Algebraic Fractions and Formulae practice questions

Secondary 2 topics, working towards the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise algebraic fractions and formulae free

What this topic covers

Worked examples

Example 1

Solve x−24−x−43=1\frac{x - 2}{4} - \frac{x - 4}{3} = 1. Find the value of xx.
Show the worked solution
  • $\frac{x - 2}{4} - \frac{x - 4}{3} = 1$
  • $3(x - 2) - 4(x - 4) = 1 \times 12 \quad \scriptsize\textit{multiply through by } 12$
  • $3x - 6 - 4x + 16 = 12$
  • $-x + 10 = 12$
  • $-x = 2$
  • $x = -2$

Answer: −2-2

Example 2

Express 4x−5−1x+3\frac{4}{x - 5} - \frac{1}{x + 3} as a single fraction.
Show the worked solution
  • $\frac{4}{x - 5} - \frac{1}{x + 3}$
  • $= \frac{4(x + 3) - 1(x - 5)}{(x - 5)(x + 3)} \quad \scriptsize\textit{LCM = }(x - 5)(x + 3)$
  • $= \frac{4x + 12 - x + 5}{(x - 5)(x + 3)}$
  • $= \frac{3x + 17}{(x - 5)(x + 3)}$

Answer: (3x+17)/((x−5)(x+3))(3x+17)/((x-5)(x+3))

Example 3

Given that 1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}, make vv the subject of the formula.
Show the worked solution
  • $\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$
  • $\frac{1}{v} = \frac{1}{f} - \frac{1}{u} \quad \scriptsize\textit{rearrange}$
  • $\frac{1}{v} = \frac{u - f}{fu} \quad \scriptsize\textit{combine fractions}$
  • $v = \frac{fu}{u - f}$

Answer: fu/(u−f)fu/(u-f)

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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