Letters can be divided
, multiplied 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
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, a1
When a letter with an exponent is divided by that same letter, we must subtract the exponents.
Read more about how to divide letters with 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:
The slider below shows a real example of how to divide letters in algebra.
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: