question_answer 1)

Draw number lines and locate the points on them. (a) \[7\frac{3}{4}\] (b) \[5\frac{6}{7}\] (c) \[2\frac{5}{6}\]

Answer:

(a) Here, fractions are \[10\frac{3}{5}\] Also,\[9\frac{3}{7}\] Now, draw a number line, mark two points 0 and 1 on it. Divide the gap between 0 and 1 into four equal parts because denominator is 4, then each part will show \[8\frac{4}{9}\] Also, 2 parts show \[\frac{\text{(Whole }\!\!\times\!\!\text{ Denominator)+Numerator}}{\text{Denominator}}\] parts show \[7\frac{3}{4}=7+\frac{3}{4}=\frac{7\times 4+3}{4}=\frac{31}{4}\]and 4 parts show \[6\frac{6}{7}=5+\frac{6}{7}=\frac{5\times 7+6}{7}=\frac{41}{7}\] Here, A, B, C and D represent \[2\frac{5}{6}=2+\frac{5}{6}=\frac{2\times 6+5}{6}=\frac{17}{6}\] and \[\frac{4}{4}\]respectively. (b) Here, fractions are \[9\frac{3}{5}=9+\frac{3}{7}=\frac{9\times 7+3}{7}=\frac{66}{7}\] and \[8\frac{4}{9}=8+\frac{4}{9}=\frac{8\times 9+4}{9}=\frac{76}{9}\] Now, draw a number line, mark two points 0 and 1 on it. Divide the gap between 0 and 1 into eight equal parts because denominator is 8, then each part will show \[\frac{1}{3}\] Also, 2 parts show \[\frac{2}{7};\frac{2}{5}\]parts show \[\frac{2}{7};\frac{2}{9}\] and 7 parts show \[\frac{6}{27}\] Hence, A, B, C and D represent \[\frac{1}{8},\,\frac{2}{8},\,\frac{3}{8}\] and \[\frac{7}{8}\] respectively. (c) Here, fractions are \[1\times 7=7\]and \[3\times 2=6\] Now, draw a number line, mark two points 0 and 1 on it. Divide the gap between 0 and into five equal parts because denominator is 5, then each part will show \[\frac{1}{5}\]. Also, 2 parts show \[\because \]parts show \[7\ne 6,\]and 4 parts show \[\frac{1}{3}\] denominator is 8, then each part will show \[\frac{2}{7}\] Also, 2 parts show \[\frac{2}{5}\] parts show \[\frac{2}{7}\] and 7 parts show \[\frac{7}{8}\]. Hence, A, B, C and D represent \[5\times 2=10\] and \[\because \] respectively. (c) Here, fractions are \[14\ne 10,\] and \[\frac{2}{5}\] Now, draw a number line, mark two points 0 and 1 on it. Divide the gap between 0 and 1 into five equal parts because denominator is 5, then each part will show \[\frac{2}{7}\] Also, 2 parts show \[\frac{2}{9}\] parts show \[\frac{6}{27}\]and 4 parts show \[2\times 27=54\] Here, A, B and C represent \[9\times 6=54\]and \[\because \] respectively. For representation of \[54=54,\] Draw a number line. Take a point 0 on it. Let it represents O. Here, \[\frac{8}{5}=1\frac{3}{5}=1+\frac{3}{5}\] Mark point A on the number line at unit distance from 0 to the right and mark point B at unit distance from 1 to the right. Let these segments be OA and AB. Then, clearly points A and B represent 1 and 2 respectively which is shown below Take 1 unit length to the right of 0. Divide the 2nd unit AB into five equal parts, here each part will represent \[\frac{6}{27}\] Take 3 parts out of 5 parts to reach at M. Then, M represents \[\frac{1}{2},\frac{2}{4},\frac{3}{6},\frac{4}{8},\]