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How to Divide Terms in Algebra (Mathematics Lesson)

Dividing Terms in Algebra

Terms can be divided.

Imagine we wanted to divide the term 4a2 by 2a.

4 a squared divided by 2 a

How to Divide Terms in Algebra

Dividing terms is easy.

An Example Question

Divide the two terms below.

4 a squared divided by 2a
Step 1

Divide the numbers that appear in the terms. In our example, the numbers are 4 and 2.

4a2 ÷ 2a

4 ÷ 2 = 2

2 will appear in the answer:

2
Step 2

Divide the letters that appear in both terms. In our example, a appears in both terms.

  • a appears in 4a2 with an exponent of 2: a2 (a squared = a × a).

  • a appears in 2a.

4a2 ÷ 2a

a2 ÷ a = a

Don't forget: When you divide letters with different exponents, you subtract the exponents according the the law of exponents (see Note).

a will appear in the answer:

a
Step 3

Write the results from the previous steps next to each other.

2 was the result of Step 1. a was the result of Step 2.

2 a
Step 4

Check the signs. In our example, both terms are positive, so their answer is positive.

We have divided the terms:

4a2 ÷ 2a = 2a

A Real Example of How to Divide Terms in Algebra

This is a more complicated example.

An Example Question

Divide the two terms below.

4 a squared b divided by 2 a c

In this example, we need to distinguish the two terms in the division.

4 a squared b is the dividend. 2 a c is the divisor.
  • The term being divided (4a2b) is called the dividend.

  • The term that we are dividing by (-2ac) is called the divisor.

This distinction is needed when we divide the terms.

Step 1

Divide the numbers that appear in the terms. In our example, the numbers are 4 and 2.

4a2b ÷ -2ac

4 ÷ 2 = 2

2 will appear in the answer:

2
Step 2

Divide the letters that appear in both terms. In our example, a appears in both terms.

4a2b ÷ -2ac

a2 ÷ a = a

Don't forget: a2 ÷ a = a2 ÷ a1 = a2 - 1 = a1 = a.

a will appear in the answer:

a
Step 3

Find letters that only appear in the dividend.

b only appears in 4a2b. b will appear in the answer:

b
Step 4

Write the results from the previous steps next to each other, and place them above a line. This term will be the numerator of an algebraic fraction.

2 was the result of Step 1. a was the result of Step 2. b was the result of Step 3.

2 a b over line
Step 5

Find letters that only appear in the divisor.

c only appears in 2ac. c will appear in the answer:

c
Step 6

Write the result from Step 5 underneath the line from Step 4. This term will be the denominator of an algebraic fraction.

c under line
Step 7

Check the signs. In our example, one term is positive, the other negative. The answer is negative.

We have divided the terms:

4a2b ÷ -2ac = -2ab/c

Another Real Example of How to Divide Terms in Algebra

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

Curriculum
Algebra Lessons
Interactive Test
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Here's a second test on dividing terms.
Here's a third test on dividing terms.

Note

What Is a Term in Algebra?

A term is a collection of numbers, letters and brackets all multiplied together.

Dividing the Same Letter from Each Other Using Exponent Notation

There is a law for dividing terms with exponents. Subtract the exponents from each other.

to divide terms with exponents, subtract the exponents

What if the exponent of the letter in the dividend is smaller than the exponent of the same letter in the divisor?

a squared divided by a squared

The same law applies, subtract the exponents:

a squared divided by a squared equals a to the minus 1

The result is a negative exponent. This means find the reciprocal of the term:

a to the minus 1 equals 1 over a
Top Tip

Rules for Signs: Division

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 terms with same signs give a positive answer

Different signs give a minus:

divide terms with different signs give a negative answer

Algebraic Fractions

Another method two divide terms is to write them as an algebraic fraction.

The algebraic fraction can then be simplified by dividing both numerator and denominator by their greatest common factor.