Question

Express -7/9 as a rational number with
(1) numerator -21 (i) numerator 28 (iii) denominator 18 (iv) denominator - 27

Convert the following rational numbers to have same denominators: -3/4 ,2/3,5/6,7/-8​

Answer 1

Step-by-step explanation:

$- \frac{7}{9} \\ \\ (i) \: \: \times 3 \\ \\ = - \frac{7}{9} \times \frac{3}{3} \\ \\ = - \frac{21}{27} \\ \\ (ii) \: \: \: \times 4 \\ \\ - \frac{7}{9} \times \frac{4}{4} \\ \\ = - \frac{28}{36} \\ \\ (iii) \: \: \: \times 2 \\ \\ - \frac{7}{9} \times \frac{2}{2} \\ \\ = - \frac{14}{18} \\ \\ (iv) \: \: \: \times 3 \\ \\ - \frac{7}{9} \times \frac{3}{3} \\ \\ = - \frac{21}{27} \\ \\ = \frac{21}{( - 27)} \\ \\ \\ (0) \: \: - \frac{3}{2} \: \: \frac{2}{3} \: \: \frac{5}{6} \: \: ( \frac{7}{ - 8} = - \frac{7}{8} ) \\ \\ now \: take \: lcm \: of \: denominators \\ \\ 2 \: \: 3 \: \: 6 \: \: 8 \\ \\ lcm \: is \: 24 \\ \\ 1. \: \: \times 12 \\ \\ = - \frac{3}{2} \times \frac{12}{12} \\ \\ = - \frac{36}{12} \\ \\ 2. \: \: \times 8 \\ \\ \frac{2}{3} \times \frac{8}{8} \\ \\ = \frac{16}{24} \\ \\ 3. \: \: \: \times 4 \\ \\ = \frac{5}{6} \times \frac{4}{4} \\ \\ = \frac{20}{24} \\ \\ 4. \: \: \: \times 3 \\ \\ = - \frac{7}{8} \times \frac{3}{ 3} \\ \\ = - \frac{21}{24}$

hope it helps