question_answer 22)

Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign \['<',\,\,'=',\,\,'>'\]between the fractions. (a) (b) (c) (i) Show \[\frac{3}{10},\frac{18}{5}\] and \[1\frac{1}{4}\] on the number line. (ii) Put appropriate signs between the fractions given. \[\frac{1}{4}\] \[\frac{\text{Remainder}}{\text{Divisor}}\] \[=\frac{17}{4}\] \[\Rightarrow \]

Answer:

(a) Here, total number of equal parts in all figures = 8 Shaded portion of figure (i) represents fraction \[\begin{align} & 4\overline{)17(}4 \\ & \,\,\,\,\,\frac{16}{1} \\ \end{align}\] Shaded portion of figure (ii) represents fraction \[=4\frac{1}{4}\] Shaded portion of figure (iii) represents fraction \[\frac{\text{(}Whole\times Denominator\text{)}+Numerator}{Deno\min ator}\] Shaded portion of figure (iv) represents fraction \[=4\frac{5}{6}\] \[=\frac{(4\times 6)+5}{6}\] Denominators of all fractions are same. So, we arrange them in ascending and descending order according to their numerators, \[\frac{1}{3}\]Ascending order of fractions \[\frac{2}{6}\] [\[\frac{3}{9}\] fraction having small numerator will be smaller and descending order of fractions \[\frac{4}{12}\] [\[\frac{4}{5}\] fraction having greatest numerator will be greatest] (b) Here, total number of equal parts in all figures = 9 Shaded portion of figure (i) represents fraction \[\frac{28}{35}.\] Shaded portion of figure (ii) represents fraction\[\times \] Shaded portion of figure (iii) represents fraction \[=4\times 35\text{ }=140\] Shaded portion of figure (iv) represents fraction \[\times \] \[=5\times 28=140\] Denominators of all fractions are same. So, we arrange them in ascending and descending order according to their numerators. \[\frac{12}{8}=\frac{12\div 4}{8\div 4}=\frac{3}{2}\]Ascending order of fractions\[\frac{3}{2}\] and descending order of fractions\[\frac{1}{14},\frac{2}{14},\frac{3}{14}\] (c) (i) Given, fractions are \[\frac{1}{15},\frac{7}{27}\] and \[\frac{11}{20}\] These fractions lie between 0 to 1. To show these fractions on a number line, divide the number line into 6 equal parts, where each part represents \[\frac{13}{20},\frac{13}{20}\] part. So, on the number line these fractions can be shown as below Points A, B, C and D represent the fractions \[\frac{2}{3}\]and \[\frac{2}{5},\frac{2}{3}\]on the number line respectively. (ii) Since, all fractions have same denominator, so fraction having larger numerator will be larger and fraction having smaller numerator will be smaller. \[\frac{2}{3}\] \[\frac{3}{4}.\] \[\frac{8}{12}\] \[\frac{9}{12},\] \[\frac{9}{12}>\frac{8}{12},\]