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## Ch. 10 Equalities and Inequalities

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**Ch. 10 Equalities and Inequalities**1.B.2.a Represent relationships using the appropriate relational symbols (>, < ,=) and one operational symbol (+,-, x, ÷ with no remainders) on either side 3.A.1.a Use technology tools, including software and hardware, from a range of teacher-selected options to learn new content or reinforce skills**Equalities**• An equality is a number sentence that says that two quantities are equal. For example: 60 x 2 = 40 x 3 60 x 2= 120 40 x 3 =120 Both sides are equal so it is an equality.**Equalities**Example 1: 322 - 63 = 279 – 20 322 279 - 63 - 20 259 259 Both sides are equal so it is an equality**Inequalities**An inequality is a number sentence that says that two quantities are NOT the same. For example: 250 + 13 317 - 42 Which symbol makes this sentence true? >, <, or =**Inequalities**Example: 36 x 9 216 + 79 Which symbol makes this sentence true? <, >, or = 36 216 x 9 + 79 324 295**Inequalities**250 + 13 317 - 42 250 317 + 13 - 42 263 275 250 + 13 < 317 - 42**Problem Solving with Equalities and Inequalities**• Read each word problem carefully. • Write an equation for each situation in the problem. • Calculate each side of the number sentence. • Use symbols to make the sentence true.**Problem Solving with Equalities and Inequalities**• On Mercury the temperatures are extremely hot! On Wednesday the low temperature was 323˚F and the high temperature was 358˚F. The next day the low temperature was 331˚F and the high temperature was 364˚F. Write an equality or inequality to represent the relationship between the differences in temperatures on both days.**Problem Solving with Equalities and Inequalities**• Wednesday High 358˚F Low 323˚F • Thursday High 364˚F Low 331˚F Write a sentence to show the difference in the high and low temperatures for Wednesday and then for Thursday.**Problem Solving with Equalities and Inequalities**• Wednesday High 358˚F Low 323˚F • Thursday High 364˚F Low 331˚F High temperatures - low temperatures to find the difference in temperatures. Wednesday Thursday 358 – 323 364-331**Problem Solving with Equalities and Inequalities**High temperatures - low temperatures to find the difference in temperatures. Wednesday Thursday 358 – 323 364-331 358 – 323 364 - 331**Problem Solving with Equalities and Inequalities**Solve for each side to determine the correct symbol to use to make the number sentence correct. 358 - 323 364 - 331 358 364 - 323 - 331 35 33**Problem Solving with Equalities and Inequalities**Solve for each side to determine the correct symbol to use to make the number sentence correct. 358 – 323 364 – 331 35 33**9**Which symbol would make the following sentence true?81 - 9 351 ÷ 9 • < • > • = • +**Which sign is missing in the following statement?340 19**> 189 + 53 8 • < • > • − • x**Which symbol would make the following sentence true?12 x**12 4 x 36 7 • < • > • = • +**Which operational symbol is missing in the following**equality?225 = 75 3 6 • x • − • ÷ • +**Which statement represents the following situation?18 times**some number is less than 226 5 • 18 x n < 226 • 18 x n > 226 • 18n > 226 • 226 + n = 18**Two sisters bought some trading cards. Kiara bought 4 packs**that contained 25 cards in each pack. Kelsy bought 12 packs of cards with 12 cards in each pack. Which equality or inequality represents this situation? 4 • 25 x 4 = 12 x 12 • 25 x 4 < 12 x 12 • 25 x 4 > 12 x 12**3**Lucus weighed 264 pounds and lost 18 during his first week of getting into shape. Tavone weighed 208 pounds at the beginning of the week and 216 and the end of the week. Which inequality represents the relationship between their current weights. • 264 +208 > 18 + 216 • 264 – 18 < 216 -208 • 264 + 18 > 208 + 8 • 264 – 18 > 208 + 8**Delmar Elementary collected cans for a local charity. The**4th grade collected 7 boxes with 36 cans in each box. The 5th grade collected 9 boxes with 28 cans in each box. Which equality or inequality represents the relationship between the amount of cans collected by the 4th and the 5th grade? 2 • 7 x 36 < 9 x 28 • 7 x 36 > 9 x 28 • 7 x 36 = 9 x 28**1**Andrew earned $15 an hour for cutting grass. He worked h hours and made a total of more than $115. Which number sentence represents this situation. • h x $15 >$115 • $115 – h > $15 • h x $15 < $115 • $115 – h < $15**James worked 36 hours this week and made $288. Mike worked**30 hours this week and made $270. Which inequality represents the relationship between the amount of money James and Mike made per hour? 0 • 36 ÷ 288 > 30 ÷ 270 • 288÷36 < 270 ÷ 30 • 250 x 25 < 168 x 4 • 250 ÷ 25 < 168 ÷ 14