Friday, November 15, 2013
Module 2 Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers
Problem Set
1.
On a number line, find the difference of each
number and 4? Complete the table to support your
answers. The first example is provided.
Number
|
Subtraction Number
Sentence
|
Addition Number
Sentence
|
Distance
(units)
|
10
|
10 - 4 = 6
|
10 + (-4) = 6
|
6
|
2
|
4 - 2 = 2
|
4 + (-2) = 2
|
2
|
-4
|
4 - (-4) = 8
|
4 + 4 = 8
|
8
|
-6
|
4 - (-6) = 10
|
4 + 6 = 10
|
10
|
1
|
4 - 1 = 3
|
4 + (-1) = 3
|
3
|
2.
You and your partner were playing the Integer
Game in class. Here are the cards in
both hands.
Your Hand: -8, 6, 1, -2 Your Partner’s Hand: 9, -5, 2, -7
a.
Find the value of each hand. Who would win based on the current scores?
(The score closest to 0 wins.)
Your Hand: (-8) + 6 + 1 + -2 (Hint: Add two integers together at a time.)
(-2) + 1 + (-2) (I added (-8) + 6 to get -2.)
(-1) + (-2) (I added (-2) + 1 to get -1.)
-3 (I added (-1) + (-2) to get -3.)
(-1) + (-2) (I added (-2) + 1 to get -1.)
-3 (I added (-1) + (-2) to get -3.)
Your Partner's Hand: 9 + (-5) + 2 + (-7)
4 + 2 + (-7) (I added 9 + (-5) to get 4.)
6 + (-7) (I added 4 + 2 to get 6.)
-1 (I added 6 + (-7) to get -1.)
6 + (-7) (I added 4 + 2 to get 6.)
-1 (I added 6 + (-7) to get -1.)
My partner would win because the value of my partner's hand is -1 and the value of my hand is -3. My partner would win because -1 is closer to 0 than -3 is.
b.
Find the value of each hand if you discarded the -2 and selected a 5, and your partner discarded
the -5 and selected a 5. Show your work to support your answer.
Your New Hand: (-8) + 6 + 1 + 5
(-2) + 1 + 5 (I added (-8) + 6 to get -2.)
(-1) + 5 (I added (-2) + 1 to get -1.)
4 (I added (-1) + 5 to get 4.)
Your Partner's New Hand: 9 + 5 + 2 + (-7)
Your New Hand: (-8) + 6 + 1 + 5
(-2) + 1 + 5 (I added (-8) + 6 to get -2.)
(-1) + 5 (I added (-2) + 1 to get -1.)
4 (I added (-1) + 5 to get 4.)
Your Partner's New Hand: 9 + 5 + 2 + (-7)
14 + 2 + (-7) (I added 9 + 5 to get 14.)
16 + (-7) (I added 14 + 2 to get 16.)
9 (I added 16 + (-7) to get 9.)
16 + (-7) (I added 14 + 2 to get 16.)
9 (I added 16 + (-7) to get 9.)
c.
Use your score values from part (b) to determine
who would win the game now.
I would win the game now because the value of my hand is 4 and the value of my partner's hand is 9. I would win because 4 is closer to 0 than 9 is.
3. Solve the following problems.
b. (-2) - (-16)
(-2) + 16
14
Subtracting is the same thing as adding the opposite of a quantity. Subtracting a negative integer is the same thing as adding a positive integer. So we change the problem to (-2) + 16, which is the same as the problem in part a.
Subtracting a positive integer is the same thing as adding a negative integer. So we change the problem to 18 + (-26). Since 18 and -26 have different signs, we subtract 26 - 18 and we get 8. Since the absolute value of -26 is bigger, our answer must be -8.
Subtracting a positive integer is the same thing as adding a negative integer so we change the problem to (-14) + (-23). Since (-14) and (-23) have the same sign, we add 14 + 23 to get 37. Since both numbers are negative, our answer must be -37.
Subtracting a negative integer is the same thing as adding a positive integer so we change the problem to 30 + 45, which equals 75.
4. Explain what is meant by the following an illustrate with an example:
"For any real numbers, p and q, p - q = p + (-q)."
Subtracting a positive integer is the same as adding a negative integer.
For example, 10 - 4 = 6 and 10 + (-4) = 6.
5. Choose an integer between -1 and -5 on the number line and label it point P. Locate and label the following points on the number line. Show your work.
a. Point A: P - 5
Example: I choose -4.
P - 5
-4 - 5
-4 + (-5)
-9
I plugged in -4 for P. I changed -4 - 5 to -4 + (-5) since subtracting is the same as adding a negative. Since -4 and -5 are both negative, I add 4 + 5 to get 9. Since -4 and -5 are both negative, my answer is -9.
b. Point B: (P - 4) + 4
Example: I choose -4.
(P - 4) + 4
(-4 - 4) + 4
[-4 + (-4)]+4
(-8) + 4
-4
I plugged in -4 for P. I changed-4 - 4 to -4 + (-4) since subtracting is the same thing as adding a negative. Since -4 and -4 are both negative, I add 4 + 4 to get 8. Since -4 and -4 are both negative, then I get -8. I now have -8 + 4. Since -8 and 4 have different signs, I subtract 8 - 4 to get 4. Since -8 has the bigger absolute value, then my answer is -4.
c. Point C: -P - (-7)
Example: I choose - 4.
-P - (-7)
-(-4) - (-7)
4 - (-7)
4 + 7
11
I plugged in -4 for P. Since -P means the opposite of P, I have to take the opposite of -4 to get 4. Since subtracting a negative is the same as adding a positive, 4 - (-7) is the same as 4 + 7 = 11.
6. CHALLENGE PROBLEM: Write two equivalent expressions that represent the situation. What is the difference of their elevations?
"An airplane flies at an altitude of 26,000 feet. A submarine dives to depth of 700 feet below sea level."
26,000 - (-700) is equivalent to 26,000 + 700.
I would win the game now because the value of my hand is 4 and the value of my partner's hand is 9. I would win because 4 is closer to 0 than 9 is.
3. Solve the following problems.
a. (-2) + 16
14
When two integers are added together with different signs, subtract the two integers. So we subtract 16-2. The number with the bigger absolute value tells us the sign. Since 16 has the bigger absolute value and it is positive, then our answer is positive 14.
14
When two integers are added together with different signs, subtract the two integers. So we subtract 16-2. The number with the bigger absolute value tells us the sign. Since 16 has the bigger absolute value and it is positive, then our answer is positive 14.
b. (-2) - (-16)
(-2) + 16
14
Subtracting is the same thing as adding the opposite of a quantity. Subtracting a negative integer is the same thing as adding a positive integer. So we change the problem to (-2) + 16, which is the same as the problem in part a.
c. 18 – 26
18 + (-26)
-8
18 + (-26)
-8
Subtracting a positive integer is the same thing as adding a negative integer. So we change the problem to 18 + (-26). Since 18 and -26 have different signs, we subtract 26 - 18 and we get 8. Since the absolute value of -26 is bigger, our answer must be -8.
d. -14 – 23
(-14) + (-23)
-37
(-14) + (-23)
-37
Subtracting a positive integer is the same thing as adding a negative integer so we change the problem to (-14) + (-23). Since (-14) and (-23) have the same sign, we add 14 + 23 to get 37. Since both numbers are negative, our answer must be -37.
e. 30 – (-45)
30 + 45
75
30 + 45
75
Subtracting a negative integer is the same thing as adding a positive integer so we change the problem to 30 + 45, which equals 75.
4. Explain what is meant by the following an illustrate with an example:
"For any real numbers, p and q, p - q = p + (-q)."
Subtracting a positive integer is the same as adding a negative integer.
For example, 10 - 4 = 6 and 10 + (-4) = 6.
5. Choose an integer between -1 and -5 on the number line and label it point P. Locate and label the following points on the number line. Show your work.
a. Point A: P - 5
Example: I choose -4.
P - 5
-4 - 5
-4 + (-5)
-9
I plugged in -4 for P. I changed -4 - 5 to -4 + (-5) since subtracting is the same as adding a negative. Since -4 and -5 are both negative, I add 4 + 5 to get 9. Since -4 and -5 are both negative, my answer is -9.
b. Point B: (P - 4) + 4
Example: I choose -4.
(P - 4) + 4
(-4 - 4) + 4
[-4 + (-4)]+4
(-8) + 4
-4
I plugged in -4 for P. I changed-4 - 4 to -4 + (-4) since subtracting is the same thing as adding a negative. Since -4 and -4 are both negative, I add 4 + 4 to get 8. Since -4 and -4 are both negative, then I get -8. I now have -8 + 4. Since -8 and 4 have different signs, I subtract 8 - 4 to get 4. Since -8 has the bigger absolute value, then my answer is -4.
c. Point C: -P - (-7)
Example: I choose - 4.
-P - (-7)
-(-4) - (-7)
4 - (-7)
4 + 7
11
I plugged in -4 for P. Since -P means the opposite of P, I have to take the opposite of -4 to get 4. Since subtracting a negative is the same as adding a positive, 4 - (-7) is the same as 4 + 7 = 11.
6. CHALLENGE PROBLEM: Write two equivalent expressions that represent the situation. What is the difference of their elevations?
"An airplane flies at an altitude of 26,000 feet. A submarine dives to depth of 700 feet below sea level."
26,000 - (-700) is equivalent to 26,000 + 700.
Module 2 Lesson 4: Efficiently Adding Integers and Other Rational Numbers
Problem Set
1. Find the sums. Show your work to justify your answer.
a. 4 + 17
21
b. -6 + (-12)
-18
When two integers that are being added together have the same sign, add the two integers together and the sign remains the same. Since 6 + 12 = 18 and both -6 and -12 are negative, then our answer is -18.
c. 2.2 + (-3.7)
-1.5
When two integers that are being added together have different signs, subtract the two integers. We subtract 3.7 - 2.2 to get 1.5. Since -3.7 has the bigger absolute value, then our answer is -1.5.
d. -3 + (-5) + 8
-8 + 8
0
When adding more than two integers, we add two integers at a time. Since -3 and -5 are both negative, we add 3 + 5 to get 8. Since -3 and -5 are both negative, then our answer is - 8. We know that -8 + 8 = 0 because opposite quantities that are added together equal zero.
e. (1/3) + (-2 & 1/4)
(1/3) + (-9/4)
(4/12) + (-27/12)
(-23/12)
-1 & 11/12
We start by changing -2 & 1/4 to an improper fraction of -9/4. We need to find a common denominator before we can add or subtract fractions. The common denominator is 12 so 1/3 = 4/12 and (-9/4) = (-27/12). When two fractions that are being added have common denominators, we can add the numerators and the denominators remain the same. So we have 4 + (-27). Since 4 and (-27) have different signs, then we subtract 27 - 4 to get 23. Since -27 has the bigger absolute value, then our answer is -23. We now have -23/12 and we change it back to the mixed number -1 & 11/12.
2. Which of these story problems describes the sum of 19 + (-12)? Check all that apply. Show your work to justify your answer.
Jared's dad paid him $19 for raking the leaves from the yard on Wednesday. Jared spent $12 at the movie theater on Friday. How much money does Jared have left?
Jared's dad paid him $19 would be represented by 19.
Jared spending $12 at the movie theater would be represented by -12.
So this story problem can be described by 19 + (-12).
Jared owed his brother $19 for raking the leaves while Jared was sick. Jared's dad gave him $12 for doing his chores for the week. How much money does Jared have now?
Jared owing his brother $19 would be represented by -19.
Jared's dad giving him $12 would be represented by 12.
So this story problem can be described by -19 + 12.
This story problem CANNOT be described by 19 + (-12).
Jared's grandmother gave him $19 for his birthday. He bought $8 worth of candy and spent another $4 on a new comic book. How much money does Jared have left over?
Jared's grandmother giving him $19 would be represented by 19.
Jared spending $8 and $4 would be a total of $12.
Jared spending a total of $12 would be represented by -12.
So this story problem can be described by 19 + (-12).
3. Use the diagram below to complete each part.
a. Label each arrow with the number the arrow represents.
Arrow 1: +5
Arrow 2: -3
Arrow 3: -7
b. How long is each arrow? What direction does each arrow point?
Arrow 1 has a length of 5 and points to the right.
Arrow 2 has a length of 3 and points to the left.
Arrow 3 has a length of 7 and points to the left.
c. Write an equation that represents the sum of the numbers. Find the sum.
5 + (-3) + (-7) = -5
WORK:
5 + (-3) + (-7)
2 + (-7)
-5
Since 5 and -3 have different signs, then we subtract 5 - 3 to get 2. Since 5 has the bigger absolute value, we get a positive 2. Since 2 and -7 have different signs, then we subtract 7 - 2 to get 5. Since -7 has a bigger absolute value, then our answer is -5.
4. Jennifer and Katie were playing the Integer Game in class. Their hands are represented below.
Jennifer's Hand: 5 and -8
Katie's Hand: -9 and 7
a. What is the value of each of their hands? Show your work to support your answer.
Jennifer's Hand: 5 + (-8) = -3
When adding two integers with different signs, we subtract 8 -5 to get 3. Since -8 has the bigger absolute value, our answer is -3.
Katie's Hand: -9 + 7 = -2
When adding two integers with different signs, we subtract 9 - 7 to get 2. Since -9 has the bigger absolute value, our answer is -2.
b. If Jennifer drew two more cards, it is possible for the value of her hand not to change? Explain why or why not.
If Jennifer drew two more cards, it is possible for the value of her hand to not change. If Jennifer drew an integer and its opposite, then the value of her hand would not change. For example, suppose that Jennifer drew 4 and -4. We know that the sum of an integer and its opposite are equal to zero. If Jennifer draws 4 and -4, then she is really adding zero to her hand, which does not change the value of her hand.
c. If Katie wanted to win the game by getting a score of 0, what card would she need? Explain.
If Katie wanted to win the game, then she would need to draw a 2. She already has a score of -2. We know that the sum of an integer and its opposite are equal to zero so -2 + 2 would make her score 0.
d. If Jennifer drew a -1 and a -2, what would be her new score? Show your work to support your answer.
-3 + (-1) + (-2)
-4 + (-2)
-6
Jennifer has a score of -3 before she draws any new cards. If she drew a -1 and a -2, then she would have -3 + (-1) + (-2). Since -3 and -1 are both negative, then -3 + (-1) = -4. Since -4 and -2 are both negative, then -4 + (-2) = -6.
1. Find the sums. Show your work to justify your answer.
a. 4 + 17
21
b. -6 + (-12)
-18
When two integers that are being added together have the same sign, add the two integers together and the sign remains the same. Since 6 + 12 = 18 and both -6 and -12 are negative, then our answer is -18.
c. 2.2 + (-3.7)
-1.5
When two integers that are being added together have different signs, subtract the two integers. We subtract 3.7 - 2.2 to get 1.5. Since -3.7 has the bigger absolute value, then our answer is -1.5.
d. -3 + (-5) + 8
-8 + 8
0
When adding more than two integers, we add two integers at a time. Since -3 and -5 are both negative, we add 3 + 5 to get 8. Since -3 and -5 are both negative, then our answer is - 8. We know that -8 + 8 = 0 because opposite quantities that are added together equal zero.
e. (1/3) + (-2 & 1/4)
(1/3) + (-9/4)
(4/12) + (-27/12)
(-23/12)
-1 & 11/12
We start by changing -2 & 1/4 to an improper fraction of -9/4. We need to find a common denominator before we can add or subtract fractions. The common denominator is 12 so 1/3 = 4/12 and (-9/4) = (-27/12). When two fractions that are being added have common denominators, we can add the numerators and the denominators remain the same. So we have 4 + (-27). Since 4 and (-27) have different signs, then we subtract 27 - 4 to get 23. Since -27 has the bigger absolute value, then our answer is -23. We now have -23/12 and we change it back to the mixed number -1 & 11/12.
2. Which of these story problems describes the sum of 19 + (-12)? Check all that apply. Show your work to justify your answer.
Jared's dad paid him $19 for raking the leaves from the yard on Wednesday. Jared spent $12 at the movie theater on Friday. How much money does Jared have left?
Jared's dad paid him $19 would be represented by 19.
Jared spending $12 at the movie theater would be represented by -12.
So this story problem can be described by 19 + (-12).
Jared owed his brother $19 for raking the leaves while Jared was sick. Jared's dad gave him $12 for doing his chores for the week. How much money does Jared have now?
Jared owing his brother $19 would be represented by -19.
Jared's dad giving him $12 would be represented by 12.
So this story problem can be described by -19 + 12.
This story problem CANNOT be described by 19 + (-12).
Jared's grandmother gave him $19 for his birthday. He bought $8 worth of candy and spent another $4 on a new comic book. How much money does Jared have left over?
Jared's grandmother giving him $19 would be represented by 19.
Jared spending $8 and $4 would be a total of $12.
Jared spending a total of $12 would be represented by -12.
So this story problem can be described by 19 + (-12).
3. Use the diagram below to complete each part.
a. Label each arrow with the number the arrow represents.
Arrow 1: +5
Arrow 2: -3
Arrow 3: -7
b. How long is each arrow? What direction does each arrow point?
Arrow 1 has a length of 5 and points to the right.
Arrow 2 has a length of 3 and points to the left.
Arrow 3 has a length of 7 and points to the left.
c. Write an equation that represents the sum of the numbers. Find the sum.
5 + (-3) + (-7) = -5
WORK:
5 + (-3) + (-7)
2 + (-7)
-5
Since 5 and -3 have different signs, then we subtract 5 - 3 to get 2. Since 5 has the bigger absolute value, we get a positive 2. Since 2 and -7 have different signs, then we subtract 7 - 2 to get 5. Since -7 has a bigger absolute value, then our answer is -5.
4. Jennifer and Katie were playing the Integer Game in class. Their hands are represented below.
Jennifer's Hand: 5 and -8
Katie's Hand: -9 and 7
a. What is the value of each of their hands? Show your work to support your answer.
Jennifer's Hand: 5 + (-8) = -3
When adding two integers with different signs, we subtract 8 -5 to get 3. Since -8 has the bigger absolute value, our answer is -3.
Katie's Hand: -9 + 7 = -2
When adding two integers with different signs, we subtract 9 - 7 to get 2. Since -9 has the bigger absolute value, our answer is -2.
b. If Jennifer drew two more cards, it is possible for the value of her hand not to change? Explain why or why not.
If Jennifer drew two more cards, it is possible for the value of her hand to not change. If Jennifer drew an integer and its opposite, then the value of her hand would not change. For example, suppose that Jennifer drew 4 and -4. We know that the sum of an integer and its opposite are equal to zero. If Jennifer draws 4 and -4, then she is really adding zero to her hand, which does not change the value of her hand.
c. If Katie wanted to win the game by getting a score of 0, what card would she need? Explain.
If Katie wanted to win the game, then she would need to draw a 2. She already has a score of -2. We know that the sum of an integer and its opposite are equal to zero so -2 + 2 would make her score 0.
d. If Jennifer drew a -1 and a -2, what would be her new score? Show your work to support your answer.
-3 + (-1) + (-2)
-4 + (-2)
-6
Jennifer has a score of -3 before she draws any new cards. If she drew a -1 and a -2, then she would have -3 + (-1) + (-2). Since -3 and -1 are both negative, then -3 + (-1) = -4. Since -4 and -2 are both negative, then -4 + (-2) = -6.
Module 2 Lesson 3: Understanding Addition of Integers
Problem Set
1.Below is a table showing the change in temperature from morning to afternoon for one week.
a. Use the vertical number line to help you complete the table. As an example, the first row is completed for you.
b. Do you agree or disagree with the statement: "A rise of -7C"? Explain.
I disagree with this statement. We would say that the temperature fell 7C when we are talking about the temperature going down.
For questions 2-3, refer to the Integer Game.
2. Terry selected two cards. The sum of her cards is -10.
a. Can both cards be positive? Explain why or why not.
Both cards cannot be positive. In order for the sum of two cards to be negative, at least one of the cards must be a negative number.
b. Can one of the cards be positive and the other be negative? Explain why or why not.
One card can be positive and one card can be negative if the negative number has a larger absolute value. For example, suppose that Terry selected the cards 10 and -20. Her sum would be represented by 10 + (-20). Since we are adding integers with different signs, we subtract 20 - 10 to get 10. Since the absolute value of -20 is larger, then our answer would be -10.
c. Can both cards be negative? Explain why or why not.
Both cards can be negative. For example, suppose that Terry selected the cards -4 and -6. Her sum would be represented by (-4) + (-6). Since we are adding two negative integers, we have 4 + 6 = 10. Since both -4 and -6 are negative, our answer is -10.
3. When playing the Integer Game, the first two cards you selected were -8 and -10.
a. What is the value of your hand? Write an equation to justify your answer.
-8 + (-10) = -18
When adding two negative integers, we add the absolute value of the integers and our answer is negative. We add 8 + 10 to get 18 and our answer would be - 18.
b. For part (a), what is the distance of the sum from -8? Does the sum lie to the right or the left of -8 on the number line?
The distance of the sum from -8 would be 10 since the distance between -8 and -18 is 10. The sum lies to the left of -8 on a number line.
c. If you discarded the -10 and then selected a 10, what would be the value of your hand? Write an equation to justify your answer.
If we discarded -10 and selected a 10, then our new hand would be -8 + 10 = 2. Since we are adding two integers with different signs, we subtract 10 - 8 to get 2. Since 10 has the bigger absolute value, then our answer is 2.
4. Given the expression 67 + (-35), can you determine, without finding the sum, the distance between 67 and the sum? Is the sum to the right or left of 67 on the number line?
Since we are adding -35 to 67, then the distance between 67 and the sum is 35. The sum would be to the left of 67 on a number line.
5. Use the information given below to write an equation. Then create an "arrow diagram" of this equation on the number line provided below.
"The p-value is -4, and the sum lies 12 units to the right of the p-value."
-4 + 12 = 8
The p-value is the starting value and sum means that this is an addition problem. Since we are adding two integers with different signs, then we subtract 12 - 4 to get 8. Since 12 has the bigger absolute value, then our answer is 8.
1.Below is a table showing the change in temperature from morning to afternoon for one week.
a. Use the vertical number line to help you complete the table. As an example, the first row is completed for you.
Change
in Temperatures from Morning to Afternoon
Morning
Temperature
|
Change
|
Afternoon Temperature
|
Number Sentence
|
1C
|
rise
of 3C
|
4C
|
1 + 3 = 4
|
2C
|
rise
of 8C
|
10C
|
2 + 8 = 10
|
-2C
|
fall
of 6C
|
-8C
|
-2 + (-6) = -8
|
-4C
|
rise
of 7C
|
3C
|
-4 + 7 = 3
|
6C
|
fall
of 9C
|
-3C
|
6 + (-9) = -3
|
-5C
|
fall
of 5C
|
-10C
|
-5 + (-5) = -10
|
7C
|
fall
of 7C
|
0C
|
7 + (-7) = 0
|
b. Do you agree or disagree with the statement: "A rise of -7C"? Explain.
I disagree with this statement. We would say that the temperature fell 7C when we are talking about the temperature going down.
For questions 2-3, refer to the Integer Game.
2. Terry selected two cards. The sum of her cards is -10.
a. Can both cards be positive? Explain why or why not.
Both cards cannot be positive. In order for the sum of two cards to be negative, at least one of the cards must be a negative number.
b. Can one of the cards be positive and the other be negative? Explain why or why not.
One card can be positive and one card can be negative if the negative number has a larger absolute value. For example, suppose that Terry selected the cards 10 and -20. Her sum would be represented by 10 + (-20). Since we are adding integers with different signs, we subtract 20 - 10 to get 10. Since the absolute value of -20 is larger, then our answer would be -10.
c. Can both cards be negative? Explain why or why not.
Both cards can be negative. For example, suppose that Terry selected the cards -4 and -6. Her sum would be represented by (-4) + (-6). Since we are adding two negative integers, we have 4 + 6 = 10. Since both -4 and -6 are negative, our answer is -10.
3. When playing the Integer Game, the first two cards you selected were -8 and -10.
a. What is the value of your hand? Write an equation to justify your answer.
-8 + (-10) = -18
When adding two negative integers, we add the absolute value of the integers and our answer is negative. We add 8 + 10 to get 18 and our answer would be - 18.
b. For part (a), what is the distance of the sum from -8? Does the sum lie to the right or the left of -8 on the number line?
The distance of the sum from -8 would be 10 since the distance between -8 and -18 is 10. The sum lies to the left of -8 on a number line.
c. If you discarded the -10 and then selected a 10, what would be the value of your hand? Write an equation to justify your answer.
If we discarded -10 and selected a 10, then our new hand would be -8 + 10 = 2. Since we are adding two integers with different signs, we subtract 10 - 8 to get 2. Since 10 has the bigger absolute value, then our answer is 2.
4. Given the expression 67 + (-35), can you determine, without finding the sum, the distance between 67 and the sum? Is the sum to the right or left of 67 on the number line?
Since we are adding -35 to 67, then the distance between 67 and the sum is 35. The sum would be to the left of 67 on a number line.
5. Use the information given below to write an equation. Then create an "arrow diagram" of this equation on the number line provided below.
"The p-value is -4, and the sum lies 12 units to the right of the p-value."
-4 + 12 = 8
The p-value is the starting value and sum means that this is an addition problem. Since we are adding two integers with different signs, then we subtract 12 - 4 to get 8. Since 12 has the bigger absolute value, then our answer is 8.
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