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# Dividing Terms in Algebra

(KS3, Year 7)

## The Lesson

Terms can be divided. Imagine we wanted to divide the term**4a**by

^{2}**2a**.

## How to Divide Terms in Algebra

Dividing terms is easy.## Question

Divide the two terms below.## Step-by-Step:

# 1

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

**4**and**2**.**4**a

^{2}÷

**2**a

**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.
4

**a**÷ 2^{2}**a****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.-
The term being divided (4a
^{2}b) is called the**dividend**. -
The term that we are dividing
*by*(−2ac) is called the**divisor**.

## Step-by-Step:

# 1

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

**4**and**2**.**4**a

^{2}b ÷ −

**2**ac

**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.
4

**a**b ÷ −2^{2}**a**c**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**

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

The same law applies, subtract the exponents:

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

## 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:

Different signs give a minus:

## 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.

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