Envision Math Accelerated Grade 7 Volume Chapter 1 Integers and Rational Numbers
Page 7 Exercise 1 Answer
Given:
The mission control uses “T minus” before lift-off.
After the rocket launch “T plus” is used while the rocket is in flight.
T represents the rocket launch.
Integer positive and negative is used to represent the situations
Finally, we concluded that the “T minus” and “T plus” as the rocket launch is used to represents the situations.
Page 7 Exercise 2 Answer
Given:
When preparing for a rocket launch, the mission control center uses the phrase
“T minus” before liftoff… T minus 3, T minus 2, T minus … After the rocket has launched
“T plus” is used while the rocket is in flight….. T plus $1,T plus 2, T plus 3…
To find:
What integers can you use to represent this situation?
Here both positive (Natural numbers) and negative (Additive inverse of Natural numbers).
Integers are represented because when the mission control center of rocket while preparing uses.
T minus (-) and when rocket is launched it is T plus (+) while the rocket is preparing in flight.
Therefore, according to the situation the integers used respectively.
Page 7 Exercise 3 Answer
Given:
When preparing for a rocket launch, the mission control center uses the phrase
“T minus” before liftoff…T minus 3, T minus 2, T minus 1… After the rocket has launched.
“T plus” is used while the rocket is in flight. …T plus 1, T plus 2, T plus 3…
To find:
How are “T minus 4” and “T plus 4” related?
T minus 4 and T plus 4 are related by an integer.
Whereas, minus 4 integers and its opposite plus 4 combines to form 0.
Here, minus 4 is the continuous of preparing to launch a rocket, and plus 4 is the continuous of flying rocket.
Therefore, by this way “T minus 4” and “T plus 4” related.
Page 8 Question 1 Answer
Any positive or negative number that does not contain decimal portions or fractions is called an integer.
All positive and negative whole numbers, as well as zero. The numbers used to count are positive integers.
The numbers are 1,2,3,4,5, and so on. They are the negative integers’ polar counterparts.
Their opposites, which are less than 0, are called negative integers. Zero is neither positive nor negative.
There is a negative integer for every positive integer, and these integers are known as opposites.
Finally, we concluded that the negative and positive representations of a number are combined in a pair of opposite integers.
Page 8 Exercise 1 Answer
To explain about how are the absolute values of integers are related
The absolute value of an integer equals the distance between it and 0, it will always be positive.
Subtracting a negative integer from its absolute value is the same as adding it.
A number’s absolute value is the distance between it and zero on a number line. The absolute value of a number n is represented by the symbol |n|.
On a number line, opposites are the same distance from 0 and are on opposing sides of 0.
Finally, we concluded that the absolute value is related to the distance from zero of a number.
Page 9 Exercise 2 Answer
Given:
The temperature was 75°
At noon, the temperature increased by 7°
By evening, the temperature decreased by 7°
To find How did the temperature changed?
Explanation:
Temperature change = temperature increase- temperature decrease
So 7° −7°=0°
Finally, we concluded that the temperature change is 7° −7° =0°.
Page 9 Exercise 3 Answer
Given:
Shaniqua has $45 in her wallet. She spends $4 on snacks and $8 on a movie ticket
To find What integer represent the change in the amount of money in Shaniqua’s wallet?
And to find How much money does she have left?
Explanation:
What integer represent the change in the amount of money in Shaniqua’s wallet is −$4−$8 =−$12
The money left in the wallet is $45−$12 = $33
Finally, we concluded that the integer represents in Shaniqua’s wallet is−$12 and the money left is$33
Page 10 Exercise 1 Answer
Given:
Opposites relate to integers because an integer’s opposite has to be the same number away from zero as the integer in question.
Example: 2,−5 are different from each other.
Two integers are opposites if their signs differ from each other in + and − signs. If the number doesn’t have the sign so the number is positive.
Page 10 Exercise 2 Answer
Given:
A helium atom has 2 protons and 2 electrons.
The helium atom has no charge, which means it has an oxidation number of 0.
Since the number of protons and electrons are equal.
The positive charge of the protons and the negative charge of electrons add up to zero.
Helium contains an equal number of positively charged particles and negatively charged particles. So, the helium atom has a zero charge.
Page 10 Exercise 3 Answer
Given:
We know the opposite of a number is called the additive inverse because the sum Of the two numbers is zero.
Add a positive number to a number by counting up from that number, and add a negative number to a.
An Integer plus its opposite sum to zero.
The opposite of a number is called the additive inverse because the two-number sum is zero. When two opposites are added together they equal to zero.
Page 10 Exercise 4 Answer
Given:
We need to use integers to represent Marcus’s location.
Let’s say the sea level is at zero.
As we assumed the surface of the ocean is at the zero.
So we need to add an integer in −18 equals to zero.
Thus the number is 18 which makes −18 equal to zero.
Hence, Marcus have to go 18 M to return to the surface.
Marcus have to go 18 M to return to the surface.
Page 10 Exercise 5 Answer
Given:
To analyze temperature for each day as follows. To measure the overall change in water temperature.
Water temperature on Sunday = 78° F
Water temperature on Monday changed by−3 degrees F
Water temperature on Tuesday changed by 3 degrees F
The total change of water temperature from Sunday to Tuesday is −3 + 3 = 0
Since overall temperature is zero, hence temperature on Sunday and on Tuesday is similar.
The water temperature on Tuesday is 78 degrees F.
Page 10 Exercise 6 Answer
Given :
To find Travis’s score
Lats assume travis’s score as x.
His score would have to be −5
−3+3 = 0
1 + 4 = 5
5 + (−5) = 0
So the sum of all scores is zero.
If we sum those, we have :3−3 + 4 + 1 + x = 0
Then x = −5, Travis score is −5 points
Hence traves’s score is−5 points.
Page 11 Exercise 7 Answer
Given:
To find: How much money he had before his purchase
The money he spent =$53
The money he left after spending money = $0
= x−53 = 0
x = 0 + 53
x = 53
Therefore he had = $53
The final solution, Therefore he had $53.
Page 11 Exercise 8 Answer
Given:
The given temperature was 8 degrees F.
It dropped to zero degrees F.
Therefore the change in temperature is−8 degrees F.
Hence the change in temperature is−8 degrees F.
Page 11 Exercise 9 Answer
Given:
Since an airplane descended 4000 feet before landing.
We have to determine the integer that represents the number of feet the airplane was above the ground before descent.
Since the distance above the ground is represented by the positive integer.
Therefore, the airplane was +4000 feet above the ground level.
Hence the airplane was +4000 feet above the ground level.
Page 11 Exercise 10 Answer
Given:
The above figure shows that the opposite of the integer represented by the point A is 7.
And the opposite of the integer represented by point B is− 8.
Therefore opposite of integers A and B is 7 and −8.
The final solution of an opposite integer is 7 and −8.
Given:
The opposite of the integer represented by the point A is 7.
And the opposite of the integer represented by point B is −8.
Therefore opposite of integers A and B is 7 and −8.
No, we don’t agree with Carolyn, because the opposite sides are different.
The final solution is above Solution I don’t agree with Carolyn because the opposite side is different.
Page 11 Exercise 11 Answer
Given:
The cost of 9 yards can be written as −9
It is given that the team has combined gain or loss of 0 yards
Let gain or lost x score in the next play
0−9 + x = 0
Now add both side by 9, and we get
x = 9
Finally, we concluded that the team must gain 9 yards.
Page 11 Exercise 12 Answer
Given:
The rise is at 12 meters
10 Drops at 6 meters
6 Starts at 1 meter
4 Above the ground level
0 Group level
−2 Drops = 4 meters
So the height of the car at end of the ride is
1−4+13−6=4
Finally, we concluded that the height of the car at the end of the ride is 4 meters.
Page 12 Exercise 13 Answer
Given:
According to the given title
= −700 + 1400 − 1100
= 700 − 1100
= − 400
Finally, we concluded that the integer that represent base price of the car to the final price is -400.
Page 12 Exercise 14 Answer
Given:
|x| = 16, |y| = 16
To find when x and y are combined they equal 0
|x| = 16, |y| = 16
It can be written as
x = −16, y = 16
Or x = 16, y = −16
When x and y are combined
x + y = 0
Finally, we concluded that when x and y are combined they equal 0 i.e x + y = 0.
Page 12 Exercise 15 Answer
Given:
The situation represents −42
The opposite of the given situation varies according to the sign. So we get 42.
Finally, we concluded that a situation that can be represented by the opposite of −42 is 42.
Page 12 Exercise 16 Answer
Given:
Ann house is located at 0.
Ben lives 7 blocks from Ann.
Ben lives a number 7 on the number line and Carol lives 2 blocks from Ben.
The possible location for carl’s house is 7,3,−7−3.
Finally, we concluded that a situation that the possible location for carl house is 7,3,−7−3.
Page 12 Exercise 17 Answer
Given:
You walk down 9 flights of stairs.
You climb up 9 flights of stairs.
The temperature drops 9’F.
You spend $9 on a book.
You earn $9 from your job.
To Find:
Which of these situations can be represented with an integer that when combined.
With the opposite of -9 and makes 0? Select all that apply.
Situation-1: You climb up 9 flights of stairs, satisfied with an integer 9 that when combined with the opposite of -9 makes 0.
This is because when you climb up the stairs it means you are climbing up. So, it becomes positive in an integer that is +9.
Situation-2: You earn $9 from your job, satisfied with an integer 9 that when combined with the opposite of -9 makes 0.
This is because if you earn $9 from your job it means you are earning. So, it is positive in an integer that is +9.
Thus, these two situations apply that +9 combined with -9 makes 0.
Page 12 Exercise 18 Answer
Given:
An airplane descends 80m.
An elevator ascends 80m.
The cost of a train ticket drops by $80.
You remove 80 songs from an MP3 player.
Suzy’s grandmother is 80 years old.
To find:
Which of these situations can be represented by the opposite of 80? Select all that apply.
Situation-1: An airplane descends 80m, satisfied with an integer -80 that when combined with the opposite of 80 makes 0.
This is because if an airplane descends it means that an airplane is landing down which in an integer is negative that is -80.
Situation-2: The cost of a train ticket drops by $80, satisfied with an integer -80 that when combined with the opposite of 80 makes 0.
This is because if the cost of a train drops it means the cost is dropping low which in an integer is negative that is -80.
Situation-3: You remove 80 songs from an MP3 player, and satisfy with an integer -80 that when combined with the opposite of 80 makes 0.
This is because if you remove 80 songs, the songs in MP3 reduces which in an integer is negative that is -80.
Thus, these two situations apply that +80 combined with -80 becomes 0.