Mathematics • Year 7 • Unit 2 • Lesson 7

Dividing Algebraic Terms

Build the basics: divide coefficients separately, cancel matching variables, subtract the powers when the same letter appears on top and bottom, and handle negative signs cleanly.

Build · I Do / We Do / You Do

1. I do, fully worked example

Read every line. Each step has a short reason on the right so you can see why, not just what.

Problem. Simplify 8x ÷ 2x (also written 8x⁄2x).

Step 1, Split into coefficients and variables.

8x ÷ 2x = (8 ÷ 2) × (x ÷ x)

Reason: a fraction can be split into "numbers over numbers" and "letters over letters".

Step 2, Divide the coefficients.

8 ÷ 2 = 4

Reason: just the numbers, basic division.

Step 3, Cancel the variables.

x ÷ x = 1

Reason: anything divided by itself is 1, so the x disappears.

Step 4, Combine.

4 × 1 = 4

Reason: the x cancelled out, so the answer is just a number.

Answer: 8x ÷ 2x = 4.

Stuck? Revisit lesson § "The Big Idea", divide the coefficients, cancel the variables.

2. We do, fill in the missing steps

Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks

Problem. Simplify 15x³ ÷ 5x.

Step 1, Split into coefficients and variables:

15x³ ÷ 5x = (____ ÷ ____) × (x³ ÷ x)

Step 2, Divide the coefficients:

____ ÷ ____ = ______

Step 3, Subtract the powers of x:

x³ ÷ x = x^{____ − ____} = x^____

Step 4, Combine:

Final answer = ____________

Stuck? Revisit lesson § "The Power Rule", same letter on top and bottom means SUBTRACT the exponents.

3. You do, independent practice

Show your working under each question. The first four are foundation, the middle two are standard, and the last two are extension.

Foundation, single step

3.1 Simplify 12x ÷ 3. 1 mark

3.2 Simplify 6x ÷ 2x. 1 mark

3.3 Simplify x⁵ ÷ x². 1 mark

3.4 Simplify 10a ÷ 5. 1 mark

Standard, combine two ideas

3.5 Simplify 9x² ÷ 3x. (Hint: divide numbers, subtract powers.) 2 marks

3.6 Simplify (−15a³) ÷ 5a. 2 marks

Extension, push your thinking

3.7 Simplify 8x²y ÷ 2xy. (Handle each variable separately.) 3 marks

3.8 Simplify (−20x³y²) ÷ (4x²y). Watch the sign, and remember each variable is cancelled separately. 3 marks

Stuck on 3.8? Neg ÷ pos = neg. Then divide each variable: x³ ÷ x² and y² ÷ y separately.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers, Do not peek before attempting

Section 2, We do (15x³ ÷ 5x)

Step 1: 15x³ ÷ 5x = (15 ÷ 5) × (x³ ÷ x).
Step 2: 15 ÷ 5 = 3.
Step 3: x³ ÷ x = x^{3 − 1} = x².
Step 4: Final answer = 3x².

3.1-12x ÷ 3

Numbers: 12 ÷ 3 = 4. Variable x stays (only on top). Answer: 4x.

3.2-6x ÷ 2x

Numbers: 6 ÷ 2 = 3. Variables: x ÷ x = 1 (cancels). Answer: 3. (Not 3x, the x cancelled out.)

3.3, x⁵ ÷ x²

Same base, subtract powers: x⁵ ÷ x² = x^{5 − 2} = x³. (You subtract, you do not divide the exponents.)

3.4-10a ÷ 5

Numbers: 10 ÷ 5 = 2. Variable a stays. Answer: 2a.

3.5-9x² ÷ 3x

Numbers: 9 ÷ 3 = 3. Variables: x² ÷ x = x^{2 − 1} = x. Answer: 3x.

3.6, (−15a³) ÷ 5a

Numbers: −15 ÷ 5 = −3 (neg ÷ pos = neg). Variables: a³ ÷ a = a². Answer: −3a².

3.7-8x²y ÷ 2xy

Numbers: 8 ÷ 2 = 4. x²÷x = x. y÷y = 1 (cancels). Answer: 4x.

3.8, (−20x³y²) ÷ (4x²y)

Numbers: −20 ÷ 4 = −5. x³÷x² = x. y²÷y = y. Answer: −5xy.