Glencoe Math Course 2 Volume 1 Common Core Chapter 3 Integers Exercise 3.2
Page 203 Exercise 1 Problem 1
If you would increase the temperature by −5° then you would obtain a temperature of 0°
−5° +5° =0°
Finally, we concluded that the temperature that would make the sum of the two temperatures 0° ⇒ 5°
Page 204 Exercise 1 Problem 2
Given:
−5 + ( −7) = _____
To Find – The sum.
Given
−5 + (−7) = −12
⇒ −12
−5 + (−7) = −12
Number line:
Finally, we find the sum ⇒ −12
Given:
−10 + (−4)=_____
To Find –The sum.
−10 + (−4)= -14
Finally, we find the sum ⇒ −14
Given:
−14 + (−16) =
To Find – The sum.
Given
−14 + (−16) = −30
⇒ −30
Number line:
Finally, we find the sum ⇒ −30
Given:
6 + (−7)=_____
To Find- The sum.
Consider the operation given and simplify
6 + (−7) = −1
⇒ −1
The value of 6 + (−7) is −1
Given:
−15 + 19 =_____
To Find – The sum.
Given
−15 + 19 = 4
⇒ 4
Number line:
Finally, we find the sum ⇒ 4
Given:
10 + (−12) =_____
To Find – The sum.
10 + (−12) =−2
= −2
Finally, we find the sum ⇒−2
Given:
−13 + 18 =_____
To Find – The sum.
−13 + 18 = 5
= 5
Finally, we find the sum ⇒ 5
Given:
−14 + (−6) + 6 =_____
To Find – The sum.
Consider the operation given and simplify
−14 + (−6) + 6 = −14 + 0
= −14
The value of −14+(−6)+6 is−14
Given:
The temperature is−3°.An hour later it drops 6° and 2 hours later it rises 4°
To Write an additional expression to describe this situation. Then find the sum and explain its meaning
The temperature drops can best be represented by a negative number, while the temperature rise back is positive number.
−3−6 + 4 =−9 + 4 = 5
= 5
Finally we find the sum ⇒ −3− 6 + 4 = 5
Page 206 Exercise 1 Problem 3
Given:
−6 + (−8) =_____
To Find – The sum.
−6 + (−8) = −14
= −14
Finally, we find the sum ⇒ −14
Page 206 Exercise 2 Problem 4
Given:
−3 + 10 =_____
To Find – The sum.
Consider the operation given and simplify
−3 + 10 =7
⇒ 7
The value of−3 + 10 is 7
Page 206 Exercise 3 Problem 5
Given:
−8 + (−4) + 12 =_____
To Find – The sum.
−8 + (−4) + 12 = − 12 + 12 = 0
⇒ 0
Finally, we find the sum ⇒ 0
Page 206 Exercise 4 Problem 6
Given:
Sofia owes her brother $25
She gives her brother the $18
To write an addition expression.
The amount owed can best be represented by a negative number, while the amount paid back is a positive number.
− 25 + 18 − 7
= −7
This means that Sofia still owes her brother
Finally, we write the addition expression ⇒ −25 + 18 = −7
Page 206 Exercise 5 Problem 7
The sum is positive
If the absolute value of the negative number is less than the absolute value of the positive number
If both numbers are positive The sum is negative
If the absolute value of the negative number is greater than the absolute value of the positive number
If both numbers are negative The sum is zero
If the absolute value of both integers is equal and if one is positive while the other is negative
Finally, we concluded that we can find a sum is positive, negative or zero without actually adding by the absolute value of the given integers.
Page 207 Exercise 1 Problem 8
Given:
−22 + (−16)
To add both numbers
Given equation is
− 22 −16
=−38
If both numbers has a different sign, add the value and put the greatest value sign
Finally, we conclude the solution using an addition expression and the solution is −38
Page 207 Exercise 2 Problem 9
Given:
−10 + (−15)
To add both numbers
If both numbers has a different sign, add the value and put the greatest value sign
−10−15
= −25
Finally, we concluded an addition expression to solve the sum and the solution is −25
Page 207 Exercise 3 Problem 10
Given:
6 + 10
To add both numbers
If both numbers have a + sign, add the value and put a positive sign
6 + 10
= 16
Finally, we concluded an addition expression to solve the sum and the solution is 16
Page 207 Exercise 4 Problem 11
Given:
21 + (−21) + (−4)
To add and subtract the numbers
If both numbers has a different sign, add the value and put the greatest value sign
21 + (−21) + (−4)
= 21−21−4
= −4
Finally, we concluded an addition expression to solve the sum and the solution is −4
Page 207 Exercise 5 Problem 12
Given:
17 + 20 + (−3)
To add and subtract the given numbers and find the result.
Add the first two numbers, then subtract 3 from their sum.
17 + 20 + (−3)
= 37 − 3
= 34
The value of 17 + 20 + (−3) is 34
Page 207 Exercise 7 Problem 13
Given:
4 + 5
To add both numbers
If both numbers have + sign, add the value and put a positive sign
4 + 5
= 9
Finally, we concluded an addition expression and the solution is 9
Page 207 Exercise 9 Problem 14
Given:
7 + (−11)
To add both numbers
If both numbers has a different sign, add the value and put the greatest value sign
7 + (−11)
= −4
Finally, we concluded the addition expression and the solution is −4
Page 207 Exercise 10 Problem 15
Given:
$152 − $20 + $84
To find the sum and explain its meaning
If both numbers has different sign, add the value and put the greatest value sign
$152 − $20 = $132
= $132 + $84
= $216
Finally, we concluded an additional expression to represent this situation is $216
Page 208 Exercise 12 Problem 16
Given:
The given transactions are
Week one $300
Week two $50
Week three $75
Week four $225
To find the sum and explain its meaning
The withdrawal represents negative (-) and the deposit represents positive (+).
So add the given values, we get
$300 + (−$50) + (−$75) + $225
= −$125+$525
= $400
The total sum using the addition expression is $400
Page 208 Exercise 14 Problem 17
The given equation x + (-x) =0 states the property of additive inverse because it has the sum of the number with opposite sides zero
The rule is to change the positive number to a negative number
Finally, we conclude the property as additive inverse property because it has the number wit opposite sides zero.
The given equations x + (-y) = −y + x states the property of commutative, because it allows you to interchange the numbers in a sum
This law simply states that with addition is commutative
Finally, we concluded the property is Commutative property because its interchanges the number in sums.
Page 208 Exercise 17 Problem 18
Given:
−9 + m + (−6)
To simplify
Given equation is
−9 + m + (−6)
= −9 + (−6) + m
=(−9 + (−6)) + m
= −15 + m
−9 + m + (−6) = −15 + m
Finally, we concluded an addition expression to solve the sum and the solution is −15 + m
Page 208 Exercise 18 Problem 19
The explanation for correct answer
(A) − 4 + 3
This is the correct answer because the blue line passing on the negative side and stop at −4 and the red line passing on the positive side and stop at 3
(B)−4 + 7
The blue line passing on the negative side and stop at −4 and the red line passing on the positive side and stop at 3, not at 7, so this is the wrong answer
(C) 3 + (−7)
The blue line passing on the negative side and stop at−4, not at 3 and the red line passing on the positive side and stop at 3, not at −7, so this is the wrong answer
(D) 0 + (−7)
The blue line passing on the negative side and stop at −4 not at 0 and the red line passing on the positive side and stop at 3, not at −7, so this is the wrong answer
Finally, we concluded that (A) −4 + 3 is the correct expression represented by the number line.
Page 209 Exercise 19 Problem 20
Given:
18 + (−5)
To add the given value
18 + (−5)
= 18 + (−5) = 18 − 5
= 13
18 + (−5) = 13
Add both the number and the greatest number sign in the result
Finally, we concluded an addition expression to solve the sum and the solution is 13
Page 209 Exercise 20 Problem 21
Given:
−19 + 24
To add the given value
−19 + 24
= −19 + 24 = 24 + (−19)
= 24 −19
= 5
−19 + 24 = 5
Add both the number and the greatest number sign in the result
Finally, we conclude the solution using addition expression and the solution is 5
Page 209 Exercise 23 Problem 22
Given:
15 + 9 + (−9)
To add the given value
15 + 9 + (−9)
= 24 + (−9)
= 24 − 9
= 15
15 + 9 + (−9) = 15
Add both the number and the greatest number sign in the result
Finally, we conclude the solution using addition expression and the solution is 15
Page 209 Exercise 24 Problem 23
Given:
−4 + 12 + (−9)
To add the given value
−4 + 12 + (−9)
= 8 + (−9)
= 8 − 9
= −1
−4 + 12 + (−9) = −1
Add both the number and the greatest number sign in the result
Finally, we conclude the solution using an addition expression and the solution is −1
Page 209 Exercise 26 Problem 24
Given:
25 + 3 + (−25)
To add the given value
25 + 3 + (−25)
= 28 + (−25)
= 28 − 25
= 3
25 + 3 + (−25) = 3
Add both the number and the greatest number sign in the result
Finally, we conclude the solution using addition expression and the solution is 3
Page 209 Exercise 27 Problem 25
Given:
7 + (−19) + (−7)
To add the given value
7 + (−19) + (−7)
= 7 − 19 − 7
= −12−7
= −19
7 + (−19) + (−7) = −19
Add both the number and the greatest number sign in the result
Finally, we conclude the solution using an addition expression and the solution is −19
Page 209 Exercise 29 Problem 26
Given:
A quarterback is sacked for a loss of 5 yards
On the next day’s play, his team losses 15 yards.
Then the team gain 12 yards on the third play
Write an additional expression to describe each situation
The gain represents the positive numbers
The losses represent negative numbers
So it can be written as −5 + (−15) + 12
−5 + (−15) + 12
= −20 + 12
= −8
−5 + (−15) + 12 = −8
Add both the number and the greatest number sign in the result
Finally, we concluded that an addition expression to describe each situation is −5 + (−15) + 12
Page 210 Exercise 31 Problem 27
Given: Temperatures at 8 A.M and 1 P.M
To find – Temperature at 10 P.M
The temperature at 8 A.M was 3°F
The temperature rose at 1 A.M was 14°F
The temperature drops at 10 P.M were
The increase is denoted by a positive number and below zero or drop is denoted by a negative number.
From given
−3 + 14 + (−12)
= 11 + (−12)
= −1
−3 + 14 + (−12) = −1
Thus, the temperature is 1°F below zero.
The temperature at 10 P.M is 1°F below zero
Page 210 Exercise 32 Problem 28
Given: −8 + 7 + (−3)
To find -The value
Given that −8 + 7 + (−3)
The answer is (−4)
Explanation:
−8 + 7 + (−3)
=−1 + (−3)
= −4
−8 + 7 + (−3) = −4
The value −8 + 7 + (−3) of is −4
Page 210 Exercise 30 Problem 29
Given: A bank deposit of $ 75
To find- Integer format for a given situation.
A bank deposit of $ 75
Explanation:
A bank deposit will increase the money that is in your bank account and thus it is represented by a positive number.
Thus, the integer representation of this situation is 75
The integer representation for bank deposits is 75.
Page 210 Exercise 36 Problem 30
Given: 13°F below zero
To find – Integer format for a given situation.
Given 13°F below zero.
Explanation:
The temperature below zero is represented by a negative number.
Thus, the integer representation of this situation is = 13°
The integer representation for temperature below zero is −13°
Page 210 Exercise 37 Problem 31
Given: A gain of 4 yards
To find- Integer format for a given situation.
A gain of 4 yards
Explanation:
The gain will increase the number that you have and hence it is represented by a positive number.
Thus, the integer representation of this situation is 4.
The integer representation for a gain of yards is 4
Page 210 Exercise 38 Problem 32
Given: Spending of $12.
To find- Integer format for a given situation.
Spending of $12.
Explanation:
Spending money will decrease the amount that you have and hence it is represented by a negative number.
Thus, the integer representation of this situation is −12.
The integer representation for spending of $12. is −12