Exercise 3.3

Q1 (i)

Prove that the following rational numbers are equal: \(\frac{2}{3}\) and \(\frac{4}{6}\)

Q1 (ii)

Prove that the following rational numbers are equal: \(\frac{5}{4}\) and \(\frac{10}{8}\)

Q1 (iii)

Prove that the following rational numbers are equal: \(\frac{−3}{5}\) and \(\frac{−6}{10}\)

Q1 (iv)

Prove that the following rational numbers are equal: \(\frac{9}{3}\) and \(3\)

Q2 (i)

Find the sum: \(\frac{2}{5}\) + \(\frac{3}{10}\)

Q2 (ii)

Find the sum: \(\frac{7}{12}\) + \(\frac{5}{8}\)

Q2 (iii)

Find the sum: \(\frac{−4}{7}\) + \(\frac{3}{14}\)

Q3 (i)

Find the difference: \(\frac{5}{6}\) − \(\frac{1}{4}\)

Q3 (ii)

Find the difference: \(\frac{11}{8}\) − \(\frac{3}{4}\)

Q3 (iii)

Find the difference: \(\frac{−7}{9}\) − \((\frac{−2}{3})\)

Q4 (i)

Find the product: \(\frac{2}{3}\) × \(\frac{3}{10}\)

Q4 (ii)

Find the product: \(\frac{7}{11}\) × \(\frac{5}{8}\)

Q4 (iii)

Find the product: \(−\frac{4}{7}\) × \(\frac{5}{14}\)

Q5 (i)

Find the quotient: \(\frac{2}{3}\) ÷ \(\frac{3}{10}\)

Q5 (ii)

Find the quotient: \(\frac{7}{11}\) ÷ \(\frac{5}{8}\)

Q5 (iii)

Find the quotient: \(\frac{−4}{7}\) ÷ \(\frac{5}{14}\)

Q6

Show that: \((\frac{1}{2}+ \frac{3}{4}) × \frac{8}{3} = \frac{1}{2} × \frac{8}{3} + \frac{3}{4} × \frac{8}{3}\)

Q7

Simplify the following using the distributive property: \(\frac{7}{9}(\frac{6}{7} − \frac{3}{4})\)

Q8

Find the rational number \(x\) such that: \(\frac{5}{6}(x + \frac{3}{5}) = \frac{5}{6}x + \frac{1}{2}\)