Chapter 2 Integers And Rational Numbers
Section 2.1: Understand Integers
Page 65 Exercise 1 Answer
Since −10° less than zero thus it represents the colder temperature.
Result
−10°
Page 65 Exercise 1a Answer
Sal is not correct.
The temperature first raised to zero, that is it changed by 4°F.
Than it raised from zero to 22°F, that is it changed by 22°F.
In total it changed by 4 + 22 = 26.
Result
Sal is not correct.
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 65 Exercise 1b Answer
The temperature first raised to zero, that is it changed by 4°F
Than it raised from zero to 22°F, that is it changed by 22°F.
In total it changed by 4 + 22 = 26.
Result
It changed by 26.
Page 66 Exercise 1 Answer
The opposite number of 4 is −4, and the other way, the opposite number of −4 is 4.
Two number are opposites if and only if their sum equals zero.
Result
The opposite of 4 is −4. The opposite of −4 is 4. Two numbers are opposite if and only if their sum equals zero.
Page 67 Exercise 2 Answer
Since both numbers are less than zero, the one closer to zero is the greater one, that is the one with the greater absolute value is the lesser one.
Thus, −2 is greater than −4.
Result
−2 > −4
Page 67 Exercise 3a Answer
A $10 debt is represented by the integer -10.
Result
−10
Page 67 Exercise 3b Answer
Six degrees below zero is represented by the integer −6.
Result
−6
Page 67 Exercise 3c Answer
Depsit of $25 is represented by the integer 25.
Result
25
Page 68 Exercise 1 Answer
Integers are the set of numbers which contains all the natural numbers, that is the number we use for counting, such as 1, 2, 3, …; a zero, and the opposites of all the natural numbers, that is all the natural numbers but with a negative sign, −1, −2, −3, …
Integers can be used to count, to represent heights, temperatures, and similar quantities.
For example, since they have negative values they are great to represent cold temperatures if zero represents the point at which the water freezes.
Result
Integers are the set of numbers which contains all the natural numbers, 0, and the opposites of all the natural numbers. Integers can be used to count, represent heights, temperatures, and similar quantities.
Page 68 Exercise 2 Answer
Two integers which are opposites have a different sign , they have the same absolute value , and when added their sum is zero.
Page 68 Exercise 3 Answer
-17 is read as negative seventeen
Result
Negative seventeen.
Page 68 Exercise 4 Answer
A debt means the amount you must give, that is you do not have $250, but you owe that money.
Result
-$250
Page 68 Exercise 5 Answer
When comparing two negative integers, the one that is closer to zero when marked on a number line is the greater number.
Or, the one which has a lesser absolute value is the greater number.
Result
When comparing two negative integers, the one that is closer to zero when marked on a number line is the greater number, or, the one which has a lesser absolute value is the greater number.
Page 68 Exercise 6 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of 1 is −1.
Result
−1
Page 68 Exercise 7 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of −1 is 1.
Result
1
Page 68 Exercise 8 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of −11 is 11.
Result
11
Page 68 Exercise 9 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of 30 is −30.
Result
−30
Page 68 Exercise 10 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of 0 is 0.
Result
0
Page 68 Exercise 11 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of −16 is 16.
Result
16
Page 68 Exercise 12 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. -(-8) = 8 The opposite of 8 is −8.
Result
−8
Page 68 Exercise 13 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of 28 is −28.
Result
−28
Page 68 Exercise 14 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. -(-65) = 65 The opposite of 65 is −65.
Result
−65
Page 68 Exercise 15 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of 98 is −98.
Result
−98
Page 68 Exercise 16 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of 100 is −100.
Result
−100
Page 68 Exercise 17 Answer
Opposites are integers that are the same distance from 0 and on opposite sides of 0 on a number line. The opposite of −33 is 33.
Result
33
Page 68 Exercise 18 Answer
We need to order the integers 2, −3, 0, and −4 from least to greatest.
Negative numbers are smaller than 0 so −3 and −4 are the smallest numbers. Positive numbers are bigger than 0 so the biggest number is 2 and the second biggest number is 0:
_, _ ,0,2
To compare negative integers, we can compare their absolute values. The larger the negative integer’s absolute value is, the smaller the negative integer is. Since −4 has a larger absolute value than −3, then −4 < −3. The order of the integers is then:
−4,−3,0,2
Result
−4,−3,0,2
Given integers in order from least to greatest: -4, -3, 0, 2.
Result
−4,−3,0,2
Page 68 Exercise 19 Answer
We need to order the integers 4, 12, −12, and −11 from least to greatest.
Negative numbers are smaller than positive numbers so −12 and −11 are the smallest numbers and 4 and 12 are the largest numbers.
To compare negative integers, we can compare their absolute values. The larger the negative integer’s absolute value is, the smaller the negative integer is. Since −12 has a larger absolute value than −11, then −12 < −11:
−12,−11, _, _
Since 4 < 12, then the order of the integers is:
−12,−11,4,12
Result
−12, −11, 4, 12
Given integers in order from least to greatest: -12, -11, 4, 12.
Result
−12, −11, 4, 12
Page 68 Exercise 20 Answer
We need to order the integers −5, 6, −7, and −8 from least to greatest.
Negative numbers are smaller than positive numbers so 6 is the biggest number:
_, _, _ ,6
To compare negative integers, we can compare their absolute values. The larger the negative integer’s absolute value is, the smaller the negative integer is. Since −8 has a largest absolute value and −5 has the smallest absolute value, then −8 < −7 < −5. The order of the integers is then:
−8,−7,−5,6
Result
−8, −7, −5, 6
Given integers in order from least to greatest: -8, -7, -5, 6.
Result
−8,−7,−5,6
Page 69 Exercise 21 Answer
Zero represents the sea level, since than every positive number represents the height above the sea level, and every negative number the depth below the sea level.
For example, a Ruppell’s Griffon flies at the heights up tp 37,000 feet above the sea level; and a dolphin swims to 150 feet below the see level.
Ruppell’s Griffon’s height can be represented by a positive number, that is 37,000 feet. Dolphin’s depth can be represented by a negative number, that is −150 feet.
Result
Zero.
Page 69 Exercise 22 Answer
A dolphin may swim to 150 feet below sea level, thus a negative integer which represents the depth is −150 .
Result
−150
Page 69 Exercise 23 Answer
The animal which can travel the greatest distance from sea level is the one whose absolute value is the greatest.
|37,000| = 37,000
|5,000| = 5,000
|-3,000| = 3,000
|-150| = 150
Thus, the animal which can travel the greatest distance from sea level is a Ruppell’s Griffon.
Result
Ruppell’s Griffon.
Page 69 Exercise 24 Answer
Elevations are positive numbers for heights above sea level and negative numbers for heights below sea level.
A Ruppell’s Griffons can fly up to 37,000 feet above sea level so its elevation is 37,000. A migrating bird flies up to 5,000 feet above sea level so its elevation is 5,000. A dolphin can swim to 150 feet below sea level so its elevation is −150. A sperm whale can swim to 3,000 feet below sea level so its elevation is −3,000.
To order the elevations from least to greatest, we must then order the numbers 37,000, 5,000, −150, and −3,000.
Positive numbers are bigger than negative numbers so the two smallest elevations are −150 and −3,000 and the two largest elevations are 37,000 and 5,000.
To compare negative integers, we can compare their absolute values. The larger the negative integer’s absolute value is, the smaller the negative integer is.
Since −3,000 has a larger absolute value than −150, then −3,000 < −150:
−3,000, −150, _, _
Since 5,000 < 37,000, then the order of the elevations is:
−3,000, −150, 5,000, 37,000
Result
−3,000, −150, 5,000, 37,000
Page 69 Exercise 25 Answer
Plot a point at -10 on the number line and label it as G.
Page 69 Exercise 26 Answer
Plot a point at 8 on the number line and label it as H.
Page 69 Exercise 27 Answer
Plot a point at -1 on the number line and label it as I.
Page 69 Exercise 28 Answer
Plot a point at 9 on the number line and label it as J.
Page 69 Exercise 29 Answer
Plot a point at 6 on the number line and label it as K.
Page 69 Exercise 30 Answer
Plot a point at -3 on the number line and label it as L.
Page 69 Exercise 31 Answer
The point A represents the integer value −7. Its opposite is 7.
Result
−7, its opposite is 7.
Page 69 Exercise 32 Answer
The point B represents the integer value 4. Its opposite is −4.
Result
4, its opposite is −4.
Page 69 Exercise 33 Answer
The point C represents the integer value 0. Its opposite is 0.
Result
0, its opposite is 0.
Page 69 Exercise 34 Answer
The point D represents the integer value −2. Its opposite is 2.
Result
−2, its opposite is 2.
Page 69 Exercise 35 Answer
The point E represents the integer value 2. Its opposite is −2.
Result
2, its opposite is −2.
Page 69 Exercise 36 Answer
The point F represents the integer value −5. Its opposite is 5.
Result
−5, its opposite is 5.
Page 70 Exercise 37a Answer
Opposite number of a number n is a number which, when added to n, gives zero 0. The opposite number for n is written as -n.
The opposite of 5 is -5.
Result
−5
Page 70 Exercise 37b Answer
Opposite number of a number n is a number which, when added to n, gives zero 0. The opposite number for n is written as -n.
The opposite of -13 is -(-13), which is 13.
Result
13
Page 70 Exercise 37c Answer
Opposite number of a number n is a number which, when added to n, gives zero 0. The opposite number for n is written as -n.
-(-22) = 22
The opposite of 22 is -22.
Result
−22
Page 70 Exercise 37d Answer
Opposite number of a number n is a number which, when added to n, gives zero 0. The opposite number for n is written as -n.
The opposite of -31 is -(-31), which is 31.
Result
31
Page 70 Exercise 37e Answer
Opposite number of a number n is a number which, when added to n, gives zero 0. The opposite number for n is written as -n.
The opposite of -50 is -(-50), which is 50.
Result
50
Page 70 Exercise 37f Answer
Opposite number of a number n is a number which, when added to n, gives zero 0. The opposite number for n is written as -n.
-(-66) = 66
The opposite of 66 is -66.
Result
−66
Page 70 Exercise 38a Answer
We need to compare the integers −5 and 1 and write the integer with the greater value.
Positive numbers are always greater than negative numbers so 1 has the greater value.
Result
1
Page 70 Exercise 38b Answer
We need to compare the integers −5 and 1 and write the integer with the greater value.
To compare negative integers, we can compare their absolute values. The negative integer with the larger absolute value is the smaller integer. Since −7 has a larger absolute value than −6, then −7 < −6. Therefore, −6 has the greater value.
Result
−6
Page 70 Exercise 38c Answer
We need to compare the integers −9 and 8 and write the integer with the greater value.
Positive numbers are always greater than negative numbers so 8 has the greater value.
Result
8
Page 70 Exercise 38d Answer
We need to compare the integers −12 and −(−10) and write the integer with the greater value.
Simplifying −(−10) gives 10.
Positive numbers are always greater than negative numbers so 10 = −(−10) has the greater value.
Result
−(−10)
Page 70 Exercise 38e Answer
Which integer has greater value: -(-9) or 11 ? -(-9) = 9 11 has greater value than 9.
Result
11
Page 70 Exercise 38f Answer
Which integer has greater value: -(-4) or 3 ? -(-4) = 4 4 has greater value than 3.
Result
−(−4)
Page 70 Exercise 39 Answer
The display gives us the temperature 4°, −5°, −7°, and 7°. We need to order these temperatures from least to greatest.
Negative numbers are always smaller than positive numbers so −5° and −7° are the two smallest numbers and 4° and 7° are the two largest numbers.
To compare negative integers, compare their absolute values. The negative integer with the larger absolute value is the smaller integer. Since −7° has a larger absolute value than −5°, then −7° < −5°:
−7°, −5°, _, _
Since 4° < 7°, then the order of the temperatures is:
−7°, −5°, 4°, 7°
The coldest temperature was −7° so it was coldest on Wednesday.
Result
−7° ,−5°, 4°, 7°
Wednesday
Page 70 Exercise 40 Answer
A paid-out expense means that the balance of your account decreased, and a deposit means it increased. Thus, negative numbers would be used to represent debits and positive numbers for credits.
Page 70 Exercise 41 Answer
An integer that would represent the electric charge of an atom with an equal number of electrons and protons must have neither a positive nor a negative sign. The only number which fits these properties is 0.
Result
0
Page 70 Exercise 42 Answer
The opposite of −24 is −(−24), which is equal to 24.
The opposite of 19 is −19.
The opposite of 24 is −24.
The opposite of −8 is 8.
Result
Connect −24 and −(−24), 19 and −19, 24 and −24, and −8 and 8.
Page 70 Exercise 43 Answer
The opposite of −5 is 5.
The opposite of −(−13), which is equal to 13, is −13.
The opposite of 2 is −2.
The opposite of 4 is −4.
Result
Connect −5 and 5, −(−13) and −13, 2 and −2, and 4 and −4.