Instruction: Answer ALL questions and clearly show ALL workings 1. In a Mathematics textbook, (2)/(5) deals with Arithmetic, (3)/(7) with Algebra and the remainder with Geometry. If the book has 210 pages, how many Geometry pages are there? (5 marks)

To find the number of Geometry pages in the Mathematics textbook, we need to determine the fraction of the book that is dedicated to Geometry.<br /><br />Given:<br />- $\frac {2}{5}$ of the book is dedicated to Arithmetic.<br />- $\frac {3}{7}$ of the book is dedicated to Algebra.<br /><br />Let's calculate the fraction of the book that is dedicated to Geometry:<br /><br />Total pages in the book = 210<br /><br />Fraction of the book dedicated to Arithmetic = $\frac {2}{5}$<br />Number of Arithmetic pages = $\frac {2}{5} \times 210 = 84$<br /><br />Fraction of the book dedicated to Algebra = $\frac {3}{7}$<br />Number of Algebra pages = $\frac {3}{7} \times 210 = 90$<br /><br />Fraction of the book dedicated to Geometry = 1 - (Fraction of Arithmetic + Fraction of Algebra)<br />Fraction of the book dedicated to Geometry = 1 - ($\frac {2}{5} + $\frac {3}{7}$)<br /><br />To find the common denominator for $\frac {2}{5}$ and $\frac {3}{7}$, we can multiply the denominators together: 5 * 7 = 35.<br /><br />$\frac {2}{5}$ = $\frac {2 \times 7}{5 \times 7}$ = $\frac {14}{35}$<br />$\frac {3}{7}$ = $\frac {3 \times 5}{7 \times 5}$ = $\frac {15}{35}$<br /><br />Fraction of the book dedicated to Geometry = 1 - ($\frac {14}{35} + $\frac {15}{35}$) = 1 - $\frac {29}{35}$ = $\frac {6}{35}$<br /><br />Number of Geometry pages = $\frac {6}{35} \times 210 = 36$<br /><br />Therefore, there are 36 Geometry pages in the Mathematics textbook.