Browse Algebraic fractions

38 questions at your level

DifficultyAll Level 2 Level 3 Level 4 Level 5

Simplifying, multiplying and dividing algebraic fractions

13 questions

LessonNot started

\dfrac{6x + 9}{3x}

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\dfrac{4x + 12}{x^2 + 3x}

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\dfrac{x^2 + 5x}{x^2 - 25}

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\dfrac{x^2 + 7x + 12}{x^2 - 9}

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\dfrac{x + 2}{3} \times \dfrac{6}{x^2 + 2x}

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\dfrac{x^2 - 2x - 15}{x^2 - 25}

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\dfrac{x^2 - 4}{x^2 + 5x + 6}

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\dfrac{2x^2 + 5x - 3}{x^2 - 9}

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\frac{2x^2 + 7x - 15}{4x^2 - 9}

can be written in the form

\dfrac{ax + b}{cx + d}

a

b

c

d

are integers.

(3 marks)

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\dfrac{2x^2 + x - 3}{x^2 - 1}

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\dfrac{x^2 - 4}{5} \div \dfrac{x + 2}{10}

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\dfrac{2x^2 - 7x - 4}{x^2 - 16}

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\dfrac{x^2 + 3x}{x^2 - 1} \div \dfrac{x + 3}{x + 1}

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Adding and subtracting algebraic fractions

13 questions

LessonNot started

\dfrac{3x}{5} + \dfrac{x}{10}

as a single fraction in its simplest form.

●●●●●Level 22 marksStart

\dfrac{x}{4} + \dfrac{x + 1}{3}

as a single fraction in its simplest form.

●●●●●Level 32 marksStart

\dfrac{2x - 1}{4} - \dfrac{x - 3}{6}

as a single fraction in its simplest form.

●●●●●Level 33 marksStart

\dfrac{5}{2x} + \dfrac{3}{4x}

as a single fraction in its simplest form.

●●●●●Level 42 marksStart

\dfrac{2}{x} + \dfrac{3}{x + 1}

as a single fraction in its simplest form.

●●●●●Level 43 marksStart

2 + \dfrac{3}{x - 1}

as a single fraction.

●●●●●Level 42 marksStart

\dfrac{5}{x + 3} + \dfrac{2}{x}

as a single fraction in its simplest form.

●●●●●Level 43 marksStart

3 - \dfrac{2}{x + 1}

as a single fraction.

●●●●●Level 42 marksStart

\dfrac{2}{x + 1} + \dfrac{3}{x - 2}

as a single fraction in its simplest form. [3]

●●●●●Level 43 marksStart

\dfrac{3}{x + 2} - \dfrac{1}{x - 1}

as a single fraction in its simplest form.

●●●●●Level 53 marksStart

\dfrac{4}{x - 1} - \dfrac{3}{x + 5}

as a single fraction in its simplest form.

●●●●●Level 53 marksStart

n

green sweets and

1

red sweet in a bag.

Leo takes at random a sweet from the bag and eats the sweet.

He then takes at random a second sweet from the bag and eats it.

Show that P(Leo eats one sweet of each colour)

= \dfrac{2}{n + 1}

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y

x

3

are white and the others are yellow.

x : y = 1 : 4

Seb takes at random two counters from the box.

Find an expression, in terms of

x

, for the probability that both counters are the same colour.

Give your answer as a fraction in the form

\dfrac{ax^2 + bx + c}{dx^2 + ex}

a

b

c

d

e

are integers.

(5 marks)

●●●●●Level 55 marksStart

Equations with algebraic fractions

12 questions

LessonNot started

\dfrac{12}{x - 1} = 3

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\dfrac{3}{x} + 4 = 5

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\dfrac{x + 2}{3} = \dfrac{2x - 5}{4}

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\dfrac{5}{x} + \dfrac{3}{2x} = \dfrac{13}{6}

●●●●●Level 43 marksStart

\dfrac{3}{x + 1} = \dfrac{5}{2x - 1}

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\dfrac{7}{x} - \dfrac{2}{3x} = \dfrac{19}{12}

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\dfrac{8}{x} = x + 2

You must show all your working.

●●●●●Level 44 marksStart

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

Give your solutions correct to 2 decimal places. (4 marks)

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\dfrac{3}{x + 2} + \dfrac{4}{2x - 3} = 1

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\dfrac{1}{x} + \dfrac{1}{x + 2} = \dfrac{3}{4}

You must show all your working.

●●●●●Level 54 marksStart

\dfrac{2}{x} + \dfrac{3}{x + 1} = 1

Give your answers correct to 2 decimal places.

You must show all your working.

●●●●●Level 54 marksStart

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

Give your answers correct to 2 decimal places.

You must show all your working.

●●●●●Level 55 marksStart