Deck 15: Summary

Question 1

Find the additive inverse of -7 on the 12-hour clock.

Answer 1

7

Question 2

Find 8 × 4 mod 12.

Answer 2

8

Question 3

Find 1 10 mod 11.

Answer 3

2

Question 4

Evaluate 3 - (11 - 5) mod 12.

Question 5

Question 6

Evaluate 2 × (7 + 5) mod 11.

Question 7

Find the multiplicative inverse of 3 on the 12-hour clock if it exists.

Question 8

Find the natural number solution to 8 - y = 9 mod 12.

Question 9

Find the additive inverse of 1 on the 12-hour clock.

Question 10

The following is an example using the 12-hour clock of which property? 3 + 2 = 2 + 3

Question 11

Evaluate (7 - 8) - 9 mod 10.

A) 0
B) 1
C) -10
D) 2

Question 12

Find the value of y using the 12-hour clock. 6 + y = 2

Question 13

Find 383 mod 12.

Question 14

Find 5 + 5 mod 10.

Question 15

Which property is not true for all numbers on the 12-hour clock?

A) Identity property for multiplication
B) Closure property for addition
C) Identity property for addition
D) Inverse property for multiplication

Question 16

Find the natural number solution to 8 + y = 4 mod 11.

Question 17

Perform the addition on the 12-hour clock. (8 + 9) + 1

Question 18

Perform the subtraction on the 12-hour clock. 7 - 8

Question 19

Find the value of y using the 12-hour clock. y - 10 = 5

Question 20

Perform the addition on the 12-hour clock. 10 + 12

Question 21

Determine which properties the given mathematical system exhibits. Identify any systems that are groups or Abelian groups.
$\begin{array}{c|ccc}\Omega & s & n & w \\\hline s & w & s & n \\n & s & n & w \\w & n & w & w\end{array}$

A) closure, commutative, identity
B) closure, commutative
C) closure, commutative, identity, inverse
D) closure, commutative, identity, inverse, associative; Abelian group

Question 22

Perform the addition on the 16-hour clock. 15 + 11

A) 11
B) 10
C) 6
D) 9

Question 23

$$\begin{array}{l}\text { Use the system shown to find } t ^ { * } \left( r ^ { * } q \right) \text {. }\\\begin{array} { c | c c c c } * & q & r & s & t \\\hline q & t & s & r & q \\r & s & q & t & r \\s & r & t & q & s \\t & q & r & s & t\end{array}\end{array}$$

A) s
B) t
C) r
D) q

Question 24

$$\begin{array}{l}\text { In the system shown, find the value for } x \text { when } q ^ { * } x = r \text {. }\\\begin{array} { c | c c c c } * & q & r & s & t \\\hline q & t & s & r & q \\r & s & q & t & r \\s & r & t & q & s \\t & q & r & s & t\end{array}\end{array}$$

A) s
B) t
C) r
D) q

Question 25

Determine whether the given system forms (a) a group and (b) an Abelian group. {-8, 0, 8} under addition

A) a group but not an Abelian group
B) Abelian group
C) not a group
D) Abelian group but not a group

Question 26

Determine which properties the given mathematical system exhibits. Identify any systems that are groups or Abelian groups.
$\begin{array}{c|ccc}\Omega & 7 & 9 & 3 \\\hline 7 & 9 & 3 & 7 \\9 & 3 & 7 & 9 \\3 & 7 & 9 & 3\end{array}$

A) closure, commutative, identity
B) closure, commutative, identity, inverse, associative; Abelian group
C) closure, commutative
D) closure, commutative, identity, inverse

Question 27

$$\begin{array}{l}\text { Is the system shown closed under the operation? }\\\begin{array} { c | c c c c } * & q & r & s & t \\\hline q & t & s & r & q \\r & s & q & t & r \\s & r & t & q & s \\t & q & r & s & t\end{array}\end{array}$$

A) No
B) Yes

Question 28

Perform the multiplication on the 12-hour clock. 10 × (3 × 2)

A) 10
B) 12
C) 9
D) 11

Question 29

Perform the multiplication on the 12-hour clock. 8 × 12

A) 12
B) 9
C) 10
D) 11

Question 30

$$\begin{array}{l}\text { Use the system shown to find } r * s \text {. }\\\begin{array} { l | l l l l } * & q & r & s & t \\\hline q & t & s & r & q \\r & s & q & t & r \\s & r & t & q & s \\t & q & r & s & t\end{array}\end{array}$$

A) t
B) q
C) r
D) s

Question 31

Find the natural number solution to 5 × y = 4 mod 9.

A) 2
B) 6
C) 8
D) 4/5

Question 32

Determine whether the given system forms (a) a group and (b) an Abelian group. Natural numbers under multiplication

A) Abelian group
B) a group but not an Abelian group
C) Abelian group but not a group
D) not a group

Question 33

Question 34

On a game board, there is a spinner that has spaces marked 1 through 11 in order. The pointer is on the 2 and Shira spins it so that it spins past 113 spaces and lands exactly on a number. What number does the spinner land on?

A) 3
B) 5
C) 4
D) 6

Question 35

Evaluate (7 + 5) + 8 mod 12.

A) 7
B) 20
C) 9
D) 8

Question 36

$$\begin{array}{l}\text { In the system shown, is the operation commutative? }\\\begin{array} { l | l l l l } * & q & r & s & t \\\hline q & t & s & r & q \\r & s & q & t & r \\s & r & t & q & s \\t & q & r & s & t\end{array}\end{array}$$

A) No
B) Yes

Question 37

Find the equivalent number on the 12-hour clock. -137

A) 5
B) 7
C) 8
D) 6

Question 38

$$\begin{array}{l}\text { Use the system shown to find } s * s \text {. }\\\begin{array} { c | c c c c } * & q & r & s & t \\\hline q & t & s & r & q \\r & s & q & t & r \\s & r & t & q & s \\t & q & r & s & t\end{array}\end{array}$$

A) s
B) r
C) t
D) q

Question 39

Perform the multiplication on the 7-hour clock. 4 × 5

A) 1
B) 2
C) 7
D) 6

Question 40

Find the equivalent number on the 12-hour clock. 254

A) 2
B) 5
C) 1
D) 3

Question 41

Evaluate (4 × 6) × 5 mod 12.

A) 1
B) 2
C) 0
D) 120