At a Glance - Algebraic Expressions
Okay, let's clear this up:
An equation is a complete mathematical sentence that includes a sign of equality (like an equal sign).
An expression is not a mathematical sentence; it is a mathematical phrase because it doesn't have an equal sign.
|5 + 2||5 + 2 = 7|
|3x||3x = 15|
|4(5 + 8x)||4(5 + 8x) = -44|
Let's break it down further.
An expression is made up of terms. Terms are each separate values in an expression. They can be separated by operations, like plus and minus signs.
There are three parts of most expressions: the variable, constant, and coefficient.
Variable: an unknown or changing number. Often represented by “x”.
Constant: a number that doesn’t change
Coefficient: the number that is multiplied by the variable
Names for algebraic expressions
|binomial||2 Terms||xy - 2x|
|trinomial||3 Terms||xy - 2x + 3y|
|quadnomial||4 Terms||xy - 2x + 3 y – 1|
Here is a chart of common phrases.
|Common Words and Phrases for:|
in addition to
In these translations we will use the letter x to represent the variable, though any letter, symbol, or emoticon would work. Smiley faces and hearts, anyone?
|Expression in Words||Expression in Symbols|
|a number increased by twelve||x + 12|
|the sum of twice a number and six||2x + 6|
|eighty less than a number||x – 80|
|twenty-eight split in half||28 ÷ 2|
|the product of a number and seven||7x|
|the quotient of a number and four||x ÷ 4|
|five greater than three times a number||3x + 5|
|a number distributed evenly among six||x ÷ 6|
|the total of forty and a number||40 + x|
|three times the total of a number and five||3(x + 5)|
|Equation in Words||Equation in Symbols|
|A number is negative ten.||x = -10|
|A number plus two is eight.||x + 2 = 8|
|The difference between a number and seven is negative three.||x – 7 = -3|
|One less than twice a number is seventeen.||2x – 1 = 17|
|Twelve is the product of a number and three.||12 = 3x|
|Half of a number is twenty.||x × ½ = 20 or ½x = 20|
|A number is equal to the sum of twice the number and negative three.||x = 2x + -3|
Look Out: be very careful with "less than". Three less than a number is translated as "x – 3". The reverse of that, "3 – x" would be a number less than three.