question_answer 25)

Look at the figures and write '<' or '>', '= between the given pairs of fractions. (a)\[\frac{1}{18}+\frac{1}{18}=\frac{1+1}{18}=\frac{2}{18}=\frac{1}{9}\] (b)\[\frac{8}{15}+\frac{3}{15}=\frac{8+3}{15}=\frac{11}{15}\] (c)\[\frac{7}{7}+\frac{5}{7}=\frac{7-5}{7}=\frac{2}{7}\] (d)\[\frac{1}{22}+\frac{21}{22}=\frac{1+21}{22}=\frac{22}{22}=1\] (e)\[\frac{12}{15}+\frac{7}{15}=\frac{12+7}{15}=\frac{5}{15}=\frac{1}{3}\] Make five more such problems and solve them with your friends.

Answer:

(a) From the given figures, \[\frac{5}{8}+\frac{3}{8}=\frac{3+3}{8}=\frac{8}{8}=1\] because \[1-\frac{2}{3}=\frac{3}{8}=\frac{3}{3}-\frac{2}{3}=\frac{3-2}{3}=\frac{1}{3}\] lies on the left of \[\left[ \begin{align} & \because 1\,\text{and}\,\frac{3}{3}\,\text{are}\,[\text{simplest}\,\text{from}] \\ & \text{equivalent}\,\text{fractions} \\ \end{align} \right]\] (b) \[\frac{1}{4}+\frac{0}{4}=\frac{1+0}{4}=\frac{1}{4}\] because \[3-\frac{12}{5}=\frac{3}{1}-\frac{12}{5}\]is on the right side of\[=\frac{3\times 5}{1\times 5}-\frac{12}{5}\] (c) \[\left[ \begin{align} & \text{converting}\,\frac{\text{3}}{1}\,\text{into}\,\text{like}\,\,\text{fractions}\,\text{by}\,\text{multiplying} \\ & \text{numberator}\,\text{and denominatory}\,\text{by 5} \\ \end{align} \right]\] because \[=\frac{15}{5}-\frac{12}{5}=\frac{15-12}{5}=\frac{3}{5}\]is on the right side of \[=\frac{2}{3}\] (d) \[=\frac{1}{3}\] because \[=\frac{2}{3}+\frac{1}{3}=\frac{2+1}{3}=\frac{3}{3}=1\]and \[\frac{7}{10}-=\frac{3}{10}\] lies on the same point. (e) \[-\frac{3}{21}=\frac{5}{21}\] because \[-\frac{3}{6}=\frac{3}{6}\] is on the left side of \[+\frac{5}{27}=\frac{12}{27}\] Five more such examples can be taken as under (i) \[\frac{7}{10}-=\frac{3}{10}\] (ii) \[\frac{7}{10}\] (iii) \[\frac{3}{10}\] (iv) \[\frac{3}{10}\] (v) \[\frac{7}{10}.\] (i) \[\frac{3}{10}\] because\[\frac{7}{10}\] lies on the left side of\[\therefore \] (ii) \[=\frac{7}{10}-\frac{3}{10}=\frac{7-3}{10}=\frac{4}{10}\] because \[\frac{2}{5}\]lies on the right side of\[\frac{7}{10}-=\frac{3}{10}\] (iii) \[-\frac{3}{21}=\frac{5}{21}\] because \[\frac{3}{6}\] lies on the right side of\[\frac{3}{6}.\] (iv) \[\frac{3}{21}\] because they lies on the same point. (v) \[\frac{5}{21}\] because they lies on the same point.