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.