How to Divide Letters in Algebra (Mathematics Lesson)
Dividing Letters in Algebra
Letters can be divided with numbers, other letters and the same letter.

A letter can be divided by a number.
Write the letter as the numerator of a fraction, and the number as the denominator.

A letter can be divided by a different letter.
Write the letter you are dividing by (b) under the letter you are dividing (a).
Dividing Letters to Make Terms
A term is a collection of letters and numbers multiplied and/or divided together.
In the examples above, the letter a has been divided by a number and the letter b to make terms.
These divisions can be combined to make a more complicated term:
Read more about how to divide terms
Dividing a Letter With the Same Letter
Dividing a letter with itself equals 1:
Letters sometimes have exponents, which tell you how many times the letter is multiplied by itself. For example, a^{1} = a, a^{2} = a × a and a^{3} = a × a × a.
When a letter with an exponent is divided by that same letter, we must subtract the exponents.

For example, imagine we wanted to divide a^{2} ÷ a. (Don't forget: if a letter does not have an exponent, it has an implicit exponent of 1):
We can see why this works if we write out the term in full, rather than using exponent notation, remembering that a^{2} = a × a. Each a on the denominator cancels out an a on the numerator, leaving only one a:

Imagine we wanted to divide a^{4} ÷ a^{2}:
We can see why this works if we write out the term in full, remembering that
a^{4} = a × a × a × a and that a^{2} = a × a. Each a on the denominator cancels out an a on the numerator, leaving two a's:
Read more about how to divide letters with exponents
A Real Example of How to Divide Letters in Algebra
The slider below shows a real example of how to divide letters in algebra.
Curriculum
Interactive Test
showHere's a second test on dividing letters.
Here's a third test on multiplying letters.