Algebraic manipulation

Written by Hassan Raza (Mathematics)

9 Class 9 Mathematics questions with answers and explanations.

Printable worksheet with answer key

All questions with answers

What is the HCF of 12x² and 18x?
- 1 36x²
- 2 x
- 3 6
- 4 6x
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Correct answer: 6x

The HCF of 12 and 18 is 6 and the common power of x is x, so 6x.

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What is the LCM of 4x and 6x²?
- 1 12x²
- 2 24x³
- 3 2x
- 4 12x
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Correct answer: 12x²

LCM of 4 and 6 is 12, and the highest power of x is x², so 12x².

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Simplify (x² - 4) / (x - 2).
- 1 2x
- 2 x - 2
- 3 x + 2
- 4 x² + 2
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Correct answer: x + 2

x² - 4 = (x + 2)(x - 2), so the fraction equals x + 2.

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Simplify 1/x + 1/y.
- 1 2/(x + y)
- 2 xy/(x + y)
- 3 (x + y)/xy
- 4 1/(xy)
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Correct answer: (x + y)/xy

1/x + 1/y = y/xy + x/xy = (x + y)/xy.

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What is the square root of 49x²?
- 1 14x
- 2 7x
- 3 7x²
- 4 49x
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Correct answer: 7x

The square root of 49 is 7 and the square root of x² is x.

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The HCF of 8x³ and 12x² is:
- 1 24x³
- 2 8x²
- 3 4x
- 4 4x²
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Correct answer: 4x²

HCF of 8 and 12 is 4 and the lowest power of x is x².

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Simplify (6x²) / (3x).
- 1 2x²
- 2 18x³
- 3 2x
- 4 3x
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Correct answer: 2x

6 / 3 = 2 and x² / x = x.

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The LCM of x and x² is:
- 1 x
- 2 1
- 3 x³
- 4 x²
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Correct answer: x²

The LCM takes the highest power.

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Simplify (x + 2)/(x² - 4).
- 1 1/(x + 2)
- 2 x + 2
- 3 1/(x - 2)
- 4 x - 2
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Correct answer: 1/(x - 2)

x² - 4 = (x + 2)(x - 2).

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