Class 9 Rationalising the Denominator — practice questions with answers

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

1. To rationalise the denominator of

\frac{1}{5}

, by what should we multiply both numerator and denominator?

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Answer: A)

5

Multiply numerator and denominator by

5

\frac{1}{5} = \frac{5}{5}

. The multiplier is

5

2. Rationalise:

\frac{2}{7}

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Answer: A)

\frac{14}{7}

\frac{2}{7} = \frac{2 x 7}{7 x 7} = \frac{14}{7}

3. When

\frac{1}{4 + 15}

is rationalised, the numerator becomes:

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Answer: A)

4 - 15

Multiply by

(4 - 15)

(4 - 15) /

(

(4)^{2} - (15)^{2}

)

= \frac{4 - 15}{16 - 15} = 4 - 15

. Numerator is

4 - 15

4. If

\frac{1}{3 + 2} = 3 - 2

, use this to find the value of

\frac{1}{3 - 2}

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Answer: A)

3 + 2

\frac{1}{3 - 2} x \frac{3 + 2}{3 + 2} = \frac{3 + 2}{3 - 2} = 3 + 2

5. If

x = \frac{3 - 1}{3 + 1} = 2 - 3

and y

= \frac{3 + 1}{3 - 1} = 2 + 3

, find the value of x*y.

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Answer: C) 1

x*y

= (2 - 3) (2 + 3) = 4 - 3 = 1. (A l so x an d y a rerec i p roc a l s, so p ro d u c t i s 1.)

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