We use algebraic expressions when we want to write a number sentence but we don't know one of the numbers involved.
For example: What is the total weight of a cat and a 10lb weight?
In this case, let's use c for the weight of the cat.
c + 10 is called an algebraic expression which is an expression that contains at least one variable.
c is called a variable. This is a symbol used to represent an unknown quantity.
Coefficients are the numerical factor in a term and are used to show how many variables we have. The variable u with a coefficient of 3 is written as 3u which means 3 \cdot u.
Terms are a number, variable, product, and/or quotient in an expression. They are the building blocks of an expression. Terms are separated by + or - signs.
Consider the expression: -\dfrac{2}{3}y+ 5
This is an expression with 2 terms.
The term -\dfrac{2}{3} y has a coefficient of -\dfrac{2}{3}. The negative belongs with the coefficient.
The term 5 has no variable. It is called a constant term.
In order to write an expression that can be used to model the total cost of a road trip, Mr. Taylor defines the variables:
Let g represent the cost per gallon of gasoline (in dollars), and m represent the cost per mile driven.
What could these expressions represent in this context?
In this context, what do the coefficients describe?
Expressions and parts of expressions, like factors and coefficients, all have unique meanings in a given context. Viewing expressions in parts and as a whole while paying attention to the quantities represented by the variables can explain the relationships described by the expressions.
For the algebraic expression -4x+\dfrac{2}{3}:
Determine the number of terms.
Identify the coefficient of the first term.
Identify the constant term.
A coffee shop charges \$4.50 per cup of specialty coffee. Write an algebraic expression for the total cost of purchasing c cups of specialty coffee.
Write an algebraic expression for the phrase "six and a quarter more than half x".
The perimeter of a rectangle can be written as 2l+2w. Explain what each part of the expression represents.
In algebra, letters, called variables, are used to represent unknown numbers.
A term consists of a number and a variable. For example: 5.2x, - \dfrac{3}{5} y and \dfrac{2p}{3} are terms.
A coefficient is a number that is placed before the variable in an algebraic term. For example: -3.7 is the coefficient of -3.7y.
If there is no number placed before the variable then the coefficient is 1. For example: w has a coefficient of 1.
A constant term is a term with no variable. For example: 8.2, - \dfrac{5}{12} and 32 are constant terms.
An algebraic expression is a combination of numbers and variables with mathematical operators. For example: 2.7x - 5y + \dfrac{11}{12} is an expression.
We can use algebra tiles to help us visualize algebraic expressions.
The tile x represents an unknown number. The tile +1 represents adding one unit and -1 represents subtracting one unit.
This table demonstrates how expressions can be built using the tiles:
Algebra tiles can also help us identify the terms of the equivalent algebraic expression. Let's break down the algebra tiles below.
Notice that there are two different types of algebra tiles. These represent the two terms in the expression.
The first term in blue, are the three tiles with the +x. This represents the term 3x where the coefficient is the 3 and the variable is the x.
The second term in orange, are the six tiles with the -1. This represents the term 6.
When we add them together, we get the algebraic expression 3x-6.
Write an equivalent algebraic expression and identify each term for the following:
Represent the following expressions using algebra tiles.
-7x+2
4x-5
We can represent algebraic expressions with visual models to better understand them.
We can rearrange models of algebraic expressions to generate equivalent expressions.