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Dividing Letters in Algebra
(KS3, Year 7)
The Lesson
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
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:
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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