Test Index

BECE Mathematics 2011 Paper

Question : 17

Total: 40

Simplify:

\;\frac{1}{3} \left(\frac{1}{2} - \frac{1}{3}\right) - \frac{1}{3} \left(\frac{1}{3} - \frac{1}{2}\right)

Solution:

Concept:

Simplify the fractions inside the brackets first, then multiply and combine carefully.

Explanation:

Start with the expression:

\frac{1}{3}\left(\frac{1}{2}-\frac{1}{3}\right)-\frac{1}{3}\left(\frac{1}{3}-\frac{1}{2}\right)

Compute the first bracket:

\frac{1}{2}-\frac{1}{3}=\frac{3-2}{6}=\frac{1}{6}

Compute the second bracket:

\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=-\frac{1}{6}

Substitute these results:

\frac{1}{3}\times\frac{1}{6}-\frac{1}{3}\times\left(-\frac{1}{6}\right)

Multiplying gives:

\frac{1}{18}-\left(-\frac{1}{18}\right)

Since subtracting a negative is the same as adding:

\frac{1}{18}+\frac{1}{18}=\frac{2}{18}

Simplify the fraction:

\frac{2}{18}=\frac{1}{9}

Answer:

\frac{1}{9}

, which is option D.

Go to Question:

Prev Question

Next Question