An expression is a mathematical statement that contains one or more numbers and variables joined together by operators and grouping symbols. An expression does not contain an equal sign or inequality symbol.
An algebraic expression is an expression that includes at least one variable.
In order to write an expression that can be used to model the total cost of buying new school supplies, Mr. Okware defines the following variables:
Let x represent the cost of a folder, y represent the cost of a calculator, and z represent the cost of a pencil pack.
What could the following 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.
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:
Create a model using algebra tiles for the following algebraic expression:
-7 + 5(1-3x)
Vincenzo runs a removalist company that charges \$ 37.50 per hour plus a one-off truck hire fee of \$ 150.00.
Write an expression that models how much he charges for a job that lasts a hours.
If the area of a square is given by the expression (2x - 1)^2, explain what 2x-1 represents in the context of the problem.
Expressions can be used to represent mathematical relationships. In an expression, sums often represent totals, coefficients and factors represent multiplication, and exponents represent repeated multiplication. When interpreting an expression in context, we can use the units to help understand the meaning.
In life, the order in which we do things is important. For example, we put on socks then shoes, rather than shoes and then socks.
The order of operations tells us the steps to evaluate expressions with multiple operations, so that the same numerical result is achieved. The order goes:
We often want to substitute values for the variables in an algebraic expression. That way we can evaluate the expression to yield a numerical result.
As an example, a concession stand sells bags of popcorn for \$2.50 each and hot dogs for \$1.50 each. The total cost of buying p bags of popcorn and h hot dogs can be represented by the expression 2.50p + 1.50h.
Riley goes the concession stand every Saturday and buys 2 bags of popcorn and 4 hot dogs for her friends, and wants to determine the total cost of her order 3 Saturdays in a row.
Since the same order will be repeated 3 times, the distributive property will be used to rewrite the expression. By substituting the values p=2 and h=4 into the new expression, we see that
\displaystyle \text{Total Spent} | \displaystyle = | \displaystyle 3\left(2.50p+1.50h\right) | Rewrite expression. |
\displaystyle = | \displaystyle 3\left(2.50 \cdot 2 +1.50 \cdot 4 \right) | Substitute values | |
\displaystyle = | \displaystyle 3(5+6) | Evaluate the multiplication | |
\displaystyle = | \displaystyle 3 \cdot 11 | Evaluate the addition |
The total cost of Riley's purchase is \$33.
Evaluate: \left(u+v\right) \left(w-y\right)when u=5,\,v=8,\,w=2,\, and y=10.
Find the value of: \dfrac{x^2}{3}+\dfrac{y^3}{2}when x=-4 and y=3.
For x=5 and y=4, evaluate: \sqrt{2x^2+4y+6}correct to two decimal places.
Substitute the given value for each variable and then apply the order of operations: