Find the sum of p and q if p = 3/4 and q =−11/4. Reduce your answer to lowest terms.
_______
To find the sum of p and q, we add their values together:
p + q = 3/4 + (-11/4)
To add fractions, we need to have a common denominator. The common denominator of 4 and 4 is 4.
p + q = (3 - 11)/4
Now we can subtract the numerators:
p + q = -8/4
The fraction -8/4 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:
p + q = -2/1
Therefore, the sum of p and q is -2.
Add (−12) and (−15).(1 point)
−3
negative 3
3
3
27
27
−27
To find the sum of -12 and -15, we add their values together:
(-12) + (-15) = -27
Therefore, the sum of -12 and -15 is -27.
Add 10.82+(−15.96).(1 point)
To add 10.82 and -15.96, we simply add their values together:
10.82 + (-15.96) = -5.14
Therefore, the sum of 10.82 and -15.96 is -5.14.
Solve the following problem:
It was 13°C yesterday, but the temperature changed by −18.6° overnight. What is the temperature now?(1 point)
____ °C
To find the current temperature, we need to subtract the change in temperature from the initial temperature:
13°C + (-18.6°C) = -5.6°C
Therefore, the current temperature is -5.6°C.
Use the additive inverse to find −492.89 − (−871.78).(1 point)
_____
To find the subtraction of -492.89 and -871.78, we can use the additive inverse.
−492.89 − (−871.78) is equivalent to −492.89 + 871.78.
Now, we can add the values together:
−492.89 + 871.78 = 378.89.
Therefore, −492.89 − (−871.78) is equal to 378.89.
Determine the distance between −18.26 and −2.45 on a number line.(1 point)
Responses
20.71
20.71
15.81
15.81
−20.71
negative 20.71
−15.81
To find the distance between -18.26 and -2.45 on a number line, we can subtract the smaller value from the larger value:
|-18.26 - (-2.45)| = |-18.26 + 2.45| = |-15.81| = 15.81
Therefore, the distance between -18.26 and -2.45 on a number line is 15.81.
Subtract 24 − (−15).(1 point)
To subtract 24 and -15, we can rewrite the expression as:
24 - (-15)
Remember that subtracting a negative is the same as adding a positive. So we can rewrite it as:
24 + 15
Now we can add the values together:
24 + 15 = 39
Therefore, the result of the subtraction 24 - (-15) is 39.
What is 17 4/9 + 5/9 − 8 − 10? (1 point)
20
0
−1
−7
To solve 17 4/9 + 5/9 - 8 - 10, we need to simplify each term and then add them together.
First, we can add the whole number and the fraction:
17 + 4/9 = 153/9 + 4/9 = 157/9
Next, we can add the other fraction:
157/9 + 5/9 = 162/9
Now, we can subtract 8 and 10:
162/9 - 8 - 10 = 162/9 - 18 - 10 = 162/9 - 28
To subtract fractions, we need a common denominator of 9:
162/9 - 28 = 162/9 - 252/9 = -90/9
Finally, we can simplify the fraction:
-90/9 = -10
Therefore, 17 4/9 + 5/9 - 8 - 10 equals -10.
Which context describes a difference of rational numbers?(1 point)
Responses
The team’s score did not change during the game.
The team’s score did not change during the game.
The team’s score increased when scoring.
The team’s score increased when scoring.
A football player loses yards on a play.
A football player loses yards on a play.
A football player gains yards on a play.
A football player loses yards on a play.
Joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was Joey from home? Write your answer as a mixed number only.(1 point)
Joey was ____ meters from home.
To find how far Joey was from home, we need to subtract the distance he walked west from the distance he walked east.
Distance from home = (Distance walked east) - (Distance walked west)
First, let's convert the mixed numbers to improper fractions.
15 2/3 = (3 * 15 + 2)/3 = 47/3
21 3/4 = (4 * 21 + 3)/4 = 87/4
Now, we can subtract the fractions:
Distance from home = 47/3 - 87/4
To subtract fractions, we need a common denominator of 12:
Distance from home = (47/3) * (4/4) - (87/4) * (3/3)
Distance from home = 188/12 - 261/12
Now, we can subtract the fractions:
Distance from home = (188 - 261)/12
Distance from home = -73/12
Therefore, Joey was -73/12 meters from home.
Which situation describes opposite quantities that when combined would equal 0?(1 point)
Responses
A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 10,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 10,000 feet. How many feet above the ground is the plane?
A plane ascends to 10,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
Solve the following word problem. The air temperature at 9 a.m. is −5.8 degrees Celsius. The air temperature at noon is −1.6 degrees Celsius. What is the change in the temperature during these three hours? Write and solve an equation to show your answer. Then explain what your answer means.(4 points)
To find the change in temperature during the three hours, we need to subtract the initial temperature from the final temperature.
Change in temperature = Final temperature - Initial temperature
Given that the air temperature at 9 a.m. is -5.8 degrees Celsius and the air temperature at noon is -1.6 degrees Celsius, we can substitute these values into the equation:
Change in temperature = -1.6 - (-5.8)
Now, let's simplify the expression:
Change in temperature = -1.6 + 5.8
Adding the values, we get:
Change in temperature = 4.2
Therefore, the change in temperature during these three hours is 4.2 degrees Celsius.
This means that the temperature increased by 4.2 degrees Celsius from 9 a.m. to noon.