Question 1

Find the prime factorization of the number
-231

Accepted Answer

A)  $3 ^ { 2 } \cdot 11$ 
B)  $21 \cdot 11$ 
C)  $7 ^ { 2 } \cdot 3$ 
D)  $3 \cdot 7 \cdot 11$

Question 2

Provide an appropriate response.
-2|6

Accepted Answer

A) True 
 B)False

Question 3

Express the repeating decimal number as a quotient of two integers.
-$0 . \overline { 4 }$

Accepted Answer

A)  $\frac { 4 } { 9 }$ 
B)  $\frac { 40 } { 999 }$ 
C)  $\frac { 40 } { 99 }$ 
D)  $\frac { 4 } { 99 }$

Question 4

Convert the mixed number into an improper fraction.
-$$15 \frac { 5 } { 11 }$$

Accepted Answer

A)  150 
B)  25 
C)  $\frac { 75 } { 11 }$ 
D)  $\frac { 170 } { 11 }$

Question 5

Solve the problem.
-The new city park is a rectangle $51 \frac { 1 } { 2 }$ yards by 42 yards. What is the area of the park in square yards?

Accepted Answer

A)  3 square yards 
B)  $2069 \frac { 1 } { 3 }$ square yards 
C)  2163 square yards 
D)  $45 \frac { 4 } { 5 }$ square yards

Question 6

Find the least common multiple (LCM).
-45, 28, and 150

Accepted Answer

A)  1,050 
B)  630 
C)  1260 
D)  6300

Question 7

Determine whether or not the first number is divisible by the second number
-652,523; 5

Accepted Answer

A)  Yes 
B)  No

Question 8

Perform the indicated operation and reduce the answer to lowest terms.
-$$\frac { 1 } { 4 } + \frac { 5 } { 16 } + \frac { 1 } { 8 }$$

Accepted Answer

A)  2 
B)  $\frac { 11 } { 16 }$ 
C)  $\frac { 11 } { 8 }$ 
D)  $\frac { 7 } { 16 }$

Question 9

Provide an appropriate response.
-If a number is divisible by 2, then every digit of the number is divisible by 2.

Accepted Answer

A) True 
 B)False

Question 10

Evaluate the expression.
--60 + 61

Accepted Answer

A)  -1 
B) -121 
C)  121 
D)  1

Question 11

Determine whether or not the first number is divisible by the second number
-22,308; 6

Accepted Answer

A)  No 
B)  Yes

Question 12

Find the greatest common divisor (GCD).
-8 and 12

Accepted Answer

A)  4 
B)  2 
C)  1 
D)  8

Question 13

Convert the mixed number into an improper fraction.
-$$- 17 \frac { 9 } { 10 }$$

Accepted Answer

A)  $- \frac { 153 } { 10 }$ 
B)  $- \frac { 26 } { 10 }$ 
C)  $- \frac { 189 } { 10 }$ 
D)  $- \frac { 179 } { 10 }$

Question 14

Find the prime factorization of the number
-468

Accepted Answer

A)  $2 ^ { 2 } \cdot 3 ^ { 2 } \cdot 13$ 
B)  $2 ^ { 3 } \cdot 3 ^ { 2 } \cdot 13$ 
C)  $3 ^ { 4 } \cdot 13$ 
D)  $2 ^ { 4 } \cdot 13$

Question 15

Perform the indicated operation and reduce the answer to lowest terms.
-$$\frac { 11 } { 15 } - \frac { 2 } { 25 }$$

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B)  $\frac { 49 } { 75 }$ 
C)  $\frac { 9 } { 25 }$ 
D)  $\frac { 9 } { 10 }$

Question 16

Find the greatest common divisor (GCD).
-30 and 19

Accepted Answer

A)  19 
B)  3 
C)  10 
D)  1

Question 17

Evaluate the expression.
-$( - 78 ) / 6$

Accepted Answer

A)  $- 23$ 
B)  $- \frac { 1 } { 13 }$ 
C)  13 
D)  $- 13$

Question 18

Perform the operation and give the answer as a fraction in lowest terms.
-$\left( \frac { 2 } { 3 } \right) \left( \frac { 1 } { 4 } \right)$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 3 } { 2 }$ 
C)  $\frac { 1 } { 6 }$ 
D)  $\frac { 3 } { 8 }$

Question 19

Convert the improper fraction into a mixed number.
-$\frac { 43 } { 8 }$

Accepted Answer

A)  $5 \frac { 3 } { 8 }$ 
B)  $5 \frac { 5 } { 8 }$ 
C)  $4 \frac { 3 } { 8 }$ 
D)  $6 \frac { 3 } { 8 }$

Question 20

Solve.
-At Lincoln High School, there are 1472 students in the Junior Class and 2576 students in the Senior Class. The teachers want to assign the students to committees with the same number of juniors in Each committee and the same number of seniors in each committee. (For example, there might be 2 Juniors and 3 seniors in every committee). What are all the possible numbers of committees they Could form and still meet this goal?

Accepted Answer

A)  4, 16, 92, 368, or 644 different committees 
B)  4, 23, 64, or 368 different committees 
C)  4, 23, 16, 92, or 368 different committees 
D)  4, 23, 16, or 64 different committees

Exam 5: Number Theory and the Real Number System

Find the prime factorization of the number -231

Provide an appropriate response. -2|6

Express the repeating decimal number as a quotient of two integers. - $0 . \overline { 4 }$

Convert the mixed number into an improper fraction. - $15 \frac { 5 } { 11 }$

Solve the problem. -The new city park is a rectangle $51 \frac { 1 } { 2 }$ yards by 42 yards. What is the area of the park in square yards?

Find the least common multiple (LCM) . -45, 28, and 150

Determine whether or not the first number is divisible by the second number -652,523; 5

Perform the indicated operation and reduce the answer to lowest terms. - $\frac { 1 } { 4 } + \frac { 5 } { 16 } + \frac { 1 } { 8 }$

Provide an appropriate response. -If a number is divisible by 2, then every digit of the number is divisible by 2.

Evaluate the expression. --60 + 61

Determine whether or not the first number is divisible by the second number -22,308; 6

Find the greatest common divisor (GCD) . -8 and 12

Convert the mixed number into an improper fraction. - $- 17 \frac { 9 } { 10 }$

Find the prime factorization of the number -468

Perform the indicated operation and reduce the answer to lowest terms. - $\frac { 11 } { 15 } - \frac { 2 } { 25 }$

Find the greatest common divisor (GCD) . -30 and 19

Evaluate the expression. - $( - 78 ) / 6$

Perform the operation and give the answer as a fraction in lowest terms. - $\left( \frac { 2 } { 3 } \right) \left( \frac { 1 } { 4 } \right)$

Convert the improper fraction into a mixed number. - $\frac { 43 } { 8 }$

Exam 5: Number Theory and the Real Number System

Find the prime factorization of the number -231

Provide an appropriate response. -2|6

Express the repeating decimal number as a quotient of two integers. - 0.4‾0 . \overline { 4 }0.4

Convert the mixed number into an improper fraction. - 1551115 \frac { 5 } { 11 }15115​

Solve the problem. -The new city park is a rectangle 511251 \frac { 1 } { 2 }5121​ yards by 42 yards. What is the area of the park in square yards?