How to Divide Terms in Algebra

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.

Question

Divide the two terms below.

4 a squared divided by 2a

Step-by-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

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

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

4

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

Answer:

We have divided the terms:

4a2 ÷ 2a = 2a

A Real Example of How to Divide Terms in Algebra

This is a more complicated 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-by-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

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

3

Find letters that only appear in the dividend.

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

b

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

5

Find letters that only appear in the divisor.

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

c

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

7

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

Answer:

We have divided the terms:

4a2b ÷ −2ac = −2ab/c

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See Also

What is algebra? What is a term? What is an exponent? The laws of exponents Dividing terms with exponents Finding terms with a negative exponent