Evaluate: - 5/6 + (-1/3)

Question

Responses
A −

− 7/6
B −

− 3/6
C

3/6
D

7/3

Answer 1

To evaluate \(-\frac{5}{6} + \left(-\frac{1}{3}\right)\), we first need to make the denominators the same.

The fraction \(-\frac{1}{3}\) can be converted to a fraction with a denominator of 6:

\[ -\frac{1}{3} = -\frac{2}{6} \]

Now we can rewrite the original expression:

\[ -\frac{5}{6} + \left(-\frac{2}{6}\right) = -\frac{5}{6} - \frac{2}{6} \]

Next, we add the fractions:

\[ -\frac{5 + 2}{6} = -\frac{7}{6} \]

Thus, the final result is:

\[ -\frac{7}{6} \]

Looking at the provided responses, the correct answer is:

A \(-\frac{7}{6}\)

Answer 2

Evaluate this expression.

(−98.2) − (−16.8)
Responses
A −115−115
B −81.4−81.4
C 81.481.4
D 115

Answer 3

To evaluate the expression \((-98.2) - (-16.8)\), we can simplify it by converting the subtraction of a negative number into addition:

\[ -98.2 - (-16.8) = -98.2 + 16.8 \]

Now, we perform the addition:

\[ -98.2 + 16.8 = -81.4 \]

Thus, the result is:

\[ -81.4 \]

Looking at the provided responses, the correct answer is:

B \(-81.4\)

Answer 4

Last Friday, the temperature at 9:00AM was 17.2°F. By midnight, the temperature had decreased by 19.5 degrees. What was the temperature at midnight?
Responses
A 36.7°F36.7°F
B 2.3°F2.3°F
C –36.7°F–36.7°F
D –2.3°F

Answer 5

To find the temperature at midnight, we need to subtract the decrease in temperature from the temperature at 9:00 AM.

The initial temperature at 9:00 AM is 17.2°F, and the temperature decreased by 19.5 degrees. Thus, we calculate:

\[ \text{Temperature at midnight} = 17.2°F - 19.5°F \]

Now, performing the subtraction:

\[ 17.2 - 19.5 = -2.3°F \]

Therefore, the temperature at midnight is:

\[ -2.3°F \]

Looking at the provided responses, the correct answer is:

D \(-2.3°F\)

Answer 6

Anna is evaluating some rational expressions. Which THREE are correct?
Responses
A 152 − 200 = −48152 − 200 = −48
B −25 + (−25) = 0−25 + (−25) = 0
C 89 − (−17) = 10689 − (−17) = 106
D 134 − (−16) = 118134 − (−16) = 118
E −39 − (−28) = −11

Answer 7

Let's evaluate each of the options to determine which three are correct.

A: \(152 - 200\)
Calculating:
\[ 152 - 200 = -48 \]
This is correct: A is true.

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B: \(-25 + (-25)\)
Calculating:
\[ -25 + (-25) = -50 \]
This is incorrect: B is false.

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C: \(89 - (-17)\)
Calculating:
\[ 89 - (-17) = 89 + 17 = 106 \]
This is correct: C is true.

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D: \(134 - (-16)\)
Calculating:
\[ 134 - (-16) = 134 + 16 = 150 \]
This is incorrect: D is false.

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E: \(-39 - (-28)\)
Calculating:
\[ -39 - (-28) = -39 + 28 = -11 \]
This is correct: E is true.

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The correct evaluations are: A, C, and E.

Answer 8

What is the vertical distance between a diver that is submerged at a depth of

7 1/2


feet below the surface of the water and a parasailor that is in the air
52 1/4



feet above the surface of the water?
feet

Answer 9

To find the vertical distance between the diver submerged at a depth of \( 7 \frac{1}{2} \) feet below the surface and the parasailor who is \( 52 \frac{1}{4} \) feet above the surface, we can follow these steps:

1. Convert the mixed numbers to improper fractions or decimals for easier calculation:

   • Convert \( 7 \frac{1}{2} \): \[ 7 \frac{1}{2} = 7 + \frac{1}{2} = \frac{14}{2} + \frac{1}{2} = \frac{15}{2} \text{ feet} \]
   • Convert \( 52 \frac{1}{4} \): \[ 52 \frac{1}{4} = 52 + \frac{1}{4} = \frac{208}{4} + \frac{1}{4} = \frac{209}{4} \text{ feet} \]

2. Calculate the total vertical distance. Since the diver is below the water surface and the parasailor is above, the total distance can be calculated as the sum of the two depths:

   \[ \text{Vertical Distance} = \text{above} + \text{below} = \frac{209}{4} + \frac{15}{2} \]

3. Get a common denominator to combine the fractions. The least common denominator of 4 and 2 is 4.

   • Convert \( \frac{15}{2} \) to a fraction with a denominator of 4: \[ \frac{15}{2} = \frac{15 \times 2}{2 \times 2} = \frac{30}{4} \]

4. Now, add the two fractions: \[ \frac{209}{4} + \frac{30}{4} = \frac{239}{4} \]

5. Convert the result back to a mixed number: \[ \frac{239}{4} = 59 \frac{3}{4} \]

So, the vertical distance between the diver and the parasailor is \( 59 \frac{3}{4} \) feet.