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.

    a divided by 2 Write the letter as the numerator of a fraction, and the number as the denominator.
  • A letter can be divided by a different letter.

    a divided by b 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:

a divided by 2 b Read more about how to divide terms

Dividing a Letter with the Same Letter

Dividing a letter with itself equals 1:

a divided by a 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):

    a squared divided by a equals a 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:

    a squared divided by a equals a
  • Imagine we wanted to divide a4 ÷ a2:

    a to the power of 4 divided by a squared equals a squared 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 to the power of 4 divided by a squared equals a squared
Read more about how to divide letters with exponents

Lesson Slides

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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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See Also

What is algebra? What is a fraction? What is a numerator? What is a denominator? What is a term? How to divide terms in algebra What is an exponent? The laws of exponents How to divide letters with exponents