Mathematics 10 — Exercise Review · Q2

Full question

The table gives long-jump distances in centimetres. Construct the cumulative-frequency polygon and determine the median, Q₁, Q₃, D₇, P₉₀ and interquartile range.

Step-by-step solution

1. Cumulative frequency means a running total. Begin with zero at the first lower boundary.

2. Class 170–180: add frequency 2 to the preceding total.

   $$0+2=2$$

3. Class 180–190: add frequency 6 to the preceding total.

   $$2+6=8$$

4. Class 190–200: add frequency 9 to the preceding total.

   $$8+9=17$$

5. Class 200–210: add frequency 12 to the preceding total.

   $$17+12=29$$

6. Class 210–220: add frequency 8 to the preceding total.

   $$29+8=37$$

7. Class 220–230: add frequency 3 to the preceding total.

   $$37+3=40$$

8. Plot each UPPER boundary against its cumulative frequency, and join adjacent points.

9. Median: find the cumulative-frequency position 1/2×40.

   $$\frac{1}{2}\times 40=20$$

10. Calculate this operation before combining the remaining terms.

    $$\left(-1\right)\times 17=-17$$

11. Keep the common denominator and add the signed numerators.

    $$\frac{5+400}{2}=\frac{405}{2}$$

12. Calculate this operation before combining the remaining terms.

    $$\frac{5}{2}+200=\frac{405}{2}$$

13. Median lies between cumulative totals 17 and 29. Interpolate along that graph segment: lower boundary + (position−previous total)/class frequency × class width.

    $$\frac{20-17}{12}\times 10+200$$

14. Calculate this operation before combining the remaining terms.

    $$20-17=3$$

15. Calculate this operation before combining the remaining terms.

    $$3\times 1=3$$

16. Calculate this operation before combining the remaining terms.

    $$1\times 12=12$$

17. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{3\times 1}{1\times 12}$$

18. Calculate these two products separately.

    $$\frac{3}{12}$$

19. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

    $$\mathrm{GCD}=3$$

20. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{3\times 1}{1\times 3}$$

21. Calculate these two products separately.

    $$\frac{3}{3}$$

22. Show the two divisions explicitly.

    $$\frac{\frac{3}{3}}{\frac{3}{3}}$$

23. Write the reduced fraction.

    $$\frac{1}{1}$$

24. Calculate this operation before combining the remaining terms.

    $$3\times \frac{1}{3}=1$$

25. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{12\times 1}{1\times 3}$$

26. Calculate these two products separately.

    $$\frac{12}{3}$$

27. Show the two divisions explicitly.

    $$\frac{\frac{12}{3}}{\frac{3}{3}}$$

28. Write the reduced fraction.

    $$4\times \frac{1}{1}$$

29. Calculate this operation before combining the remaining terms.

    $$12\times \frac{1}{3}=4$$

30. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{1\times 1}{1\times 4}$$

31. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{4}=\frac{1}{4}$$

32. Show the two divisions explicitly.

    $$\frac{\frac{3}{3}}{\frac{12}{3}}$$

33. Evaluate the numerator division.

    $$\frac{3}{3}=1$$

34. Evaluate the denominator division.

    $$\frac{12}{3}=4$$

35. Write the reduced fraction.

    $$\frac{1}{4}$$

36. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{1\times 1}{1\times 12}$$

37. Calculate these two products separately.

    $$\frac{1}{12}$$

38. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{12}=\frac{1}{12}$$

39. Calculate this operation before combining the remaining terms.

    $$3\times \frac{1}{12}=\frac{1}{4}$$

40. Calculate this operation before combining the remaining terms.

    $$1\times 10=10$$

41. Calculate this operation before combining the remaining terms.

    $$4\times 1=4$$

42. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{10\times 1}{1\times 4}$$

43. Calculate this operation before combining the remaining terms.

    $$10\times \frac{1}{4}=\frac{5}{2}$$

44. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{1\times 10}{4\times 1}$$

45. Calculate these two products separately.

    $$\frac{10}{4}$$

46. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

    $$\mathrm{GCD}=2$$

47. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{10\times 1}{1\times 2}$$

48. Calculate these two products separately.

    $$\frac{10}{2}$$

49. Show the two divisions explicitly.

    $$\frac{\frac{10}{2}}{\frac{2}{2}}$$

50. Evaluate the denominator division.

    $$\frac{2}{2}=1$$

51. Write the reduced fraction.

    $$5\times \frac{1}{1}$$

52. Calculate this operation before combining the remaining terms.

    $$10\times \frac{1}{2}=5$$

53. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{4\times 1}{1\times 2}$$

54. Calculate these two products separately.

    $$\frac{4}{2}$$

55. Show the two divisions explicitly.

    $$\frac{\frac{4}{2}}{\frac{2}{2}}$$

56. Write the reduced fraction.

    $$2\times \frac{1}{1}$$

57. Calculate this operation before combining the remaining terms.

    $$4\times \frac{1}{2}=2$$

58. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{5\times 1}{1\times 2}$$

59. Calculate this operation before combining the remaining terms.

    $$5\times \frac{1}{2}=\frac{5}{2}$$

60. Show the two divisions explicitly.

    $$\frac{\frac{10}{2}}{\frac{4}{2}}$$

61. Evaluate the numerator division.

    $$\frac{10}{2}=5$$

62. Evaluate the denominator division.

    $$\frac{4}{2}=2$$

63. Write the reduced fraction.

    $$\frac{5}{2}$$

64. Calculate this operation before combining the remaining terms.

    $$\frac{1}{4}\times 10=\frac{5}{2}$$

65. To add these fractions, first use a common denominator: the least common multiple of their denominators.

    $$\mathrm{LCD}=2$$

66. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

    $$200\times \frac{1}{1}=\frac{200\times 2}{1\times 2}$$

67. Calculate the converted numerator; the denominator is now common.

    $$\frac{400}{2}$$

68. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

    $$\frac{5}{2}=\frac{5\times 1}{2\times 1}$$

69. Calculate the converted numerator; the denominator is now common.

    $$\frac{5}{2}$$

70. Calculate this operation before combining the remaining terms.

    $$400+5=405$$

71. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{405\times 1}{1\times 2}$$

72. Calculate these two products separately.

    $$\frac{405}{2}$$

73. Calculate this operation before combining the remaining terms.

    $$405\times \frac{1}{2}=\frac{405}{2}$$

74. Keep the common denominator and add the signed numerators.

    $$\frac{400+5}{2}=\frac{405}{2}$$

75. Calculate this operation before combining the remaining terms.

    $$200+\frac{5}{2}=\frac{405}{2}$$

76. Median ≈ 202.500.

    $$\frac{405}{2}$$

77. Q1: find the cumulative-frequency position 1/4×40.

    $$\frac{1}{4}\times 40=10$$

78. Calculate this operation before combining the remaining terms.

    $$\left(-1\right)\times 8=-8$$

79. Keep the common denominator and add the signed numerators.

    $$\frac{20+1710}{9}=\frac{1730}{9}$$

80. Calculate this operation before combining the remaining terms.

    $$\frac{20}{9}+190=\frac{1730}{9}$$

81. Q1 lies between cumulative totals 8 and 17. Interpolate along that graph segment: lower boundary + (position−previous total)/class frequency × class width.

    $$\frac{10-8}{9}\times 10+190$$

82. Calculate this operation before combining the remaining terms.

    $$10-8=2$$

83. Calculate this operation before combining the remaining terms.

    $$2\times 1=2$$

84. Calculate this operation before combining the remaining terms.

    $$1\times 9=9$$

85. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{2\times 1}{1\times 9}$$

86. Calculate these two products separately.

    $$\frac{2}{9}$$

87. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{1\times 1}{1\times 9}$$

88. Calculate these two products separately.

    $$\frac{1}{9}$$

89. Calculate this operation before combining the remaining terms.

    $$1\times \frac{1}{9}=\frac{1}{9}$$

90. Calculate this operation before combining the remaining terms.

    $$2\times \frac{1}{9}=\frac{2}{9}$$

91. Calculate this operation before combining the remaining terms.

    $$2\times 10=20$$

92. Calculate this operation before combining the remaining terms.

    $$9\times 1=9$$

93. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{20\times 1}{1\times 9}$$

94. Calculate this operation before combining the remaining terms.

    $$20\times \frac{1}{9}=\frac{20}{9}$$

95. For multiplication of fractions, multiply the numerators together and the denominators together.

    $$\frac{2\times 10}{9\times 1}$$

96. Calculate these two products separately.

    $$\frac{20}{9}$$

97. Calculate this operation before combining the remaining terms.

    $$\frac{2}{9}\times 10=\frac{20}{9}$$

98. To add these fractions, first use a common denominator: the least common multiple of their denominators.

    $$\mathrm{LCD}=9$$

99. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

    $$190\times \frac{1}{1}=\frac{190\times 9}{1\times 9}$$

100. Calculate the converted numerator; the denominator is now common.

     $$\frac{1710}{9}$$

101. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$\frac{20}{9}=\frac{20\times 1}{9\times 1}$$

102. Calculate the converted numerator; the denominator is now common.

     $$\frac{20}{9}$$

103. Calculate this operation before combining the remaining terms.

     $$1710+20=1730$$

104. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{1730\times 1}{1\times 9}$$

105. Calculate these two products separately.

     $$\frac{1730}{9}$$

106. Calculate this operation before combining the remaining terms.

     $$1730\times \frac{1}{9}=\frac{1730}{9}$$

107. Keep the common denominator and add the signed numerators.

     $$\frac{1710+20}{9}=\frac{1730}{9}$$

108. Calculate this operation before combining the remaining terms.

     $$190+\frac{20}{9}=\frac{1730}{9}$$

109. Q1 ≈ 192.222.

     $$\frac{1730}{9}$$

110. Q3: find the cumulative-frequency position 3/4×40.

     $$\frac{3}{4}\times 40=30$$

111. Calculate this operation before combining the remaining terms.

     $$\left(-1\right)\times 29=-29$$

112. Keep the common denominator and add the signed numerators.

     $$\frac{5+840}{4}=\frac{845}{4}$$

113. Calculate this operation before combining the remaining terms.

     $$\frac{5}{4}+210=\frac{845}{4}$$

114. Q3 lies between cumulative totals 29 and 37. Interpolate along that graph segment: lower boundary + (position−previous total)/class frequency × class width.

     $$\frac{30-29}{8}\times 10+210$$

115. Calculate this operation before combining the remaining terms.

     $$30-29=1$$

116. Calculate this operation before combining the remaining terms.

     $$1\times 1=1$$

117. Calculate this operation before combining the remaining terms.

     $$1\times 8=8$$

118. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{1\times 1}{1\times 8}$$

119. Calculate these two products separately.

     $$\frac{1}{8}$$

120. Calculate this operation before combining the remaining terms.

     $$1\times \frac{1}{8}=\frac{1}{8}$$

121. Calculate this operation before combining the remaining terms.

     $$8\times 1=8$$

122. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{10\times 1}{1\times 8}$$

123. Calculate this operation before combining the remaining terms.

     $$10\times \frac{1}{8}=\frac{5}{4}$$

124. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{1\times 10}{8\times 1}$$

125. Calculate these two products separately.

     $$\frac{10}{8}$$

126. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

     $$\mathrm{GCD}=2$$

127. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{8\times 1}{1\times 2}$$

128. Calculate these two products separately.

     $$\frac{8}{2}$$

129. Show the two divisions explicitly.

     $$\frac{\frac{8}{2}}{\frac{2}{2}}$$

130. Calculate this operation before combining the remaining terms.

     $$8\times \frac{1}{2}=4$$

131. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{5\times 1}{1\times 4}$$

132. Calculate this operation before combining the remaining terms.

     $$5\times \frac{1}{4}=\frac{5}{4}$$

133. Show the two divisions explicitly.

     $$\frac{\frac{10}{2}}{\frac{8}{2}}$$

134. Evaluate the numerator division.

     $$\frac{10}{2}=5$$

135. Evaluate the denominator division.

     $$\frac{8}{2}=4$$

136. Write the reduced fraction.

     $$\frac{5}{4}$$

137. Calculate this operation before combining the remaining terms.

     $$\frac{1}{8}\times 10=\frac{5}{4}$$

138. To add these fractions, first use a common denominator: the least common multiple of their denominators.

     $$\mathrm{LCD}=4$$

139. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$210\times \frac{1}{1}=\frac{210\times 4}{1\times 4}$$

140. Calculate the converted numerator; the denominator is now common.

     $$\frac{840}{4}$$

141. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$\frac{5}{4}=\frac{5\times 1}{4\times 1}$$

142. Calculate the converted numerator; the denominator is now common.

     $$\frac{5}{4}$$

143. Calculate this operation before combining the remaining terms.

     $$840+5=845$$

144. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{845\times 1}{1\times 4}$$

145. Calculate these two products separately.

     $$\frac{845}{4}$$

146. Calculate this operation before combining the remaining terms.

     $$845\times \frac{1}{4}=\frac{845}{4}$$

147. Keep the common denominator and add the signed numerators.

     $$\frac{840+5}{4}=\frac{845}{4}$$

148. Calculate this operation before combining the remaining terms.

     $$210+\frac{5}{4}=\frac{845}{4}$$

149. Q3 ≈ 211.250.

     $$\frac{845}{4}$$

150. D7: find the cumulative-frequency position 7/10×40.

     $$\frac{7}{10}\times 40=28$$

151. Keep the common denominator and add the signed numerators.

     $$\frac{55+1200}{6}=\frac{1255}{6}$$

152. Calculate this operation before combining the remaining terms.

     $$\frac{55}{6}+200=\frac{1255}{6}$$

153. D7 lies between cumulative totals 17 and 29. Interpolate along that graph segment: lower boundary + (position−previous total)/class frequency × class width.

     $$\frac{28-17}{12}\times 10+200$$

154. Calculate this operation before combining the remaining terms.

     $$28-17=11$$

155. Calculate this operation before combining the remaining terms.

     $$11\times 1=11$$

156. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{11\times 1}{1\times 12}$$

157. Calculate these two products separately.

     $$\frac{11}{12}$$

158. Calculate this operation before combining the remaining terms.

     $$11\times \frac{1}{12}=\frac{11}{12}$$

159. Calculate this operation before combining the remaining terms.

     $$11\times 10=110$$

160. Calculate this operation before combining the remaining terms.

     $$12\times 1=12$$

161. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{110\times 1}{1\times 12}$$

162. Calculate this operation before combining the remaining terms.

     $$110\times \frac{1}{12}=\frac{55}{6}$$

163. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{11\times 10}{12\times 1}$$

164. Calculate these two products separately.

     $$\frac{110}{12}$$

165. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

     $$\mathrm{GCD}=2$$

166. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{110\times 1}{1\times 2}$$

167. Calculate these two products separately.

     $$\frac{110}{2}$$

168. Show the two divisions explicitly.

     $$\frac{\frac{110}{2}}{\frac{2}{2}}$$

169. Write the reduced fraction.

     $$55\times \frac{1}{1}$$

170. Calculate this operation before combining the remaining terms.

     $$110\times \frac{1}{2}=55$$

171. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{12\times 1}{1\times 2}$$

172. Calculate these two products separately.

     $$\frac{12}{2}$$

173. Show the two divisions explicitly.

     $$\frac{\frac{12}{2}}{\frac{2}{2}}$$

174. Write the reduced fraction.

     $$6\times \frac{1}{1}$$

175. Calculate this operation before combining the remaining terms.

     $$12\times \frac{1}{2}=6$$

176. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{55\times 1}{1\times 6}$$

177. Calculate this operation before combining the remaining terms.

     $$55\times \frac{1}{6}=\frac{55}{6}$$

178. Show the two divisions explicitly.

     $$\frac{\frac{110}{2}}{\frac{12}{2}}$$

179. Evaluate the numerator division.

     $$\frac{110}{2}=55$$

180. Evaluate the denominator division.

     $$\frac{12}{2}=6$$

181. Write the reduced fraction.

     $$\frac{55}{6}$$

182. Calculate this operation before combining the remaining terms.

     $$\frac{11}{12}\times 10=\frac{55}{6}$$

183. To add these fractions, first use a common denominator: the least common multiple of their denominators.

     $$\mathrm{LCD}=6$$

184. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$200\times \frac{1}{1}=\frac{200\times 6}{1\times 6}$$

185. Calculate the converted numerator; the denominator is now common.

     $$\frac{1200}{6}$$

186. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$\frac{55}{6}=\frac{55\times 1}{6\times 1}$$

187. Calculate the converted numerator; the denominator is now common.

     $$\frac{55}{6}$$

188. Calculate this operation before combining the remaining terms.

     $$1200+55=1255$$

189. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{1255\times 1}{1\times 6}$$

190. Calculate these two products separately.

     $$\frac{1255}{6}$$

191. Calculate this operation before combining the remaining terms.

     $$1255\times \frac{1}{6}=\frac{1255}{6}$$

192. Keep the common denominator and add the signed numerators.

     $$\frac{1200+55}{6}=\frac{1255}{6}$$

193. Calculate this operation before combining the remaining terms.

     $$200+\frac{55}{6}=\frac{1255}{6}$$

194. D7 ≈ 209.167.

     $$\frac{1255}{6}$$

195. P90: find the cumulative-frequency position 9/10×40.

     $$\frac{9}{10}\times 40=36$$

196. Keep the common denominator and add the signed numerators.

     $$\frac{35+840}{4}=\frac{875}{4}$$

197. Calculate this operation before combining the remaining terms.

     $$\frac{35}{4}+210=\frac{875}{4}$$

198. P90 lies between cumulative totals 29 and 37. Interpolate along that graph segment: lower boundary + (position−previous total)/class frequency × class width.

     $$\frac{36-29}{8}\times 10+210$$

199. Calculate this operation before combining the remaining terms.

     $$36-29=7$$

200. Calculate this operation before combining the remaining terms.

     $$7\times 1=7$$

201. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{7\times 1}{1\times 8}$$

202. Calculate these two products separately.

     $$\frac{7}{8}$$

203. Calculate this operation before combining the remaining terms.

     $$7\times \frac{1}{8}=\frac{7}{8}$$

204. Calculate this operation before combining the remaining terms.

     $$7\times 10=70$$

205. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{70\times 1}{1\times 8}$$

206. Calculate this operation before combining the remaining terms.

     $$70\times \frac{1}{8}=\frac{35}{4}$$

207. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{7\times 10}{8\times 1}$$

208. Calculate these two products separately.

     $$\frac{70}{8}$$

209. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

     $$\mathrm{GCD}=2$$

210. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{70\times 1}{1\times 2}$$

211. Calculate these two products separately.

     $$\frac{70}{2}$$

212. Show the two divisions explicitly.

     $$\frac{\frac{70}{2}}{\frac{2}{2}}$$

213. Write the reduced fraction.

     $$35\times \frac{1}{1}$$

214. Calculate this operation before combining the remaining terms.

     $$70\times \frac{1}{2}=35$$

215. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{35\times 1}{1\times 4}$$

216. Calculate this operation before combining the remaining terms.

     $$35\times \frac{1}{4}=\frac{35}{4}$$

217. Show the two divisions explicitly.

     $$\frac{\frac{70}{2}}{\frac{8}{2}}$$

218. Evaluate the numerator division.

     $$\frac{70}{2}=35$$

219. Evaluate the denominator division.

     $$\frac{8}{2}=4$$

220. Write the reduced fraction.

     $$\frac{35}{4}$$

221. Calculate this operation before combining the remaining terms.

     $$\frac{7}{8}\times 10=\frac{35}{4}$$

222. To add these fractions, first use a common denominator: the least common multiple of their denominators.

     $$\mathrm{LCD}=4$$

223. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$210\times \frac{1}{1}=\frac{210\times 4}{1\times 4}$$

224. Calculate the converted numerator; the denominator is now common.

     $$\frac{840}{4}$$

225. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$\frac{35}{4}=\frac{35\times 1}{4\times 1}$$

226. Calculate the converted numerator; the denominator is now common.

     $$\frac{35}{4}$$

227. Calculate this operation before combining the remaining terms.

     $$840+35=875$$

228. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{875\times 1}{1\times 4}$$

229. Calculate these two products separately.

     $$\frac{875}{4}$$

230. Calculate this operation before combining the remaining terms.

     $$875\times \frac{1}{4}=\frac{875}{4}$$

231. Keep the common denominator and add the signed numerators.

     $$\frac{840+35}{4}=\frac{875}{4}$$

232. Calculate this operation before combining the remaining terms.

     $$210+\frac{35}{4}=\frac{875}{4}$$

233. P90 ≈ 218.750.

     $$\frac{875}{4}$$

234. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{\left(-1\right)\times 1730}{1\times 9}$$

235. Calculate these two products separately.

     $$-\frac{1730}{9}$$

236. Calculate this operation before combining the remaining terms.

     $$\left(-1\right)\times \frac{1730}{9}=-\frac{1730}{9}$$

237. Interquartile range is Q3−Q1.

     $$\frac{845}{4}-\frac{1730}{9}$$

238. To add these fractions, first use a common denominator: the least common multiple of their denominators.

     $$\mathrm{LCD}=36$$

239. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$\frac{845}{4}=\frac{845\times 9}{4\times 9}$$

240. Calculate the converted numerator; the denominator is now common.

     $$\frac{7605}{36}$$

241. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{\left(-1730\right)\times 1}{1\times 9}$$

242. Calculate this operation before combining the remaining terms.

     $$\left(-1730\right)\times \frac{1}{9}=-\frac{1730}{9}$$

243. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

     $$-\frac{1730}{9}=\frac{\left(-1730\right)\times 4}{9\times 4}$$

244. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{\left(-6920\right)\times 1}{1\times 36}$$

245. The numerator and denominator have this greatest common divisor. Divide BOTH by it.

     $$\mathrm{GCD}=4$$

246. Show the two divisions explicitly.

     $$\frac{-\frac{6920}{4}}{\frac{36}{4}}$$

247. Evaluate the numerator division.

     $$-\frac{6920}{4}=-1730$$

248. Evaluate the denominator division.

     $$\frac{36}{4}=9$$

249. Calculate this operation before combining the remaining terms.

     $$\left(-6920\right)\times \frac{1}{36}=-\frac{1730}{9}$$

250. Calculate the converted numerator; the denominator is now common.

     $$-\frac{6920}{36}$$

251. Calculate this operation before combining the remaining terms.

     $$\left(-1\right)\times 6920=-6920$$

252. Calculate this operation before combining the remaining terms.

     $$7605-6920=685$$

253. For multiplication of fractions, multiply the numerators together and the denominators together.

     $$\frac{685\times 1}{1\times 36}$$

254. Calculate these two products separately.

     $$\frac{685}{36}$$

255. Calculate this operation before combining the remaining terms.

     $$685\times \frac{1}{36}=\frac{685}{36}$$

256. Keep the common denominator and add the signed numerators.

     $$\frac{7605-6920}{36}=\frac{685}{36}$$

257. Calculate this operation before combining the remaining terms.

     $$\frac{845}{4}-\frac{1730}{9}=\frac{685}{36}$$

Answer

Median ≈ 202.5; Q1 ≈ 192.222; Q3 ≈ 211.25; D7 ≈ 209.167; P90 ≈ 218.75; IQR ≈ 19.028