- 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: 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**: We can see why this works if we write out the term in full, remembering that^{2}

**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:

## Beware

## 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:

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