Higher levels of mathematics have both expressions and equations. Since both use variables and numbers it can be confusing at first, however, there is an easy way to distinguish between the two.
An expression has different combinations of variables, symbols and numbers for you to calculate. An equation has expressions in it that are separated by an equals sign. So, look for an equals sign to identify an equation easily. In simple terms, an equation has an equals sign to link two equivalent expressions, while expressions are more like "mathematical phrases. In order to get the correct answer in math, you must use the correct order of operations.
You will need to understand this fundamental before you solve equations and expressions. A tanker starts to fill the tank at a rate of two hundred gallons per minute. We might be asked to find an expression for the amount of fuel, in gallons, that the tank would contain after m minutes.
This will of course be the number of minutes that have elapsed m , multiplied by the rate at which we are filling the tank two hundred gallons per minute , plus the fuel already in the tank one thousand gallons.
We could write this as:. Once we have values for all of the variables used in an expression, we can evaluate the expression by replacing the variables with the actual values. The expression then essentially becomes an arithmetic expression, rather than an algebraic one. If we know, for example, that the tanker in the above example is filling the fuel tank for exactly fifteen minutes, we can substitute the number fifteen in our expression to get:.
An equation is essentially a statement that says that two expressions are equal to one another. We use equations to find the value of one or more unknown quantities. We do this by re-arranging and simplifying the terms in an equation, in order that the unknown quantities can be expressed in terms of known values, so that we can calculate their value.
We call this solving the equation. If we are trying to find the value of a particular variable in an equation, we say that we are solving for that variable. So, if the variable we want the value for is called x , we say that we are solving for x. Depending on the type of problem we are dealing with, it may not always be possible to solve an equation.
Thankfully, equations that have no solution do not normally appear in exams, but they often occur in the real world because very often we just don't have all the information we need. If that were not the case, we would surely have already discovered the answer to life, the universe and everything apologies to Douglas Adams. Anyway, here are some examples of equations:. As you can see from the above, equations vary in their format and complexity. The next two equations can be solved relatively easily, since we can re-arrange and simplify them to get the answers:.
This equation is not so easy to solve, and we will not provide a worked solution here. Suffice it to say that this kind of equation does come up in exams, it can be solved without too much pain, and we will be looking at quadratic equations in some depth on a separate page. A sentence has a subject and a verb. In algebra, we have expressions and equations.
An expression is like a phrase. Here are some examples of expressions and how they relate to word phrases:. Notice that the phrases do not form a complete sentence because the phrase does not have a verb. An equation is two expressions linked with an equal sign. When you read the words the symbols represent in an equation, you have a complete sentence in English. For example, let us take an algebraic expression and try to reduce it to its lowest form in order to understand the concept better.
Let our expression be:. Algebraic formulas are the derived short formulas that help us in solving the equations easily. They are just a rearrangement of the given terms in order to create a better expression that is easy to memorize. Find below a list of some of the basic formulas that are being used widely. Have a look at this page in order to understand the algebraic formulas better.
The types of algebraic expressions are based on the variables found in that particular expression, the number of the terms of that expression, and the values of the exponents of the variables in each expression. Given below is a table that divides the algebraic expressions into five different categories. Let us have a look at the table.
An expression with only one term where the exponents of all the variables are non-negative integers. An expression with one or more terms the exponents of variables can be either positive or negative. Example 1: There are 25 oranges in a bag. Write the algebraic expression for the number of oranges in x number of bags.
Every binomial is a polynomial as well. So the correct answers are: binomial and polynomial. An algebraic expression is described using its terms, and operations on the terms.
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