Add & Subtract Rational Numbers
Abraham needs one-half of a point to get an A– in Math. What rational number can be used to represent the number of points needed for Abraham to get an A–?(1 point)
Place the following numbers in order as they would appear on a number line, left to right: −2.0, 0.25, −1.02, 1.98.(1 point)
The rational number that can represent the number of points needed for Abraham to get an A– is 1/2.
The numbers in order from left to right on a number line would be:
-2.0, -1.02, 0.25, 1.98.
Find the sum of p and q if p=34 and q=−114. Reduce your answer to lowest terms.
The sum of p and q is found by adding the values of p and q together:
p + q = 34 + (-114) = -80.
The sum, -80, is already in its simplest form, so there is no need to reduce it any further.
Which of the following is a real-world problem that could be solved with the sum 102.50+(−39.95)?
A real-world problem that could be solved with the sum 102.50 + (-39.95) could be a situation involving money or finances. For example:
Sarah went shopping and bought items totaling $102.50. However, she returned one item that cost $39.95. What is the remaining total that she spent after accounting for the return?
In this case, the sum 102.50 + (-39.95) would give us the answer to the problem, which is the remaining amount that Sarah spent after subtracting the cost of the returned item.
Which of the following is a real-world problem that could be solved with the sum 102.50+(−39.95)?(1 point)
Responses
A. Nevaeh earned $102.50 last weekend. He then received $39.95 from his mom. How much money does he now have?
B. Nevaeh earned $102.50 last weekend. He then received $39.95 from his mom. How much money does he now have?
C.Nevaeh earned $102.50 last weekend. He then spent $39.95 on a new game. How much money from his weekend earnings does he have left?
D.Nevaeh has $102.50 in his bank account. He then deposits $39.95 into his bank account. How much money does he now have in his bank account?
C. Nevaeh earned $102.50 last weekend. He then spent $39.95 on a new game. How much money from his weekend earnings does he have left?
It was 13°C yesterday, but the temperature changed by −18.6° overnight. What is the temperature now?
To find the temperature now, we need to subtract the change in temperature from the initial temperature.
Initial temperature: 13°C
Change in temperature: -18.6°C
Temperature now = Initial temperature + Change in temperature
Temperature now = 13°C + (-18.6°C) = -5.6°C
Therefore, the temperature now is -5.6°C.
Use the additive inverse to find −492.89−(−871.78).
To find -492.89 - (-871.78), we can use the additive inverse of the second term to change subtracting a negative into addition.
Taking the additive inverse of -871.78, we get 871.78. Now, the expression becomes:
-492.89 + 871.78
Adding the two numbers together:
= 378.89
Therefore, -492.89 - (-871.78) equals 378.89.
Determine the distance between −18.26 and −2.45 on a number line.
To find the distance between two numbers on a number line, we can subtract the smaller number from the larger number and then take the absolute value of the result.
Distance = |larger number - smaller number|
In this case, the larger number is -2.45 and the smaller number is -18.26.
Distance = |-2.45 - (-18.26)|
= |-2.45 + 18.26|
= |15.81|
= 15.81
Therefore, the distance between -18.26 and -2.45 on a number line is 15.81 units.
What is 17 4/9 + 59 − 8 − 10?
To solve the expression 17 4/9 + 59 - 8 - 10, we follow the order of operations, which is often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
First, we simplify the addition of the whole numbers and the mixed number:
17 + 59 = 76
Next, we subtract the other numbers:
76 - 8 - 10 = 58
Therefore, 17 4/9 + 59 - 8 - 10 equals 58.
Which context describes a difference of rational numbers?(1 point)
Responses
A. A football player gains yards on a play.
B. A football player loses yards on a play.
C. The team’s score did not change during the game.
D. The team’s score increased when scoring.
B. A football player loses yards on a play.
Joey walked east for 1523 meters from home. Then, he walked west for 2134 meters. How far was Joey from home?
To determine how far Joey was from home, we must find the total distance he walked in both directions.
Distance walked east: 1523 meters
Distance walked west: 2134 meters
To find the total distance from home, we subtract the distance walked west from the distance walked east:
Total distance from home = Distance walked east - Distance walked west
Total distance from home = 1523 meters - 2134 meters
To subtract these values, we must take the difference between the two numbers:
Total distance from home = -611 meters
Therefore, Joey was 611 meters from home.
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?
To determine the total distance Joey walked from home, we need to add the distances he walked east and west.
Distance walked east: 15 2/3 meters
Distance walked west: 21 3/4 meters
To add these fractions, we need to first find a common denominator. In this case, the least common denominator between 3 and 4 is 12.
Converting the fractions to have a denominator of 12:
Distance walked east: 15 * (12/3) + 2/3 = 60/3 + 2/3 = 62/3 meters
Distance walked west: 21 * (12/4) + 3/4 = 84/4 + 3/4 = 87/4 meters
Now we can add the distances:
Total distance from home = Distance walked east + Distance walked west
Total distance from home = 62/3 + 87/4
To add these fractions, we need a common denominator again. The least common denominator between 3 and 4 is 12.
Converting the fractions to have a denominator of 12:
Total distance from home = (62/3) * (4/4) + (87/4) * (3/3)
Total distance from home = 248/12 + 261/12
Total distance from home = 509/12 meters
Therefore, Joey was 509/12 meters from home.
Which situation describes opposite quantities that when combined would equal 0?
A situation that describes opposite quantities that, when combined, would equal 0 is:
B. A person deposits $50 into their bank account and then withdraws $50 from the same account.
Which situation describes opposite quantities that when combined would equal 0?(1 point)
Responses
A. A plane ascends to 10,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
B. A plane ascends to 15,000 feet and then descends 15,000 feet. How many feet above the ground is the plane?
C. A plane ascends to 15,000 feet and then descends 10,000 feet. How many feet above the ground is the plane?
D. A plane ascends to 15,000 feet and then ascends 15,000 feet. How many feet above the ground is the plane?
B. 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.
To find the change in temperature, we subtract the initial temperature from the final temperature:
Change in temperature = Final temperature - Initial temperature
Given:
Initial temperature = -5.8 degrees Celsius
Final temperature = -1.6 degrees Celsius
Change in temperature = -1.6 - (-5.8) = -1.6 + 5.8 = 4.2 degrees Celsius
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.