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Fraction Division

Directions: Use the digits 0 through 9, without repeats, to solve the problem below.

Hint

Hint

How do you divide by a fraction?

Answer

Answer

Here is one possible solution

Number of Unique Solutions: 338

1:  1/2 ÷ 3/4 = 6/9

2:  1/2 ÷ 3/9 = 6/4

3:  1/2 ÷ 6/4 = 3/9

4:  1/2 ÷ 6/9 = 3/4

5:  1/3 ÷ 2/4 = 6/9

6:  1/3 ÷ 2/9 = 6/4

7:  1/3 ÷ 4/8 = 6/9

8:  1/3 ÷ 4/9 = 6/8

9:  1/3 ÷ 6/4 = 2/9

10:  1/3 ÷ 6/8 = 4/9

11:  1/3 ÷ 6/9 = 2/4

12:  1/3 ÷ 6/9 = 4/8

13:  1/4 ÷ 3/8 = 6/9

14:  1/4 ÷ 3/9 = 6/8

15:  1/4 ÷ 6/8 = 3/9

16:  1/4 ÷ 6/9 = 3/8

17:  1/6 ÷ 2/4 = 3/9

18:  1/6 ÷ 2/9 = 3/4

19:  1/6 ÷ 3/4 = 2/9

20:  1/6 ÷ 3/8 = 4/9

21:  1/6 ÷ 3/9 = 2/4

22:  1/6 ÷ 3/9 = 4/8

23:  1/6 ÷ 4/8 = 3/9

24:  1/6 ÷ 4/9 = 3/8

25:  2/1 ÷ 4/3 = 9/6

26:  2/1 ÷ 4/6 = 9/3

27:  2/1 ÷ 4/8 = 36/9

28:  2/1 ÷ 4/9 = 36/8

29:  2/1 ÷ 9/3 = 4/6

30:  2/1 ÷ 9/6 = 4/3

31:  2/4 ÷ 1/3 = 9/6

32:  2/4 ÷ 1/6 = 9/3

33:  2/4 ÷ 1/8 = 36/9

34:  2/4 ÷ 1/9 = 36/8

35:  2/4 ÷ 9/3 = 1/6

36:  2/4 ÷ 9/6 = 1/3

37:  2/9 ÷ 1/3 = 4/6

38:  2/9 ÷ 1/6 = 4/3

39:  2/9 ÷ 4/3 = 1/6

40:  2/9 ÷ 4/6 = 1/3

41:  3/1 ÷ 2/5 = 60/8

42:  3/1 ÷ 2/8 = 60/5

43:  3/1 ÷ 4/2 = 9/6

44:  3/1 ÷ 4/6 = 9/2

45:  3/1 ÷ 6/5 = 20/8

46:  3/1 ÷ 6/8 = 20/5

47:  3/1 ÷ 8/4 = 9/6

48:  3/1 ÷ 8/6 = 9/4

49:  3/1 ÷ 9/2 = 4/6

50:  3/1 ÷ 9/4 = 8/6

51:  3/1 ÷ 9/6 = 4/2

52:  3/1 ÷ 9/6 = 8/4

53:  3/2 ÷ 1/5 = 60/8

54:  3/2 ÷ 1/8 = 60/5

55:  3/2 ÷ 6/5 = 10/8

56:  3/2 ÷ 6/7 = 14/8

57:  3/2 ÷ 6/8 = 10/5

58:  3/2 ÷ 6/8 = 14/7

59:  3/4 ÷ 1/2 = 9/6

60:  3/4 ÷ 1/6 = 9/2

61:  3/4 ÷ 9/2 = 1/6

62:  3/4 ÷ 9/6 = 1/2

63:  3/6 ÷ 1/5 = 20/8

64:  3/6 ÷ 1/8 = 20/5

65:  3/6 ÷ 2/5 = 10/8

66:  3/6 ÷ 2/7 = 14/8

67:  3/6 ÷ 2/8 = 10/5

68:  3/6 ÷ 2/8 = 14/7

69:  3/8 ÷ 1/4 = 9/6

70:  3/8 ÷ 1/6 = 9/4

71:  3/8 ÷ 9/4 = 1/6

72:  3/8 ÷ 9/6 = 1/4

73:  3/9 ÷ 1/2 = 4/6

74:  3/9 ÷ 1/4 = 8/6

75:  3/9 ÷ 1/6 = 4/2

76:  3/9 ÷ 1/6 = 8/4

77:  3/9 ÷ 4/2 = 1/6

78:  3/9 ÷ 4/6 = 1/2

79:  3/9 ÷ 8/4 = 1/6

80:  3/9 ÷ 8/6 = 1/4

81:  4/1 ÷ 3/5 = 60/9

82:  4/1 ÷ 3/6 = 72/9

83:  4/1 ÷ 3/9 = 60/5

84:  4/1 ÷ 3/9 = 72/6

85:  4/1 ÷ 6/5 = 30/9

86:  4/1 ÷ 6/9 = 30/5

87:  4/1 ÷ 8/3 = 9/6

88:  4/1 ÷ 8/6 = 27/9

89:  4/1 ÷ 8/6 = 9/3

90:  4/1 ÷ 8/9 = 27/6

91:  4/1 ÷ 9/3 = 8/6

92:  4/1 ÷ 9/6 = 8/3

93:  4/2 ÷ 3/1 = 6/9

94:  4/2 ÷ 3/9 = 6/1

95:  4/2 ÷ 6/1 = 3/9

96:  4/2 ÷ 6/9 = 3/1

97:  4/3 ÷ 1/6 = 72/9

98:  4/3 ÷ 1/9 = 60/5

99:  4/3 ÷ 1/9 = 72/6

100:  4/3 ÷ 2/1 = 6/9

101:  4/3 ÷ 2/9 = 6/1

102:  4/3 ÷ 6/1 = 2/9

103:  4/3 ÷ 6/5 = 10/9

104:  4/3 ÷ 6/9 = 10/5

105:  4/3 ÷ 6/9 = 2/1

106:  4/6 ÷ 1/9 = 30/5

107:  4/6 ÷ 2/1 = 3/9

108:  4/6 ÷ 2/9 = 3/1

109:  4/6 ÷ 3/1 = 2/9

110:  4/6 ÷ 3/5 = 10/9

111:  4/6 ÷ 3/9 = 10/5

112:  4/6 ÷ 3/9 = 2/1

113:  4/8 ÷ 1/3 = 9/6

114:  4/8 ÷ 1/6 = 27/9

115:  4/8 ÷ 1/6 = 9/3

116:  4/8 ÷ 1/9 = 27/6

117:  4/8 ÷ 9/3 = 1/6

118:  4/8 ÷ 9/6 = 1/3

119:  4/9 ÷ 1/3 = 8/6

120:  4/9 ÷ 1/6 = 8/3

121:  4/9 ÷ 8/3 = 1/6

122:  4/9 ÷ 8/6 = 1/3

123:  5/1 ÷ 2/3 = 60/8

124:  5/1 ÷ 2/8 = 60/3

125:  5/1 ÷ 3/4 = 60/9

126:  5/1 ÷ 3/9 = 60/4

127:  5/1 ÷ 6/3 = 20/8

128:  5/1 ÷ 6/4 = 30/9

129:  5/1 ÷ 6/8 = 20/3

130:  5/1 ÷ 6/9 = 30/4

131:  5/2 ÷ 1/3 = 60/8

132:  5/2 ÷ 1/8 = 60/3

133:  5/2 ÷ 3/6 = 40/8

134:  5/2 ÷ 3/8 = 40/6

135:  5/2 ÷ 3/8 = 60/9

136:  5/2 ÷ 3/9 = 60/8

137:  5/2 ÷ 4/6 = 30/8

138:  5/2 ÷ 4/8 = 30/6

139:  5/2 ÷ 6/3 = 10/8

140:  5/2 ÷ 6/8 = 10/3

141:  5/2 ÷ 6/8 = 30/9

142:  5/2 ÷ 6/9 = 30/8

143:  5/3 ÷ 1/4 = 60/9

144:  5/3 ÷ 2/8 = 40/6

145:  5/3 ÷ 2/8 = 60/9

146:  5/3 ÷ 4/8 = 20/6

147:  5/3 ÷ 6/4 = 10/9

148:  5/3 ÷ 6/8 = 20/9

149:  5/4 ÷ 2/6 = 30/8

150:  5/4 ÷ 2/8 = 30/6

151:  5/4 ÷ 3/6 = 20/8

152:  5/4 ÷ 3/8 = 20/6

153:  5/6 ÷ 1/4 = 30/9

154:  5/6 ÷ 1/8 = 20/3

155:  5/6 ÷ 2/8 = 10/3

156:  5/6 ÷ 2/8 = 30/9

157:  5/6 ÷ 3/4 = 10/9

158:  5/6 ÷ 3/8 = 20/9

159:  6/1 ÷ 3/4 = 72/9

160:  6/1 ÷ 3/9 = 72/4

161:  6/1 ÷ 4/2 = 9/3

162:  6/1 ÷ 4/3 = 9/2

163:  6/1 ÷ 8/3 = 9/4

164:  6/1 ÷ 8/4 = 27/9

165:  6/1 ÷ 8/4 = 9/3

166:  6/1 ÷ 8/9 = 27/4

167:  6/1 ÷ 9/2 = 4/3

168:  6/1 ÷ 9/3 = 4/2

169:  6/1 ÷ 9/3 = 8/4

170:  6/1 ÷ 9/4 = 8/3

171:  6/2 ÷ 3/5 = 40/8

172:  6/2 ÷ 3/8 = 40/5

173:  6/2 ÷ 4/5 = 30/8

174:  6/2 ÷ 4/8 = 30/5

175:  6/3 ÷ 1/4 = 72/9

176:  6/3 ÷ 1/9 = 72/4

177:  6/3 ÷ 2/5 = 40/8

178:  6/3 ÷ 2/8 = 40/5

179:  6/3 ÷ 4/5 = 20/8

180:  6/3 ÷ 4/8 = 20/5

181:  6/4 ÷ 1/2 = 9/3

182:  6/4 ÷ 1/3 = 9/2

183:  6/4 ÷ 2/5 = 30/8

184:  6/4 ÷ 2/8 = 30/5

185:  6/4 ÷ 3/5 = 20/8

186:  6/4 ÷ 3/8 = 20/5

187:  6/4 ÷ 9/2 = 1/3

188:  6/4 ÷ 9/3 = 1/2

189:  6/8 ÷ 1/3 = 9/4

190:  6/8 ÷ 1/4 = 27/9

191:  6/8 ÷ 1/4 = 9/3

192:  6/8 ÷ 1/9 = 27/4

193:  6/8 ÷ 9/3 = 1/4

194:  6/8 ÷ 9/4 = 1/3

195:  6/9 ÷ 1/2 = 4/3

196:  6/9 ÷ 1/3 = 4/2

197:  6/9 ÷ 1/3 = 8/4

198:  6/9 ÷ 1/4 = 8/3

199:  6/9 ÷ 4/2 = 1/3

200:  6/9 ÷ 4/3 = 1/2

201:  6/9 ÷ 8/3 = 1/4

202:  6/9 ÷ 8/4 = 1/3

203:  7/2 ÷ 4/8 = 63/9

204:  7/2 ÷ 4/9 = 63/8

205:  7/2 ÷ 6/3 = 14/8

206:  7/2 ÷ 6/8 = 14/3

207:  7/4 ÷ 2/8 = 63/9

208:  7/4 ÷ 2/9 = 63/8

209:  7/4 ÷ 6/8 = 21/9

210:  7/4 ÷ 6/9 = 21/8

211:  7/6 ÷ 2/8 = 14/3

212:  7/6 ÷ 4/8 = 21/9

213:  8/1 ÷ 2/3 = 60/5

214:  8/1 ÷ 2/5 = 60/3

215:  8/1 ÷ 4/2 = 36/9

216:  8/1 ÷ 4/9 = 36/2

217:  8/1 ÷ 6/3 = 20/5

218:  8/1 ÷ 6/5 = 20/3

219:  8/2 ÷ 1/3 = 60/5

220:  8/2 ÷ 1/5 = 60/3

221:  8/2 ÷ 3/5 = 40/6

222:  8/2 ÷ 3/5 = 60/9

223:  8/2 ÷ 3/6 = 40/5

224:  8/2 ÷ 3/9 = 60/5

225:  8/2 ÷ 4/5 = 30/6

226:  8/2 ÷ 4/6 = 30/5

227:  8/2 ÷ 4/7 = 63/9

228:  8/2 ÷ 4/9 = 63/7

229:  8/2 ÷ 6/3 = 10/5

230:  8/2 ÷ 6/3 = 14/7

231:  8/2 ÷ 6/5 = 10/3

232:  8/2 ÷ 6/5 = 30/9

233:  8/2 ÷ 6/7 = 14/3

234:  8/2 ÷ 6/9 = 30/5

235:  8/3 ÷ 2/6 = 40/5

236:  8/3 ÷ 2/9 = 60/5

237:  8/3 ÷ 4/1 = 6/9

238:  8/3 ÷ 4/6 = 20/5

239:  8/3 ÷ 4/9 = 6/1

240:  8/3 ÷ 6/1 = 4/9

241:  8/3 ÷ 6/5 = 20/9

242:  8/3 ÷ 6/9 = 20/5

243:  8/3 ÷ 6/9 = 4/1

244:  8/4 ÷ 1/2 = 36/9

245:  8/4 ÷ 1/9 = 36/2

246:  8/4 ÷ 2/5 = 30/6

247:  8/4 ÷ 2/6 = 30/5

248:  8/4 ÷ 2/7 = 63/9

249:  8/4 ÷ 2/9 = 63/7

250:  8/4 ÷ 3/1 = 6/9

251:  8/4 ÷ 3/5 = 20/6

252:  8/4 ÷ 3/6 = 20/5

253:  8/4 ÷ 3/9 = 6/1

254:  8/4 ÷ 6/1 = 3/9

255:  8/4 ÷ 6/7 = 21/9

256:  8/4 ÷ 6/9 = 21/7

257:  8/4 ÷ 6/9 = 3/1

258:  8/6 ÷ 1/3 = 20/5

259:  8/6 ÷ 2/3 = 10/5

260:  8/6 ÷ 2/3 = 14/7

261:  8/6 ÷ 2/7 = 14/3

262:  8/6 ÷ 2/9 = 30/5

263:  8/6 ÷ 3/1 = 4/9

264:  8/6 ÷ 3/5 = 20/9

265:  8/6 ÷ 3/9 = 20/5

266:  8/6 ÷ 3/9 = 4/1

267:  8/6 ÷ 4/1 = 3/9

268:  8/6 ÷ 4/7 = 21/9

269:  8/6 ÷ 4/9 = 21/7

270:  8/6 ÷ 4/9 = 3/1

271:  9/1 ÷ 3/4 = 60/5

272:  9/1 ÷ 3/4 = 72/6

273:  9/1 ÷ 3/5 = 60/4

274:  9/1 ÷ 3/6 = 72/4

275:  9/1 ÷ 4/2 = 36/8

276:  9/1 ÷ 4/8 = 36/2

277:  9/1 ÷ 6/4 = 30/5

278:  9/1 ÷ 6/5 = 30/4

279:  9/1 ÷ 8/4 = 27/6

280:  9/1 ÷ 8/6 = 27/4

281:  9/2 ÷ 3/1 = 6/4

282:  9/2 ÷ 3/4 = 6/1

283:  9/2 ÷ 3/5 = 60/8

284:  9/2 ÷ 3/8 = 60/5

285:  9/2 ÷ 4/7 = 63/8

286:  9/2 ÷ 4/8 = 63/7

287:  9/2 ÷ 6/1 = 3/4

288:  9/2 ÷ 6/4 = 3/1

289:  9/2 ÷ 6/5 = 30/8

290:  9/2 ÷ 6/8 = 30/5

291:  9/3 ÷ 1/4 = 60/5

292:  9/3 ÷ 1/4 = 72/6

293:  9/3 ÷ 1/5 = 60/4

294:  9/3 ÷ 1/6 = 72/4

295:  9/3 ÷ 2/1 = 6/4

296:  9/3 ÷ 2/4 = 6/1

297:  9/3 ÷ 2/5 = 60/8

298:  9/3 ÷ 2/8 = 60/5

299:  9/3 ÷ 4/1 = 6/8

300:  9/3 ÷ 4/8 = 6/1

301:  9/3 ÷ 6/1 = 2/4

302:  9/3 ÷ 6/1 = 4/8

303:  9/3 ÷ 6/4 = 10/5

304:  9/3 ÷ 6/4 = 2/1

305:  9/3 ÷ 6/5 = 10/4

306:  9/3 ÷ 6/5 = 20/8

307:  9/3 ÷ 6/8 = 20/5

308:  9/3 ÷ 6/8 = 4/1

309:  9/4 ÷ 1/2 = 36/8

310:  9/4 ÷ 1/8 = 36/2

311:  9/4 ÷ 2/7 = 63/8

312:  9/4 ÷ 2/8 = 63/7

313:  9/4 ÷ 3/1 = 6/8

314:  9/4 ÷ 3/8 = 6/1

315:  9/4 ÷ 6/1 = 3/8

316:  9/4 ÷ 6/7 = 21/8

317:  9/4 ÷ 6/8 = 21/7

318:  9/4 ÷ 6/8 = 3/1

319:  9/6 ÷ 1/4 = 30/5

320:  9/6 ÷ 1/5 = 30/4

321:  9/6 ÷ 2/1 = 3/4

322:  9/6 ÷ 2/4 = 3/1

323:  9/6 ÷ 2/5 = 30/8

324:  9/6 ÷ 2/8 = 30/5

325:  9/6 ÷ 3/1 = 2/4

326:  9/6 ÷ 3/1 = 4/8

327:  9/6 ÷ 3/4 = 10/5

328:  9/6 ÷ 3/4 = 2/1

329:  9/6 ÷ 3/5 = 10/4

330:  9/6 ÷ 3/5 = 20/8

331:  9/6 ÷ 3/8 = 20/5

332:  9/6 ÷ 3/8 = 4/1

333:  9/6 ÷ 4/1 = 3/8

334:  9/6 ÷ 4/7 = 21/8

335:  9/6 ÷ 4/8 = 21/7

336:  9/6 ÷ 4/8 = 3/1

337:  9/8 ÷ 1/4 = 27/6

338:  9/8 ÷ 1/6 = 27/4

Source: Shaun Errichiello

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9 comments

  1. I think these are all the possibilities, listed here in form a/b divided by c/d, but where a and d can be switched and/or b and c can be switched:

    5/2 divided by 4/6 = 30/8
    5/2 divided by 3/8 = 40/6 [as above]
    7/2 divided by 4/9 = 63/8

  2. Would this a possible solution also? Or would it be invalid?

    9/3 divided by 1/6 equals 72/4

    • I think 9/3 divided by 1/6 would be 72/3. I think it might be cool to have a class of solutions like this, where there is 1 repeated digit. In this case, the 1.

    • 9/3 divided by 1/6 would actually be 54/3 so it wouldn’t work since the “3” is repeated.

      • “9/3 divided by 1/6 equals 72/4” was original query

        9/3 divided by 1/6 reduces to 54/3 hence 18
        72/4 reduces to 18

        Hence 18=18

        I suppose the question is of repeats in original equation or no repeats in all the equations as you simplify and reduce.

  3. My student found this solution:
    9/2 divided by 4/7 equals 63/8

  4. 5/4 divided by 2/6 = 30/8

    5/3 divided by 2/8 = 40/6

    7/2 divided by 4/9 = 63/8

    9/4 divided 2/7 = 63/8

  5. 5 / 2 divide 3/8 =40 / 6

  6. 6/4 divided by 2/5 equal 30/8

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