How to Divide Terms in Algebra
Dividing Terms in Algebra
Imagine we wanted to divide the term 4a^{2} by 2a.
How to Divide Terms in Algebra
Dividing terms is easy.
Question
Divide the two terms below.
StepbyStep:
1
Divide the numbers that appear in the terms. In our example, the numbers are 4 and 2.
4a^{2} ÷ 2a
4 ÷ 2 = 2
2 will appear in the answer:
2
Divide the letters that appear in both terms. In our example, a appears in both terms.
4a^{2} ÷ 2a
a^{2} ÷ 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:
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.
4
Check the signs. In our example, both terms are positive, so their answer is positive.
Answer:
We have divided the terms:
4a^{2} ÷ 2a = 2a
A Real Example of How to Divide Terms in Algebra
This is a more complicated example.
Question
Divide the two terms below.
In this example, we need to distinguish the two terms in the division.

The term being divided (4a^{2}b) 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.
StepbyStep:
1
Divide the numbers that appear in the terms. In our example, the numbers are 4 and 2.
4a^{2}b ÷ −2ac
4 ÷ 2 = 2
2 will appear in the answer:
2
Divide the letters that appear in both terms. In our example, a appears in both terms.
4a^{2}b ÷ −2ac
a^{2} ÷ a = a
Don't forget: a^{2} ÷ a = a^{2} ÷ a^{1} = a^{2 − 1} = a^{1} = a.
a will appear in the answer:
3
Find letters that only appear in the dividend.
b only appears in 4a^{2}b. b will appear in the answer:
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.
5
Find letters that only appear in the divisor.
c only appears in 2ac. c will appear in the answer:
6
Write the result from Step 5 underneath the line from Step 4. This term will be the denominator of an algebraic fraction.
7
Check the signs. In our example, one term is positive, the other negative. The answer is negative.
Answer:
We have divided the terms:
4a^{2}b ÷ −2ac = −2ab/c