expression uses letters to represent numbers.
• An algebraic expression can be written to represent a problem situation. Sometimes more than one algebraic expression may represent the same problem situation. These algebraic expressions have the same value and are equivalent.
• The properties of operations can be used to make long algebraic expressions shorter:
• The commutative property of addition states that changing the order of the addends does not change the end result:
a + b = b + a.
• The associative property of addition states that changing the grouping of the addends does not change the end result:
(a + b) + c = a + (b + c).
• The distributive property of multiplication over addition states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together:
a(b + c) = ab + ac.

# Goals and Learning Objectives

• Write algebraic expressions that describe lengths of freight trains.
• Use properties of operations to shorten those expressions.