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Dividing Letters in Algebra
(KS3, Year 7)

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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 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
how to divide letters with exponents

Lesson Slides

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

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: divide_same_signs_plus Different signs give a minus: divide_different_signs_minus
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This page was written by Stephen Clarke.

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