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.
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