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.

EqualitiesExample 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 =

InequalitiesExample:

36 x 9 216 + 79

36 216 x 9 + 79 324 295

Which symbol makes this sentence true? <, >, or =

Inequalities

250 + 13 < 317 - 42

250 + 13 317 - 42

250 317 + 13 - 42 263 275

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

Let’s Practice!10

Which symbol would make the following sentence true? 81 - 9 351 ÷ 9

9

1 2 3 4 5

0% 0%0%0%

a. <b. >c. =d. +

1 2 3 4 5

8Which sign is missing in the following statement? 340 19 > 189 + 53

0% 0%0%0%

a. <b. >c. −d. x

1 2 3 4 5

7Which symbol would make the following sentence true? 12 x 12 4 x 36

0% 0%0%0%

a. <b. >c. =d. +

Which operational symbol is missing in the following equality? 225 = 75 3

1 2 3 4 5

6

0% 0%0%0%

a. xb. −c. ÷d. +

Which statement represents the following situation?

18 times some number is less than 226

1 2 3 4 5

5

0% 0%0%0%

a. 18 x n < 226b. 18 x n > 226c. 18n > 226d. 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?

1 2 3 4 5

4

25 x

4 =

12

x 12

25 x

4 >

12

x 12

25 x

4 <

12

x 12

0% 0%0%

a. 25 x 4 = 12 x 12b. 25 x 4 < 12 x 12c. 25 x 4 > 12 x 12

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.

1 2 3 4 5

3

0% 0%0%0%

a. 264 +208 > 18 + 216b. 264 – 18 < 216 -208c. 264 + 18 > 208 + 8d. 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?

1 2 3 4 5

2

0% 0%0%

a. 7 x 36 < 9 x 28b. 7 x 36 > 9 x 28c. 7 x 36 = 9 x 28

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.

1 2 3 4 5

1

0% 0%0%0%

a. h x $15 >$115b. $115 – h > $15c. h x $15 < $115d. $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?

1 2 3 4 5

0

0% 0%0%0%

a. 36 ÷ 288 > 30 ÷ 270b. 288÷36 < 270 ÷ 30c. 250 x 25 < 168 x 4d. 250 ÷ 25 < 168 ÷ 14