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What is an expression?
By Swati (P85) on May 6, 1998:

Is 8+5=13 considered an expression? It's written in our book but our teacher says it has to have letters?

Swati

By David Sanders on May 11, 1998:

Dear Swati,

I would not say that '8+5=13' is an expression. I would call it an equation, because it says that two things are equal. I would call '8+5' on its own an 'expression'. By this I just mean that it is a set of mathematical symbols put together in a way that means something mathematical. Moreover, this expression can be used in place of another one to get another valid expression.

For example, in the expression 3×4, if we replace '3' by '8+5', then we get (8+5)×4, which is also a valid, meaningful expression. Note that I had to use brackets to tell you which bits of the new expression go together.

In the second part of your question, you say that your teacher said an expression had to have letters in it. This is also a valid expression, however I don't think there need to be any letters there. However, if you're learning about algebra at the moment, then most of the expressions and equations you see will contain letters.

Finally, let me just say that an equation has an expression on the left of the equals sign, and one (usually a different one) on the right. The equation expresses the fact that these two expressions are equal. Sometimes the equation is true only in the particular problem or question that you are doing. For example, if you solve the equation 2a = 4, you get the equation a = 2. This is not always true -- in a different question, a might equal 3 instead. However, some equations are always true. For example, a+b = b+a is ALWAYS true, whatever a and b are. Such equations are sometimes called identities, and the two expressions are said to be identically equal. This is sometimes written with 3 horizontal bars one on top of the other instead of just 2.

I hope that was useful. If you have any more questions, or I haven't answered your question, then please write back!

David.