Question 1

Simplify the following expression. $- \frac { 3 } { 5 } - \left( - \frac { 4 } { 9 } \right)$
A) $- \frac { 1 } { 45 }$
B) $\frac { 1 } { 45 }$
C) $\frac { 7 } { 45 }$
D) $- 1$
E) $- \frac { 7 } { 45 }$

Accepted Answer

The answer of Simplify the following expression. \(- \frac {...

Question 2

Simplify the following expression. $\left( - \frac { 5 } { 19 } \right) \div \left( - \frac { 1 } { 3 } \right)$
A) $- \frac { 15 } { 19 }$
B) $\frac { 15 } { 76 }$
C) $\frac { 15 } { 19 }$
D) $\frac { 5 } { 26 }$
E) $- \frac { 5 } { 26 }$

Accepted Answer

Dividing two negative fractions results in a positive fraction. Simplify by multiplying the first fraction by the reciprocal of the second: $\left( - \frac { 5 } { 19 } \right) \div \left( - \frac { 1 } { 3 } \right) = \frac { 5 } { 19 } \times \frac { 3 } { 1 } = \frac { 15 } { 19 }$.

Question 3

Simplify the following expression. $\left( - \frac { 51 } { 71 } \right) \left( \frac { 19 } { 30 } \right)$
A) $\frac { 323 } { 710 }$
B) $\frac { 323 } { 647 }$
C) $- \frac { 323 } { 710 }$
D) $- \frac { 323 } { 970 }$
E) $\frac { 323 } { 970 }$

Accepted Answer

Multiplying the fractions $\left( - \frac { 51 } { 71 } \right) \left( \frac { 19 } { 30 } \right)$ gives $- \frac { 969 } { 2130 }$, which simplifies to $- \frac { 323 } { 710 }$ after dividing both the numerator and the denominator by their greatest common divisor, 3.

Question 4

Simplify the following expression. $- \frac { 2 } { 3 } - \frac { 1 } { 16 }$
A) $\frac { 35 } { 48 }$
B) $\frac { 1 } { 48 }$
C) $- \frac { 35 } { 48 }$
D) $1$
E) $- \frac { 1 } { 48 }$

Accepted Answer

To simplify the expression, find a common denominator for the fractions, which is 48 in this case. Convert $-\frac{2}{3}$ to $-\frac{32}{48}$ and $-\frac{1}{16}$ to $-\frac{3}{48}$. Adding these gives $-\frac{35}{48}$.

Question 5

Simplify: $- 5.1 \times 7.1$
A) 2
B) -36.21
C) -12.2
D) -2
E) 36.21

Accepted Answer

Multiplying -5.1 by 7.1 gives -36.21.

Question 6

Simplify the following expression. $\frac { 3 } { 7 } - \frac { 1 } { 2 }$
A) $- \frac { 1 } { 14 }$
B) $\frac { 29 } { 14 }$
C) $\frac { 1 } { 14 }$
D) $1$
E) $\frac { 5 } { 11 }$

Accepted Answer

To simplify the expression, find a common denominator, which is 14 in this case. Convert each fraction: $\frac{3}{7} = \frac{6}{14}$ and $\frac{1}{2} = \frac{7}{14}$. Then, $\frac{6}{14} - \frac{7}{14} = -\frac{1}{14}$.

Question 7

Simplify: -1.46 + (-7.93)
A) 6.47
B) -9.39
C) -9.69
D) -9.49
E) -6.47

Accepted Answer

When you add two negative numbers, you add their absolute values and keep the negative sign. So, -1.46 + (-7.93) = -(1.46 + 7.93) = -9.39.

Question 8

Simplify the following expression. $- \frac { 8 } { 21 } \div \frac { 3 } { 5 }$
A) $- \frac { 40 } { 63 }$
B) $\frac { 63 } { 190 }$
C) $\frac { 40 } { 63 }$
D) $- \frac { 40 } { 81 }$
E) $\frac { 40 } { 81 }$

Accepted Answer

To simplify the expression $- \frac { 8 } { 21 } \div \frac { 3 } { 5 }$, you multiply by the reciprocal of the second fraction: $- \frac { 8 } { 21 } \times \frac { 5 } { 3 } = - \frac { 40 } { 63 }$.

Question 9

Simplify: $( - 1.8 ) ( - 8.29 )$
A) 14.922
B) 0.014922
C) 14,922
D) -0.014922
E) -14.922

Accepted Answer

The product of two negative numbers is positive, and multiplying 1.8 by 8.29 gives 14.922.

Question 10

Simplify the following expression. $\left( \frac { 5 } { 7 } \right) \left( - \frac { 1 } { 6 } \right) \left( - \frac { 14 } { 19 } \right)$
A) $- \frac { 5 } { 57 }$
B) $\frac { 5 } { 11 }$
C) $\frac { 5 } { 16 }$
D) $\frac { 5 } { 57 }$
E) $- \frac { 5 } { 16 }$

Accepted Answer

Multiplying the fractions together, the negatives cancel out, and the result is $\frac{5}{7} \times \frac{1}{6} \times \frac{14}{19} = \frac{5 \times 1 \times 14}{7 \times 6 \times 19} = \frac{5}{57}$.

Question 11

Simplify the following expression. $\left( - \frac { 4 } { 9 } \right) \left( - \frac { 2 } { 3 } \right)$
A) $\frac { 8 } { 27 }$
B) $\frac { 8 } { 25 }$
C) $- \frac { 8 } { 27 }$
D) $\frac { 8 } { 17 }$
E) $- \frac { 8 } { 17 }$

Accepted Answer

When multiplying two negative fractions, the negatives cancel out, and you multiply the numerators together and the denominators together: $(- \frac { 4 } { 9 }) (- \frac { 2 } { 3 }) = \frac { 4 \times 2 } { 9 \times 3 } = \frac { 8 } { 27 }$.

Question 12

Simplify: -9.8 + 8 - 9.3
A) 27.1
B) 8.5
C) -27.1
D) 7.5
E) -11.1

Accepted Answer

Simplifying the expression, we get -9.8 + 8 - 9.3 = -11.1. Therefore, the correct choice is E, which represents -11.1.

Question 13

The patients enrolled in a clinical trial for a new weight-loss drug had a combined weight loss of -18 lb during the first month. There were nine patients in the clinical trial. What was the average weight loss per patient?
A) -1 lb
B) 3 lb
C) -2 lb
D) 1 lb
E) -3 lb

Accepted Answer

To find the average weight loss per patient, we divide the total weight loss (-18 lb) by the number of patients (9): -18/9 = -2. Therefore, the average weight loss per patient is -2 lb, making the correct answer choice (C).

Question 14

Simplify the following expression. $- \frac { 1 } { 2 } + \frac { 2 } { 3 }$
A) $\frac { 1 } { 6 }$
B) $\frac { 13 } { 6 }$
C) $- \frac { 1 } { 6 }$
D) $1$
E) $- \frac { 13 } { 6 }$

Accepted Answer

To simplify the expression, find a common denominator, which in this case is 6. Convert each fraction: $- \frac { 1 } { 2 } = - \frac { 3 } { 6 }$ and $\frac { 2 } { 3 } = \frac { 4 } { 6 }$. Adding these gives $- \frac { 3 } { 6 } + \frac { 4 } { 6 } = \frac { 1 } { 6 }$.

Question 15

Simplify the following expression. $\left( \frac { 7 } { 11 } \right) \div \left( - \frac { 3 } { 8 } \right)$
A) $- \frac { 56 } { 33 }$
B) $\frac { 56 } { 169 }$
C) $\frac { 56 } { 33 }$
D) $- \frac { 56 } { 113 }$
E) $\frac { 56 } { 113 }$

Accepted Answer

Dividing by a fraction is the same as multiplying by its reciprocal. Thus, $\left( \frac { 7 } { 11 } \right) \div \left( - \frac { 3 } { 8 } \right) = \left( \frac { 7 } { 11 } \right) \times \left( - \frac { 8 } { 3 } \right) = - \frac { 56 } { 33 }$.

Question 16

Simplify: -6.1 + 9.1
A) 15.2
B) 3
C) -15.2
D) 8
E) -3

Accepted Answer

When we combine -6.1 and 9.1, we get a positive result of 3. Therefore, the answer is B) 3.

Question 17

The combined scores of the top twelve golfers in a tournament equaled -48 (48 under par). What was the average score of the twelve golfers?
A) 36
B) -4
C) -1
D) -36
E) 4

Accepted Answer

Since the combined scores of the top twelve golfers equaled -48 (48 under par), we can find the average score by dividing the total by 12. (-48/12 = -4) Therefore, the average score of the twelve golfers was -4. Choice B is the only option that matches this result.

Question 18

The patients enrolled in a clinical trial for a new weight-loss drug had a combined weight loss of -30 lb during the first month. During the second month of the clinical trial, the patients lost twice as much weight as they had the first month. What was their combined weight loss the second month?
A) +30 lb
B) -59lb
C) -58 lb
D) -60 lb
E) +58lb

Accepted Answer

In the second month, the patients lost twice as much weight as they did in the first month. Since they lost -30 lb in the first month, twice that amount is -60 lb, indicating a greater weight loss.

Question 19

Simplify the following expression. $- \frac { 11 } { 12 } - \left( - \frac { 3 } { 9 } \right) + \frac { 2 } { 7 }$
A) $- \frac { 1 } { 84 }$
B) $\frac { 1 } { 84 }$
C) $\frac { 25 } { 84 }$
D) $- 1$
E) $- \frac { 25 } { 84 }$

Accepted Answer

First, simplify the expression by converting all fractions to have a common denominator, which in this case is 84 (the least common multiple of 12, 9, and 7). The expression becomes $- \frac { 77 } { 84 } + \frac { 28 } { 84 } + \frac { 24 } { 84 }$. Adding these fractions together yields $- \frac { 25 } { 84 }$.

Question 20

Simplify the following expression. $\left( \frac { 5 } { 11 } \right) \left( - \frac { 5 } { 8 } \right)$
A) $\frac { 25 } { 88 }$
B) $\frac { 25 } { 51 }$
C) $- \frac { 25 } { 88 }$
D) $- \frac { 25 } { 76 }$
E) $\frac { 25 } { 76 }$

Accepted Answer

To simplify the expression, multiply the numerators together and the denominators together: $ \left( \frac { 5 } { 11 } \right) \left( - \frac { 5 } { 8 } \right) = - \frac { 25 } { 88 }$.

Quiz 11: Introduction to Algebra

Simplify the following expression. $- \frac { 3 } { 5 } - \left( - \frac { 4 } { 9 } \right)$

Simplify the following expression. $\left( - \frac { 5 } { 19 } \right) \div \left( - \frac { 1 } { 3 } \right)$

Simplify the following expression. $\left( - \frac { 51 } { 71 } \right) \left( \frac { 19 } { 30 } \right)$

Simplify the following expression. $- \frac { 2 } { 3 } - \frac { 1 } { 16 }$

Simplify: $- 5.1 \times 7.1$

Simplify the following expression. $\frac { 3 } { 7 } - \frac { 1 } { 2 }$

Simplify: -1.46 + (-7.93)

Simplify the following expression. $- \frac { 8 } { 21 } \div \frac { 3 } { 5 }$

Simplify: $( - 1.8 ) ( - 8.29 )$

Simplify the following expression. $\left( \frac { 5 } { 7 } \right) \left( - \frac { 1 } { 6 } \right) \left( - \frac { 14 } { 19 } \right)$

Simplify the following expression. $\left( - \frac { 4 } { 9 } \right) \left( - \frac { 2 } { 3 } \right)$

Simplify: -9.8 + 8 - 9.3

The patients enrolled in a clinical trial for a new weight-loss drug had a combined weight loss of -18 lb during the first month. There were nine patients in the clinical trial. What was the average weight loss per patient?

Simplify the following expression. $- \frac { 1 } { 2 } + \frac { 2 } { 3 }$

Simplify the following expression. $\left( \frac { 7 } { 11 } \right) \div \left( - \frac { 3 } { 8 } \right)$

Simplify: -6.1 + 9.1

The combined scores of the top twelve golfers in a tournament equaled -48 (48 under par) . What was the average score of the twelve golfers?

The patients enrolled in a clinical trial for a new weight-loss drug had a combined weight loss of -30 lb during the first month. During the second month of the clinical trial, the patients lost twice as much weight as they had the first month. What was their combined weight loss the second month?

Simplify the following expression. $- \frac { 11 } { 12 } - \left( - \frac { 3 } { 9 } \right) + \frac { 2 } { 7 }$

Simplify the following expression. $\left( \frac { 5 } { 11 } \right) \left( - \frac { 5 } { 8 } \right)$

Quiz 11: Introduction to Algebra

Simplify the following expression. −35−(−49) - \frac { 3 } { 5 } - \left( - \frac { 4 } { 9 } \right) −53​−(−94​)

Simplify the following expression. (−519) ÷(−13) \left( - \frac { 5 } { 19 } \right) \div \left( - \frac { 1 } { 3 } \right) (−195​) ÷(−31​)

Simplify the following expression. (−5171) (1930) \left( - \frac { 51 } { 71 } \right) \left( \frac { 19 } { 30 } \right) (−7151​) (3019​)

Simplify the following expression. −23−116- \frac { 2 } { 3 } - \frac { 1 } { 16 }−32​−161​

Simplify: −5.1×7.1- 5.1 \times 7.1−5.1×7.1

Simplify the following expression. 37−12\frac { 3 } { 7 } - \frac { 1 } { 2 }73​−21​