# 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:

# 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, a1 = a, a2 = a × a and a3 = 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 a2 ÷ 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 a2 = a × a. Each a on the denominator cancels out an a on the numerator, leaving only one a:

• Imagine we wanted to divide a4 ÷ a2:

We can see why this works if we write out the term in full, remembering that
a4 = a × a × a × a and that a2 = a × a. Each a on the denominator cancels out an a on the numerator, leaving two a's:

# A Real Example of How to Divide Letters in Algebra

The slider below shows a real example of how to divide letters in algebra.

Algebra Lessons
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# Be Careful With Signs

Letters can have different signs: a + sign if they are positive, and a - sign if they are negative.

Remember the rules for dividing different signs:

Same signs give a plus:

Different signs give a minus: