when multiplying two rational numbers how is the sign of the product determined?

Question

a. the product is positive if the signs of the factors are the same.
b. the product is negative if the signs of the factors are the same.
c. the sign of the product is always the same as the the larger factor
d. the sign of the product is always the same as the smaller factor

Answer 1

The correct answer is:

a. the product is positive if the signs of the factors are the same.

When multiplying two rational numbers, if both numbers have the same sign (both positive or both negative), the product will be positive. If one number is positive and the other is negative, the product will be negative.

Answer 2

on a given morning the temperature was 81ºF. the temperature dropped 9ºF and rose 5ºF how much does the temperature need to drop/rise to get back to 81ºF
a. rise 4º
b.rise9º
c. fall 4º
d. fall 5º

Answer 3

Let's break down the temperature changes step by step:

1. Initial temperature: 81ºF
2. Temperature drops by 9ºF: \[ 81 - 9 = 72ºF \]
3. Temperature rises by 5ºF: \[ 72 + 5 = 77ºF \]

Now, to return to the original temperature of 81ºF, we need to find out how much the temperature needs to rise from 77ºF:

\[ 81 - 77 = 4ºF \]

Thus, the temperature needs to rise 4ºF to get back to 81ºF.

The correct answer is:

a. rise 4º.

Answer 4

divide -3/17 by -2/3
a. 9/34
b. 2/17
c. -2/17
d. -9/34

Answer 5

To divide two fractions, you can multiply by the reciprocal of the second fraction.

Here’s how to do it step by step:

1. Write the problem: \[ \frac{-3}{17} \div \frac{-2}{3} \]

2. Multiply by the reciprocal of \(-\frac{2}{3}\): \[ \frac{-3}{17} \times \frac{3}{-2} \]

3. The negatives cancel out: \[ = \frac{-3 \times 3}{17 \times -2} = \frac{9}{34} \]

So, the result of the division is: \[ \frac{9}{34} \]

The correct answer is:

a. 9/34.

Answer 6

find the product
4/7(-20/2)
a. -2/35
b. 5 5/7
c. -5 5/7
d. -9 3/7

Answer 7

To find the product \( \frac{4}{7} \left(-\frac{20}{2}\right) \), we will first simplify \(-\frac{20}{2}\):

1. Calculate \(-\frac{20}{2}\): \[ -\frac{20}{2} = -10 \]

2. Now we can multiply: \[ \frac{4}{7} \times (-10) \]

3. To multiply, rewrite \(-10\) as \(-\frac{10}{1}\) so we have: \[ \frac{4}{7} \times \frac{-10}{1} = \frac{4 \times -10}{7 \times 1} = \frac{-40}{7} \]

4. Now let's express \(\frac{-40}{7}\) as a mixed number: \[ -40 \div 7 = -5 \quad \text{remainder } 5 \] Thus, we can write: \[ \frac{-40}{7} = -5 \frac{5}{7} \]

The final answer is:

c. -5 5/7.

Answer 8

the elevation of the basement floor in a building is -15ft the elevation of the roof is 37 feet what is the distance from the basement floor to the roof?
a. 22 feet
b.-52 feet
c. 37 feet
d. 52 feet

Answer 9

To find the distance from the basement floor to the roof, you need to calculate the difference between the elevation of the roof and the elevation of the basement floor.

1. The elevation of the basement floor is \(-15\) feet.
2. The elevation of the roof is \(37\) feet.

To find the distance, you can use the formula:

\[ \text{Distance} = \text{Elevation of the roof} - \text{Elevation of the basement} \]

Substituting the values:

\[ \text{Distance} = 37 - (-15) \] \[ \text{Distance} = 37 + 15 = 52 \text{ feet} \]

The distance from the basement floor to the roof is 52 feet.

The correct answer is:

d. 52 feet.