unit 7 rational explorations: numbers & their opposites

UNIT 7

Rational Explorations: Numbers & their Opposites

Review

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20

#1

What does the absolute value of a number tell you about the number?

#1 Answer

The absolute value of a number tells you the distance the number is from zero on the number line.

#2

Describe how to use a number line to order integers

#2 Answer

When numbers are graphed on a number line, the numbers can be read from left to right to order them from least to greatest.

#3 Evaluate:

a)

b)

c)

7

4

15

# 3 AnswerEvaluate:

a) = 7

b) = 4

c) = -15

7

4

15

#4Plot and label the following points on

the coordinate plane.A: (6, 0), B: (0, -5),C: (4, 3), D: (-3, -2),E: (5, -4), F: (5, 2)

#4 AnswerA: (6, 0)

B: (0, -5)

C: (4, 3)

D: (-3, 2)

E: (5, -4)

F: (5, 2)

#5

Plot 7 and its opposite on a number line. Label both numbers.

0 1-1

#5 Answer

Plot 7 and its opposite on a number line. Label both numbers.

0 1-1

#6

Order from least to greatest.

10, -4, -8, 6, 0, -2, 5

#6 Answer

Order from least to greatest.

10, -4, -8, 6, 0, -2, 5

-8, -4, -2, 0, 5, 6, 10

#7

Connie is on a mountain at 17, 465 feet above sea level. How many more feet must she walk down the mountain to reach sea level if she has descended 2, 580 feet?

#7 Answer

Connie is on a mountain at 17,465 feet above sea level. How many more feet must she walk down the mountain to reach sea level if she has descended 2,580 feet?

17,465 – 2,580 = 14,885 ft

#8 The table shows the average daily temperature

in December for 5 cities in Canada. Write an inequality statement comparing the temperature of Toronto and Edmonton.

City Temperature ( C)⁰

Vancouver, BC 0°

Edmonton, AB -19°

Yellowknife, NWT -31°

Toronto, ON -10°

Winnepeg, MB -23°

#8 AnswerThe table shows the average daily temperature in

December for 5 cities in Canada. Write an inequality statement comparing the temperature of Toronto and Edmonton.

-10 > -19City Temperature ( C)⁰

Vancouver, BC 0°

Edmonton, AB -19°

Yellowknife, NWT -31°

Toronto, ON -10°

Winnepeg, MB -23°

#9 Graph point A (-6, 4) on the coordinate

plane. Reflect the point across the X-axis. What is the distance between

point A and the reflected point? Justify your answer with an equation.

#9 AnswerGraph point A (-6, 4) on the coordinate plane. Reflect

the point across the X-axis. What is the distance between point A and the reflected point? Justify your answer with an equation.

#10 Graph (-7, 6) and (-7, -3) on the coordinate

plane. Reflect both points across the y-axis to form the vertices of a rectangle. Name the two reflected ordered pairs. What is the perimeter of the rectangle? What is the area of the rectangle?

#10 AnswerGraph (-7, 6) and (-7, -3) on the coordinate plane. Reflect

both points across the y-axis to form the vertices of a rectangle. Name the two reflected ordered pairs. What is the perimeter of the rectangle? What is the area of the rectangle?

#11 How far is the library from the school? Write an expression to show your answer.

#11 Answer

How far is the library from the school? Write an expression to show your answer.

#12

If you reflected the ordered pair

(-8, 7) across the y-axis, what would be the coordinates of the reflection?

#12 AnswerIf you reflected the ordered pair (-8, 7) across the

y-axis, what would be the coordinates of the reflection?

(8,7)

#13

If you reflected the ordered pair

(-5, -3) across the x-axis, what would be the coordinates of the reflection?

#13 Answer

If you reflected the ordered pair (-5, -3) across the x-axis, what would be the coordinates of the reflection?

(-5, 3)

#14

Which statement is NOT true?

a) -3 > -8

b) -4 < -2

c)

d) -10 > -12

5 5

#14 AnswerWhich statement is NOT true?

a) -3 > -8

b) -4 < -2

c)

d) -10 > -12

5 5

#15 It is 85 degrees in Los Angeles. It is 13

degrees below zero in Anchorage. How many degrees warmer is it in Los Angeles than in Anchorage?

#15 Answer

It is 85 degrees in Los Angeles. It is 13 degrees below zero in Anchorage. How many degrees warmer is it in Los Angeles than in Anchorage?

98 degrees warmer

#16

Tigger is jumping around the number line. He starts at -4 and jumps 10 spaces to the right. Where is he now on the number line?

0 1-1

#16 Answer

Tigger is jumping around the number line. He starts at -4 and jumps 10 spaces to the right. Where is he now on the number line?

6

0 1-1

#17 Cara owes $7 to her mom for a game

she bought at the store. Represent this value on the number line. Ethan owes $4 to his mom for a book he bought. Represent this number on the number line. How much more does Cara owe than Ethan? Explain how you could use the number line to determine your answer.

0 1-1

#17 Answer

Cara owes $7 to her mom for a game she bought at the store. Represent this value on the number line. Ethan owes $4 to his mom for a book he bought. Represent this number on the number line. How much more does Cara owe than Ethan? Explain how you could use the number line to determine your answer.

0 1-1