Class 8 Dividing Algebraic Expressions — practice questions with answers

Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. Divide: 6x² by 2x.

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Answer: A) 3x

\frac{6 x ^{2}}{2 x} = \frac{6}{2} \cdot \frac{x ^{2}}{x} = 3 x

2. Divide: 16p⁴q² by 8p²q².

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Answer: A) 2p²

\frac{16 p ^{4} q ^{2}}{8 p ^{2} q ^{2}} = \frac{16}{8} \cdot \frac{p ^{4}}{p ^{2}} \cdot \frac{q ^{2}}{q ^{2}} = 2 p^{2}

3. Find the value of: 49a²b² divided by 7ab.

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Answer: A) 7ab

\frac{49 a ^{2} b ^{2}}{7 ab} = \frac{49}{7} \cdot \frac{a ^{2}}{a} \cdot \frac{b ^{2}}{b} = 7 ab

4. A juice carton in Nagpur holds (x³ + 2x²) ml of juice. It is poured equally into x² small glasses.
How much juice (in ml) does each glass hold?

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Answer: A) x + 2

Per glass =

\frac{x ^{3} + 2 x ^{2}}{x ^{2}} = \frac{x ^{3}}{x ^{2}} + \frac{2 x ^{2}}{x ^{2}} = x + 2

5. A long ribbon of length (x³ - 4x) m is cut into equal pieces, each (x + 2) m long.
How many pieces are obtained?

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Answer: A) x² - 2x

x³ - 4x = x(x² - 4) = x(x - 2)(x + 2). Pieces =

\frac{x ^{3} - 4 x}{x + 2} = x (x - 2) = x^{2} - 2 x

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