Question 1

Which property of the real numbers is illustrated by the following statement? 2 + 17 = 17 + 2
A) Identity property for addition
B) Commutative property of addition
C) Associative property of addition
D) Closure property for addition

Accepted Answer

The commutative property of addition states that the order of the addends does not affect the sum. In this case, 2 + 17 = 17 + 2 because the sum is the same regardless of the order in which the numbers are added.

Question 2

Which property of the real numbers is illustrated by the following statement? (15 7)  4 = 15 (7 4)
A) Associative property of multiplication
B) Distributive property
C) Identity property for multiplication
D) Commutative property of multiplication

Accepted Answer

The associative property of multiplication states that the way in which numbers are grouped does not change their product. Here, (15 × 7) × 4 = 15 × (7 × 4) illustrates this property.

Question 3

Perform the indicated operations and simplify the answer.
$$\sqrt { 7 } ( \sqrt { 63 } - \sqrt { 175 } )$$

A) $- 112 \sqrt { 15 }$

B) $- 112$

C) $- 14 \sqrt { 15 }$

D) $- 14$

Accepted Answer

The answer of Perform the indicated operations and simplify the...

Question 4

Reduce the fraction to the lowest terms. $\frac { 748 } { 8712 }$
A) $\frac { 748 } { 198 }$

B) $\frac { 17 } { 198 }$

C) $\frac { 17 } { 8712 }$

D) $\frac { 187 } { 2178 }$

Accepted Answer

The answer of Reduce the fraction to the lowest terms....

Question 5

Find the greatest common factor of 20 and 21.
A) 1
B) 21
C) 20
D) 420

Accepted Answer

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. Since 20 and 21 are consecutive integers, they have no common factors other than 1.

Question 6

Perform the indicated operations. 2[1 + (-12) - (-7)]
A) -3
B) -36
C) -17
D) -8

Accepted Answer

The answer of Perform the indicated operations. 2[1 + (-12)...

Question 7

Perform the indicated operations and reduce the answer to lowest terms.
$$\left( \frac { 7 } { 8 } - \frac { 5 } { 6 } \right) \times \frac { 4 } { 5 }$$
A) $\frac { 4 } { 5 }$

B) $\frac { 5 } { 24 }$

C) $\frac { 1 } { 30 }$

D) $\frac { 10 } { 3 }$

Accepted Answer

The answer of Perform the indicated operations and reduce the...

Question 8

A company decided to fine its workers for parking violations on its property. The first offense carries a fine of $12, the second offense is $18, the third offense is $24, and so on. What is the fine for the eighth offense?
A) $42
B) $48
C) $60
D) $54

Accepted Answer

The fines increase by $6 for each subsequent offense. The sequence of fines is an arithmetic sequence: $12, $18, $24, ..., with a common difference of $6. The nth term of an arithmetic sequence is given by the formula: a_n = a_1 + (n-1)d. For the eighth offense, a_8 = 12 + (8-1)*6 = 12 + 42 = $54.

Question 9

Perform the indicated operations and simplify the answer.
$$- 2 \sqrt { 5 } + 7 \sqrt { 45 } + 8 \sqrt { 80 }$$

A) $51 \sqrt { 5 }$

B) Cannot be simplified.

C) $189 \sqrt { 5 }$

D) $51 \sqrt { 60 }$

Accepted Answer

The answer of Perform the indicated operations and simplify the...

Question 10

Change the fraction to a decimal. $\frac { 5 } { 24 }$
A) $0.2 \overline { 083 }$

B) $0 . \overline { 2083 }$

C) $0.20 \overline { 83 }$

D) $0.208 \overline { 3 }$

Accepted Answer

The answer of Change the fraction to a decimal. \(\frac...

Question 11

Perform the indicated operation and simplify the answer.
$$5 \sqrt { 24 } + 3 \sqrt { 54 }$$
A) $8 \sqrt { 78 }$

B) $19 \sqrt { 6 }$

C) $47 \sqrt { 6 }$

D) Cannot be simplified.

Accepted Answer

The answer of Perform the indicated operation and simplify the...

Question 12

A bakery makes three types of muffins to be distributed to local grocery stores: chocolate chip, blueberry, and banana nut. Each morning, the bakers produce 360 chocolate chip muffins, 420 blueberry muffins, and 180 banana nut. They want to package the muffins efficiently for shipping. The plan is to pack them in boxes so that every box has just one kind of muffin, and every box has the same number of muffins. What's the smallest number of boxes they can ship in total?
A) 16 boxes
B) 960 boxes
C) 3 boxes
D) 60 boxes

Accepted Answer

The smallest number of boxes they can ship in total is the least common multiple of 360, 420, and 180. The LCM of 360, 420, and 180 is 360, so the smallest number of boxes they can ship in total is 360.

Question 13

The following statement illustrates the property of addition. -3 + 1 is a real number.
A) associative
B) identity
C) commutative
D) closure

Accepted Answer

The closure property states that the sum of any two real numbers is also a real number.

Question 14

Determine whether the sequence is an arithmetic sequence, a geometric sequence, or neither. -10, -12, -14, -16, -18
A) geometric
B) neither
C) arithmetic

Accepted Answer

The sequence is arithmetic because each term is obtained by subtracting 2 from the previous term, indicating a common difference of -2.

Question 15

Rationalize the denominator and simplify. $\sqrt { \frac { 3 } { 275 } }$
A) $\frac { \sqrt { 3 } } { 5 }$

В) $\frac { \sqrt { 33 } } { 5 }$

C) $\frac { \sqrt { 3 } } { 55 }$

D) $\frac { \sqrt { 33 } } { 55 }$

Accepted Answer

The answer of Rationalize the denominator and simplify. \(\sqrt {...

Question 16

Write each number in scientific notation and then divide. Give the answer in scientific notation.
$$\frac { 0.0000000000012 } { 0.0004 }$$

A) $3 \times 10 ^ { - 7 }$
B) $3 \times 10 ^ { - 9 }$
C) $3 \times 10 ^ { - 8 }$
D) $3 \times 10 ^ { - 10 }$

Accepted Answer

The answer of Write each number in scientific notation and...

Question 17

Change the decimal to a reduced fraction. 0.12 A) $\frac { 6 } { 5 }$

B) $\frac { 3 } { 250 }$

C) $\frac { 3 } { 25 }$

D) $\frac { 3 } { 2500 }$

Accepted Answer

The answer of Change the decimal to a reduced fraction....

Question 18

Find the greatest common factor of 14 and 21.
A) 42
B) 6
C) 7
D) 1

Accepted Answer

The greatest common factor (GCF) of 14 and 21 is 7, as it is the largest number that divides both 14 and 21 without leaving a remainder.

Question 19

Find the least common multiple of 13, 17, and 59.
A) 767
B) 221
C) 13,039
D) 1003

Accepted Answer

The least common multiple (LCM) of prime numbers is their product. Since 13, 17, and 59 are all prime, their LCM is 13 * 17 * 59 = 13,039.

Question 20

Linda and Deepti are walking and jogging on a circular trail. Linda can complete one circuit in 24 minutes, and Deepti can complete the circuit in 16 minutes. If they both start at the same place at the same time, when will they be at the starting place at the same time?
A) 384 minutes
B) 24 minutes
C) 8 minutes
D) 48 minutes

Accepted Answer

The least common multiple of 24 and 16 is 48, so they will both be at the starting place at the same time after 48 minutes.

Quiz 5: The Real Number System

Which property of the real numbers is illustrated by the following statement? 2 + 17 = 17 + 2

Which property of the real numbers is illustrated by the following statement? (15 7)  4 = 15 (7 4)

Perform the indicated operations and simplify the answer. $\sqrt { 7 } ( \sqrt { 63 } - \sqrt { 175 } )$ A) $- 112 \sqrt { 15 }$ B) $- 112$ C) $- 14 \sqrt { 15 }$ D) $- 14$

Reduce the fraction to the lowest terms. $\frac { 748 } { 8712 }$ A) $\frac { 748 } { 198 }$ B) $\frac { 17 } { 198 }$ C) $\frac { 17 } { 8712 }$ D) $\frac { 187 } { 2178 }$

Find the greatest common factor of 20 and 21.

Perform the indicated operations. 2[1 + (-12) - (-7) ]

Perform the indicated operations and reduce the answer to lowest terms. $\left( \frac { 7 } { 8 } - \frac { 5 } { 6 } \right) \times \frac { 4 } { 5 }$ A) $\frac { 4 } { 5 }$ B) $\frac { 5 } { 24 }$ C) $\frac { 1 } { 30 }$ D) $\frac { 10 } { 3 }$

A company decided to fine its workers for parking violations on its property. The first offense carries a fine of $12, the second offense is $18, the third offense is $24, and so on. What is the fine for the eighth offense?

Perform the indicated operations and simplify the answer. $- 2 \sqrt { 5 } + 7 \sqrt { 45 } + 8 \sqrt { 80 }$ A) $51 \sqrt { 5 }$ B) Cannot be simplified. C) $189 \sqrt { 5 }$ D) $51 \sqrt { 60 }$

Change the fraction to a decimal. $\frac { 5 } { 24 }$ A) $0.2 \overline { 083 }$ B) $0 . \overline { 2083 }$ C) $0.20 \overline { 83 }$ D) $0.208 \overline { 3 }$

Perform the indicated operation and simplify the answer. $5 \sqrt { 24 } + 3 \sqrt { 54 }$ A) $8 \sqrt { 78 }$ B) $19 \sqrt { 6 }$ C) $47 \sqrt { 6 }$ D) Cannot be simplified.

The following statement illustrates the property of addition. -3 + 1 is a real number.

Determine whether the sequence is an arithmetic sequence, a geometric sequence, or neither. -10, -12, -14, -16, -18

Rationalize the denominator and simplify. $\sqrt { \frac { 3 } { 275 } }$ A) $\frac { \sqrt { 3 } } { 5 }$ В) $\frac { \sqrt { 33 } } { 5 }$ C) $\frac { \sqrt { 3 } } { 55 }$ D) $\frac { \sqrt { 33 } } { 55 }$

Write each number in scientific notation and then divide. Give the answer in scientific notation. $\frac { 0.0000000000012 } { 0.0004 }$ A) $3 \times 10 ^ { - 7 }$ B) $3 \times 10 ^ { - 9 }$ C) $3 \times 10 ^ { - 8 }$ D) $3 \times 10 ^ { - 10 }$

Change the decimal to a reduced fraction. 0.12 A) $\frac { 6 } { 5 }$ B) $\frac { 3 } { 250 }$ C) $\frac { 3 } { 25 }$ D) $\frac { 3 } { 2500 }$

Find the greatest common factor of 14 and 21.

Find the least common multiple of 13, 17, and 59.

Linda and Deepti are walking and jogging on a circular trail. Linda can complete one circuit in 24 minutes, and Deepti can complete the circuit in 16 minutes. If they both start at the same place at the same time, when will they be at the starting place at the same time?