1. Integers and the Number Line

2. Natural Numbers
1, 2, 3, 4, 5, ...

3. Natural Numbers
1, 2, 3, 4, 5, ...

4. Natural Numbers
1, 2, 3, 4, 5, ...
Whole Numbers
0, 1, 2, 3, 4, 5, ...

5. Natural Numbers
1, 2, 3, 4, 5, ...
Whole Numbers
0, 1, 2, 3, 4, 5, ...

6. For the number 1 there will be an opposite number

7. For the number 1 there will be an opposite number

8. For the number 1 there will be an opposite number -1.

9. For the number 1 there will be an opposite number -1.

10. For the number 1 there will be an opposite number -1.

11. For the number 1 there will be an opposite number -1.

12. For the number 1 there will be an opposite number -1.

13. For the number 1 there will be an opposite number -1.

14. For the number 1 there will be an opposite number -1.

15. Natural Numbers
1, 2, 3, 4, 5, 6, ...
Whole numbers
0, 1, 2, 3, 4, 5, 6, ...

16. Natural Numbers
1, 2, 3, 4, 5, 6, ...
Whole numbers
0, 1, 2, 3, 4, 5, 6, ...
Integers
... -4, -3, -2, -1, 0, 1, 2, 3, 4, ...

17. EXAMPLE Tell which integer corresponds to this situation:
The temperature is 4 degrees below zero.

18. The integer -4 corresponds to the situation.
EXAMPLE Tell which integer corresponds to this situation:
The temperature is 4 degrees below zero.
The integer -4 corresponds to the situation.

19. The integer -4 corresponds to the situation. The temperature is -4
EXAMPLE Tell which integer corresponds to this situation:
The temperature is 4 degrees below zero.
The integer -4 corresponds to the situation.
The temperature is -4

20. EXAMPLE Tell which integer corresponds to this situation:
A contestant missed a $600 question on the television game show “Jeopardy.”

21. EXAMPLE Tell which integer corresponds to this situation:
A contestant missed a $600 question on the television game show “Jeopardy.”

22. EXAMPLE Tell which integer corresponds to this situation:
A contestant missed a $600 question on the television game show “Jeopardy.”

23. EXAMPLE Tell which integer corresponds to this situation:
A contestant missed a $600 question on the television game show “Jeopardy.”

24. EXAMPLE Tell which integer corresponds to this situation:
The shores of California’s largest lake, the Salton Sea are 227 feet below sea level.

25. EXAMPLE Tell which integer corresponds to this situation:
The shores of California’s largest lake, the Salton Sea are 227 feet below sea level.

26. EXAMPLE Tell which integer corresponds to this situation:
The shores of California’s largest lake, the Salton Sea are 227 feet below sea level.

27. EXAMPLE Tell which integer corresponds to this situation:
The shores of California’s largest lake, the Salton Sea are 227 feet below sea level.
The integer -227 corresponds to the situation.
The elevation is -227 feet.

28. Example 4 Stock Price Change.
Tell which integers correspond to this situation:
Hal owns a stock whose price decreased $16 per share over a recent period.

29. Example 4 Stock Price Change.
Tell which integers correspond to this situation:
Hal owns a stock whose price decreased $16 per share over a recent period.
The integer – 16 corresponds to the decrease in the stock value.

30. Example 4 Stock Price Change.
Tell which integers correspond to this situation:
Hal owns another stock whose price increases $2 per share over the same period.

31. Example 4 Stock Price Change.
Tell which integers correspond to this situation:
Hal owns another stock whose price increases $2 per share over the same period.
The integer 2 corresponds to the increase in the stock value.

32. We created the set of integers by obtaining a negative number for each natural number and also including 0. -5 5

33. To create a larger number system, called the set of rational numbers, we consider quotients of integers with
nonzero divisors.

34. The following are some examples of rational numbers:

35. The following are some examples of rational numbers:

36. The following are some examples of rational numbers:

37. The following are some examples of rational numbers:

38. The following are some examples of rational numbers:

39. The following are some examples of rational numbers:

40. The following are some examples of rational numbers:

41. The following are some examples of rational numbers:

42. The following are some examples of rational numbers:

43. The following are some examples of rational numbers:

44. The number

45. The number
(read “negative two-thirds”) can also be named

46. The number
(read “negative two-thirds”) can also be named

47. The number
(read “negative two-thirds”) can also be named

48. The number
(read “negative two-thirds”) can also be named

49. That is

50. That is

51. That is

52. That is

88. That is

89. The set of rational numbers is the set of numbers
Where a and b are integers and b is not equal to 0.

90. The set of rational numbers contains the whole numbers, the integers, the positive and negative fractions.

91. The set of rational numbers contains the whole numbers, the integers, the positive and negative fractions.

92. The set of rational numbers contains the whole numbers, the integers, the positive and negative fractions.

93. The set of rational numbers contains the whole numbers, the integers, the positive and negative fractions.

94. We picture the rational numbers on a number line as follows:-5 5

95. We picture the rational numbers on a number line as follows:-5
-2.7 5

96. We picture the rational numbers on a number line as follows:-5
-2.7 5

97. We picture the rational numbers on a number line as follows:-5
-2.7 5

98. We picture the rational numbers on a number line as follows:-5
-2.7 5

99. We picture the rational numbers on a number line as follows:
1.5 -5
-2.7 5

100. We picture the rational numbers on a number line as follows:
1.5 -5
-2.7 5

101. We picture the rational numbers on a number line as follows:
1.5 -5
-2.7 5 4

102. We picture the rational numbers on a number line as follows:
1.5 -5
-2.7 5 4

103. Graph -5 5

104. Graph -5 5

105. Graph -5 5

106. Graph -5 5

107. Graph -5 5

108. Graph -5 5

109. Graph -5 5

110. Graph -5 5

111. Graph -5 5

112. Convert to decimal notation

113. Divide

114. Divide

115. Divide

116. Divide

117. Divide

118. Divide

119. Divide

120. Divide

121. Divide

122. Divide

123. Divide

124. Divide

125. Divide

126. Convert to decimal notation

127. Convert to decimal notation

128. Divide

129. Divide

130. Divide

131. Divide

132. Divide

133. Divide

134. Divide

135. Divide

136. Divide

137. Divide

138. Divide

139. Divide

140. Divide

141. Divide

142. Divide

143. Each rational number can be expressed in either terminating or repeating decimal notation.

144. The following are other examples to show how each rational number can be named using fraction

145. The following are other examples to show how each rational number can be named using fraction or decimal notation:

146. The following are other examples to show how each rational number can be named using fraction or decimal notation:

147. The following are other examples to show how each rational number can be named using fraction or decimal notation:

148. The following are other examples to show how each rational number can be named using fraction or decimal notation:

149. The following are other examples to show how each rational number can be named using fraction or decimal notation:

150. The following are other examples to show how each rational number can be named using fraction or decimal notation:

151. The following are other examples to show how each rational number can be named using fraction or decimal notation:

152. The following are other examples to show how each rational number can be named using fraction or decimal notation:

153. The following are other examples to show how each rational number can be named using fraction or decimal notation:

154. Each rational number has a point on the number line.

155. Each rational number has a point on the number line
Each rational number has a point on the number line. However, there are some points on the line for which there are no rational numbers.

156. Each rational number has a point on the number line
Each rational number has a point on the number line. However, there are some points on the line for which there are no rational numbers. These points correspond to what are called

157. Each rational number has a point on the number line
Each rational number has a point on the number line. However, there are some points on the line for which there are no rational numbers. These points correspond to what are called irrational numbers.

158. What kinds of number are irrational?

159. What kinds of number are irrational? One example is the number pi,

160. What kinds of number are irrational
What kinds of number are irrational? One example is the number pi, which is used in finding the area and the circumference of a circle:

161. What kinds of number are irrational
What kinds of number are irrational? One example is the number pi, which is used in finding the area and the circumference of a circle:

162. What kinds of number are irrational
What kinds of number are irrational? One example is the number pi, which is used in finding the area and the circumference of a circle:

163. Another example of an irrational number is the square root of 2,

164. Another example of an irrational number is the square root of 2, named

165. It is the length of the diagonal of a square with sides of length l.

166. It is the length of the diagonal of a square with sides of length l.

167. It is the length of the diagonal of a square with sides of length l.1

168. It is the length of the diagonal of a square with sides of length l.1 1

169. It is the length of the diagonal of a square with sides of length l.1 1

170. It is the length of the diagonal of a square with sides of length l.1 1

171. It is the length of the diagonal of a square with sides of length l.1 1

172. It is the length of the diagonal of a square with sides of length l.1 1

173. It is the length of the diagonal of a square with sides of length l.1 1

174. It is the length of the diagonal of a square with sides of length l.1 1

175. It is the length of the diagonal of a square with sides of length l.1 1

176. It is the length of the diagonal of a square with sides of length l.1 1

177. It is the length of the diagonal of a square with sides of length l.1 1

178. It is the length of the diagonal of a square with sides of length l.1 1

179. It is also the number that when multiplied by itself gives 2—that is

180. It is also the number that when multiplied by itself gives 2—that is

181. It is also the number that when multiplied by itself gives 2—that is

182. It is also the number that when multiplied by itself gives 2—that is

183. 1.4 is an approximation of

184. 1.4 is an approximation of
because (1.4)2 = 1.96

185. 1.4 is an approximation of
because (1.4)2 = 1.96
1.41 is a better approximation of

186. 1.4 is an approximation of
because (1.4)2 = 1.96
1.41 is a better approximation of
because (1.41)2 =

187. 1.4 is an approximation of
because (1.4)2 = 1.96
1.41 is a better approximation of
because (1.41)2 =
1.414 is a better approximation of

188. 1.4 is an approximation of
because (1.4)2 = 1.96
1.41 is a better approximation of
because (1.41)2 =
1.414 is a better approximation of
because (1.414)2 =

189. Decimal notation for rational numbers either

190. Decimal notation for rational numbers either terminates

191. Decimal notation for rational numbers either terminates or repeats.

192. Decimal notation for rational numbers either terminates or repeats.
Decimal notation for irrational numbers neither terminates

193. Decimal notation for rational numbers either terminates or repeats.
Decimal notation for irrational numbers neither terminates nor repeats.

194. Some other examples of irrational numbers are

195. Some other examples of irrational numbers are

196. Some other examples of irrational numbers are

197. Some other examples of irrational numbers are

198. Some other examples of irrational numbers are…

199. The rational numbers and the irrational numbers together correspond to all the points on a number line and make up what is called the real-number system.

200. The set of Real Numbers —The set of all numbers corresponding to points on the number line.

209. Real numbers are named in order on the number line,-5 5

210. Real numbers are named in order on the number line, with larger numbers named farther to the right.-5 5

211. Real numbers are named in order on the number line, with larger numbers named farther to the right.-5 5

212. Real numbers are named in order on the number line, with larger numbers named farther to the right.-5 5

213. Real numbers are named in order on the number line, with larger numbers named farther to the right.-5 5

214. Real numbers are named in order on the number line, with larger numbers named farther to the right.-5 5

215. For any two numbers on the line, the one to the left is-5 5

216. For any two numbers on the line, the one to the left is less than the one to the right.-5 5

218. We use the symbol < to mean “is less than.”

219. We use the symbol < to mean “is less than.” The sentence -8<6

220. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”

221. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”

222. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”
The symbol >

223. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”
The symbol > means “is greater than.”

224. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”
The symbol > means “is greater than.”
then sentences -8<6

225. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”
The symbol > means “is greater than.”
then sentences -8<6 and -3>-7

226. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”
The symbol > means “is greater than.”
then sentences -8<6 and -3>-7 are inequalities.

227. We use the symbol < to mean “is less than
We use the symbol < to mean “is less than.” The sentence -8<6 means “-8 is less than 6”
The symbol > means “is greater than.”
then sentences -8<6 and -3>-7 are inequalities.

228. 5 10

229. 5 10

230. 5 10 2

231. 5 10 2 9

232. 5 10 2 9

233. 5 10 2 9

234. 5 10 2 9

235. 5 10 2 9

238. -7

239. -7 3

240. -7 3

241. -7 3

242. -7 3

243. -7 3

246. 6

247. -12 6

248. -12 6

249. -12 6

250. -12 6

251. -12 6

254. -18

255. -18 -5

256. -18 -5

257. -18 -5

258. -18 -5

259. -18 -5

260. -5 5

261. -5 5

262. -5 5

263. -5 5

264. -5 5

265. -5 5

266. -5 5

267. -5 5

268. -5 5

269. -5 5

270. -5 5

271. -5 5

272. -5 5

273. -5 5

274. -5 5

275. -5 5

284. -5 5

285. -5 5

286. -5 5

287. -5 5

288. -5 5

289. -5 5

290. -5 5

291. -5 5

292. -5 5

293. -5 5

294. -5 5

295. -5 5

296. -5 5

297. -5 5

298. -5 5

299. -5 5

300. -3 5

301. -3 5

302. -3 5

303. -3 5

304. 5

305. -3 5

306. -3 5

307. -3 5

308. -3 5

309. -3 5

310. -3 5

311. -3 5

312. -3 5

313. -3 5

314. -3 5

315. -3 5

340. Write another inequality with the same meaning.

341. Write another inequality with the same meaning.

342. Write another inequality with the same meaning.

343. Write another inequality with the same meaning.

344. Write another inequality with the same meaning.

345. Write another inequality with the same meaning.

346. Write another inequality with the same meaning.

347. Write another inequality with the same meaning.

348. Write another inequality with the same meaning.

349. Write another inequality with the same meaning.

350. Write another inequality with the same meaning.

351. Write another inequality with the same meaning.

352. Write another inequality with the same meaning.

353. Write another inequality with the same meaning.

354. Write another inequality with the same meaning.

355. Write another inequality with the same meaning.

356. Write another inequality with the same meaning.

357. Write another inequality with the same meaning.

358. Write another inequality with the same meaning.

359. Write another inequality with the same meaning.

360. Write another inequality with the same meaning.

361. If b is a positive real number then

362. If b is a positive real number then

363. If b is a positive real number then

364. If b is a positive real number then

365. If a is a negative real number then

366. If a is a negative real number then

367. If a is a negative real number then

368. If a is a negative real number then

369. -4 5

370. -4 5

371. -4 5

372. -4 5

373. -4 5

374. -4 5

375. -4 5

381. -5 5

382. -5 5

383. -5 5

384. -5 5

385. -5 5

386. -5 5

387. -5 5

389. Find the absolute value.

390. Find the absolute value..

391. Find the absolute value.

392. Find the absolute value.

393. Find the absolute value.

394. Find the absolute value.

395. Find the absolute value..

396. Find the absolute value.

397. Find the absolute value.

398. Find the absolute value.

399. L 1.2 Numbers