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1.5 Day 2 Distance Between Two Rational Numbers

Total questions: 92

Worksheet time: 2hrs 7mins

Name
Class
Date
1.

Imagine you are a superhero who can see numbers in a unique way. You have the power to arrange them from the largest to the smallest. Can you do it with these numbers?

a)

20, 6, -2, -13

b)

-2, 6, -13, 20

c)

-13, -2, 6, 20

d)

20, -13, 6, -2

2.

Let's play a game! Can you tell me if the absolute value is always positive and give me a reason why?

a)

Yes, it's always positive because it's like measuring distance, and distance can't be negative!

b)

No, sometimes it can be negative because we deal with negative numbers too.

c)

Yes, it's always positive because all real numbers have to be positive, right?

d)

No, nothing in this world is absolute, so why should absolute value be?

3.

Imagine you're on a number line adventure and you stumble upon -18. Can you tell us its absolute value?

a)

18

b)

-18

c)

36

d)

-36

4.

Let's play a fun game! Can you solve this puzzle?

What's the value of I 5 I ?

a)

5

b)

-5

5.

Imagine you are a super cool mathematician and you have to solve this: -17 + (-3). What's your answer?

a)

-20

b)

-14

c)

14

d)

20

6.

Can you spot the smallest integer from the following options? It's a fun challenge!

a)

1

b)

-1

c)

-2

d)

-8

7.

Let's play a fun math game! Can you solve this?
What is the sum of the absolute value of -5 and 8?

a)

3

b)

13

c)

-13

d)

-3

8.

Can you arrange these numbers from the smallest to the largest? Give it a try, it's fun!

a)

− 9, -5, -3, 0, 4, 3

b)

− 9, -5, -3, 0,  3, 4

c)

− 5, -9, -3, 0, 4, 3

d)

 3, 4, 0, -3, -5, -9

9.

Let's play a game of numbers! Can you figure out the result of this expression?
|–15 + 11|

a)

26

b)

4

c)

-4

d)

-26

10.

Why do you think the absolute value always shows up as a positive number? Is it because...

a)

Absolute value is a chatterbox about numbers, so it just has to be positive!

b)

Absolute value is a rebel, it doesn't always have to be positive.

c)

Absolute value is like a clock, always ticking forward with positive numbers.

d)

Absolute value is like a marathon runner, always measuring distance in positive strides.

11.

Imagine you're a mathematician exploring the world of numbers. Can you tell me the absolute value of |-37|?

a)

0

b)

37

c)

-37

d)

30

12.

Imagine you have 7 apples and you gave 14 apples to your friend. How many apples do you have now?

a)

7 apples

b)

21 apples

c)

-21 apples

d)

-7 apples

13.

Let's play a fun game of comparing numbers! Can you tell me which symbol fits best between these two numbers?
<  >   =
What about | -4 | and 4? Which one is correct?

a)

<

b)

>

c)

=

14.

Let's play a fun game with numbers and symbols! Can you tell which symbol fits best between -5 and -7? Remember, your options are:
<  >   =

a)

<

b)

>

c)

=

15.

Imagine you are a math wizard and you have to solve this magical equation: |6| + |-3|. What's the result?

a)

3

b)

-3

c)

-9

d)

9

16.

Imagine you are a super mathematician in a parallel universe. You have -2 apples and suddenly a wormhole opens and throws out -10 apples. How many apples do you have now?

a)

8 apples

b)

-8 apples

c)

12 apples

d)

-12 apples

17.

Let's play a game of numbers! Can you tell me what you get when you take the absolute value of 24 and then make it negative?

a)

-24

b)

24

c)

98

d)

11

18.

Imagine you are a super mathematician. You have a magical equation in front of you: | 5 - 7 | = _____. Can you solve it?

a)

2

b)

-2

c)

12

d)

-12

19.

Let's play a fun game! Can you arrange these numbers from the smallest to the biggest?

-2, I8I, 5, I-10I, 6

a)

-2, I8I, 5, I-10I, 6

b)

-2, 5, 6, I8I, I-10I

c)

-10, -2, 5, 6, 8

d)

I-10I, -2, 5, 6. I8I

20.

Imagine you're a math wizard! Can you solve this magical equation: |3| + |-2| = _____?

a)

1

b)

5

c)

-1

d)

-5

21.
Integers are
a)
all positive numbers only.
b)
all negative numbers only.
c)
all counting numbers and their opposites
d)
percentages, fractions, & square root.
22.
Express an integer: a debt of $50
a)
50
b)
-50
c)
+50
23.
Express as an integer:  at sea level
a)
0
b)
-0
c)
1
d)
-10
24.
Order from least to greatest:
[10, -5, 3, 16, -1, 0, 1]
a)
-1, -5, 0, 1, 3, 10, 16
b)
16, 10, 3, 1, 0, -1, -5
c)
-5, -1, 0, 1, 3, 10, 16
d)
0, -1, 1, 3, -5, 10, 16
25.

-8 ____ -9

a)

<

b)

>

c)

=

26.

Which set of numbers is in order from least to greatest?

a)

17, 10, 8, 6, 2, -4, -9

b)

-9, -4, 2, 6, 8, 10, 17

c)

neither

d)

both

27.

Choose ALL correct statements about the integers -7 and 7.

a)

they are opposites

b)

they are equal

c)

they have nothing in common

d)

they have the same absolute value

28.

Zero...

a)

has an absolute value of zero

b)

is its own opposite

c)

is not positive or negative

d)

all of the above are correct

29.

Which integer has the GREATEST value?

a)
-33
b)
-31
c)
-28
d)
-17
30.
What is the reason that absolute value is always written as a positive?
a)
Absolute value is talking about numbers so it must be positive.
b)
Absolute value does not always have to be positive.
c)
Absolute value is like a clock it has only positive numbers.
d)
Absolute value is talking about distance, distance is always measured by positive numbers.
31.
What is the absolute value of |-26|.
a)
26
b)
-26
c)
0
d)
-20
32.
Compare: -3 ___ -5
a)
-3 > -5
b)
-3 = -5
c)
-3 < -5
33.

You owe $20

a)
Positive
b)
Negative
c)
Zero
34.
The shark swam 50 feet below sea level
a)
Positive
b)
Negative
c)
Zero
35.
Opposite of 142
a)
-142
b)
142
c)
+142
36.
Which integer represents a gain of 10 yards on a football play?
a)
+10
b)
-10
37.

True or False: The value of Negative numbers are larger the closer they are to zero.

a)

True

b)

False

38.
Britney deposits $450 into her checking account. 
a)
$450 
b)
-$450
c)
$0
39.

The Eagles lose 20 yards during the first quarter.

a)

20 yards

b)

-20 yards

c)

0

40.
The elevator takes Whitney 4 floors below ground level. 
a)
4
b)
-4
c)
0
41.
Pearlie made a withdraw of $100 from her checking account. 
a)
$100
b)
-$100
c)
0
42.
Boston has a temperature of -20 degrees. It is colder in New York than in Boston. Select the value that could represent the temperature of New York
a)
0
b)
30
c)
-30
d)
-19
43.

What is the OPPOSITE  of −10?

a)

10

b)

0

c)

−110-\frac{1}{10}

d)

110\frac{1}{10}

44.
Which situation could the integer -50 represent?
a)
An increase of $50 in a bank account
b)
The temperature on a warm spring day
c)
The distance driven on the way to the beach
d)
A decrease of 50 employees
45.
Evaluate the following expression:
I -7 I
a)
-7
b)
7
c)
3
d)
0
46.
-5  _____  0
a)
<
b)
>
c)
=
47.
Is the absolute value the same for both of the following numbers?
I 7 I   and I -7 I
a)
yes they both have an absolute value of 7
b)
yes, they both have an absolute value of -7
c)
no 
48.

What is the opposite of l 5 l ?

a)

5

b)

-5

c)

0

d)

1/5

49.

What is the opposite of l -12 l ?

(a)  

50.

What is the opposite of l -9 l ?

a)

9

b)

-9

c)

1/9

d)

-1/9

51.

The table shows the heights of four students are rock climbing. The positive numbers represent locations ABOVE sea level and the negative numbers represent locations BELOW sea level. Which student is FARTHEST from sea level?

a)

Allie

b)

Derek

c)

Lydia

d)

Christopher

52.

What number is in the box?

a)

3

b)

-3

c)

-2

d)

0

53.

Name point A on the number line.

a)

7

b)

-9

c)

-7

d)

Not sure

54.

Which letter on the number line represents -1?

a)

A

b)

B

c)

C

d)

D

55.
Compare: -12 ____ -2
a)
-12 < -2
b)
-12 > -2
c)
-12 = -2
56.

Which location correctly shows the rational number shown (-4.5)?

a)

A

b)

B

c)

C

d)

D

57.

A scuba diver is 9.5 meters below sea level. Which letter correctly shows the scuba diver's location?

a)

A

b)

B

c)

C

d)

D

58.
Alaska is -3 degrees, Iowa is 5 degrees, Idaho is -7 degrees, New York is 9 degrees, and Maine is -1. Which state has the coldest temperature?
a)
Alaska
b)
Iowa
c)
Maine
d)
Idaho
59.
Which of the marks would represent 7.8 correctly?
a)
Blue
b)
Green
c)
Red
d)
Orange
60.

Order from least to greatest:


2.3, 0, 2.14, -1.5, -1.32

a)

0, -1.5, -1.32, 2.3, 2.14

b)

-1.32, -1.5, 0, 2.3, 2.14

c)

-1.5, -1.32, 0, 2.14, 2.3

d)

2.3, 2.14, 0, -1.32, -1.5

61.

Client #1 has a checking account balance of -$82. Client #2 has a checking account balance of -$79. Which client has a greater debt? Also, choose the explanation that goes with your answer.

a)

Client 2

b)

Client 1

c)

-79 has an absolute value of 79 because it is 79 units from zero on the number line. Therefore the debt of Client 2 is greater than the debt of Client 1. |-79| > |-82|

d)

-82 has an absolute value of 82 because it is 82 units from zero on the number line. Therefore the debt of Client 1 is greater than the debt of Client 2. |-82| > |-79|

62.
2 - 4
a)
2
b)
-8
c)
6
d)
-2
63.
-5 - (- 3)
a)
-8
b)
8
c)
-2
d)
15
64.
6 - (-4)
a)
10
b)
2
c)
-2
d)
-10
65.
-18 +(-6)
a)
3
b)
-3
c)
-12
d)
-24
66.
-2 + (-8)
a)
-6
b)
6
c)
-10
d)
10
67.
-9 - 5
a)
-14
b)
4
c)
-4
d)
45
68.
-3 +(- 2)
a)
-1
b)
5
c)
-5
d)
-6
69.
-4 - 2
a)
6
b)
-2
c)
-8
d)
-6
70.
8 - (-5)
a)
1
b)
-15
c)
13
d)
15
71.
12 - (-12)
a)
24
b)
-24
c)
0
d)
-144
72.
-8 - (-6)
a)
2
b)
14
c)
-2
d)
-14
73.
(-4)(-5)
a)
-9
b)
-20
c)
9
d)
20
74.
3 - (-8)
a)
11
b)
-11
c)
5
d)
-5
75.
-32/8
a)
-4
b)
-5
c)
4
d)
24
76.
-2 + (-5)
a)
-3
b)
3
c)
-7
d)
7
77.

Which integer represents a $25 gain?

a)

− $25

b)

$25

78.

Which integer represents a $75 loss?

a)

− $75

b)

$75

79.

Which situation can be represented by -16? (You must choose ALL correct answers.)

a)

A fish jumps 16 inches out of the water.

b)

A player loses 16 yards in a football game.

c)

A depth of 16 feet below sea level.

d)

An elevator is on the 16th floor.

80.

Which situation is NOT represented by -35?

a)

A fish swims 35 feet below sea level.

b)

Losing 35 points in a game.

c)

35 degrees on the thermometer.

d)

Descending 35 flights of stairs.

81.

Which number is an integer?

a)

0

b)

3.5

c)

-6.8

d)

53\frac{5}{3}  

82.

Identify each true answer. (You must choose ALL correct answers)

a)

-15 < -30

b)

-15 > -30

c)

-20 > -1

d)

-20 < -1

83.

Identify all integers less than -10. (You must choose ALL correct answers.)

a)

-9

b)

-5

c)

-15

d)

-22

e)

8

84.

Put the integers in ascending order (least to greatest)

a)

-5

b)

-4

c)

-3

d)

-2

e)

-1

1)
2)
3)
4)
5)
85.

Which set of integers is in ascending order (least to greatest)?

a)

-15, -8, -2, 0, 5

b)

-2, -8, -15, 0, 5

c)

-8, -15, -2, 0, 5

d)

0, -15, -8, -2, 5

86.

Put the integers in descending order (greatest to least)

a)

-1

b)

-2

c)

-3

d)

-4

e)

-5

1)
2)
3)
4)
5)
87.

Which set of integers is in descending order (greatest to least)?

a)

20, 8, 3, 0, -2

b)

-2, 0, 3, 8, 20

c)

20, 8, 3, -2, 0

d)

0, -2, 3, 8, 20

88.

Which comparison is true?

a)

− 425 > − 45

b)

− 32 > 8

c)

− 6,231 > − 7,850

d)

62 < − 75

89.

Which points on the number line have an absolute value greater than 2? (Absolute value is the distance a number is from zero.)

a)

3 and 4

b)

2, 3 and 4

c)

− 4, − 3, 3, 4

d)

− 2, − 3, − 4, 2, 3, 4

90.

The absolute value of − 5 and 5 is ? (hint: absolute value is the distance a number is from zero)

a)

5

b)

5 and − 5

c)

− 25

d)

1/5

91.

Put the integers in ascending order (least to greatest)

a)

-42

b)

-25

c)

-2

d)

0

e)

5

1)
2)
3)
4)
5)
92.

Put the integers in descending order (greatest to least).

a)

-2

b)

-10

c)

-18

d)

-24

e)

-52

1)
2)
3)
4)
5)

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