Download Math Fundamentals for Statistics I (Math 52) Homework Unit 3

Math Fundamentals for
Statistics I (Math 52)
Homework Unit 3:
Addition and Subtraction
By Scott Fallstrom and Brent Pickett
“The ‘How’ and ‘Whys’ Guys”
This work is licensed under a Creative Commons AttributionNonCommercial-ShareAlike 4.0 International License
3rd Edition (Summer 2016)
Math 52 – Homework Unit 3 – Page 1
Table of Contents
This will show you where the homework problems for a particular section start.
3.1: Place Value – The Addition Edition ....................................................................................................2
3.2: Addition .................................................................................................................................................3
3.3: Addition Properties...............................................................................................................................5
3.4: Adding Integers using Chips................................................................................................................5
3.5: Adding Integers Without Chips ..........................................................................................................6
3.6: Adding Fractions (Rational Numbers) ...............................................................................................9
3.7: Adding Decimals .................................................................................................................................12
3.8: Adding Values on a Number Line .....................................................................................................13
3.9: Applications of Addition and Concept Questions ............................................................................14
3.10: Addition Wrap-Up (Practice) ..........................................................................................................16
3.11: Subtraction ........................................................................................................................................18
3.12: Subtracting Integers using Chips ....................................................................................................19
3.13: Subtracting Integers (without chips) ..............................................................................................20
3.14: Number Sense and Addition/Subtraction ......................................................................................21
3.15: Subtracting with Number Lines ......................................................................................................23
3.16: Subtracting Fractions, Decimals, and More ...................................................................................24
3.17: Estimation, Property Review, and Magic Boxes ............................................................................25
3.18: Subtraction Summary ......................................................................................................................27
3.1: Place Value – The Addition Edition
Vocabulary and symbols – write out what the following mean:

No New Terms
Concept questions:
1. Could you write 3,000 as groups of ten? What about groups of hundred?
2. A question on Jeopardy was “The amount of pennies for $6,000.” A contestant answered “six
thousand hundred and Alex Trebek said the answer was incorrect. Later, the judges reversed the
decision. Explain why.
Exercises:
3. What are two different ways we could describe the following values but using different names (as
above):
a. 650
b. 9,800
c. 510,000
d. 3,800,000
Math 52 – Homework Unit 3 – Page 2
4. Re-write the following in standard notation. “16 tens” would be written as 160 in standard place value
notation.
a. 8.3 tens
e. 0.413 ten thousand
b. 6.2 hundreds
f. 400 tenths
c. 57 thousands
g. 2,900 hundredths
d. 13.25 million
h. 0.0038 million
5. What is the appropriate value (way to write) for:
a. Eleven $10 bills and fifteen $1 bills?
b. Twenty-five $10 bills and thirty-one $1 bills?
c. Four $100 bills and fifty-three $10 bills and fourteen $1 bills?
Wrap-up and look back:
6. Write in words what you learned from this first section.
7. Are there different ways to write a number and keep the same value?
8. Can you read 8,000 in more than one way? Give at least two.
9. Is it acceptable to read 800 as “eighty hundreds”?
10. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.2: Addition
Vocabulary and symbols – write out what the following mean:


Addends
Sum


Algorithm
Regrouping


Like Terms
+
Concept questions:
1. Can you add 3 pencils and 5 pens? Why or why not?
2. Markus says 8 cherries and 4 pears is 12 pieces of fruit. Is this correct?
3. Can we add 3 sevenths to 5 eighths? Why or why not?
4. Can we add 5 glorks to 23 glorks? Why or why not?
Exercises:
5. Add like terms.
a. 11 hats + 4 coats + 7 coats + 5 hats + 3 coats
b. 7 negatives + 2 positives + 4 negatives + 2 negatives + 8 positives
c. 8x + 7y + 2x + 5x + 12y
d.
e.
f.
g.
2 6  7 19  5 6  3 19  19
4 sevenths + 9 fifths + 3 sevenths + 2 fifths
4 A  3B  2C  3D  4B  3D  4C  6B  5D  3A
6  7  9  20  5  61  10
Math 52 – Homework Unit 3 – Page 3
6. Rewrite using regrouped addends.
a. (at least two ways) 37 =
b. (at least two ways) 55 =
c. (at least four ways) 628 =
d. (at least four ways) 90 =
7. Use any of the algorithms shown to practice doing addition. Rewrite the following and add vertically –
regroup when necessary:
a. 58 + 37
e. 3,944 + 899
b. 629 + 421
f. 8,384 + 2,998
c. 89 + 53
g. 5,204 + 3,788
d. 54 + 25
h.
19,388,135  62,483,984
Wrap-up and look back:
8. Write in words what you learned from this first section.
9. Which algorithm was your favorite? Why?
10. Do you see any strengths or weaknesses for different algorithms?
11. Did you grow up learning about “carrying”? Why do we not say “carrying” anymore?
12. A neighbor is learning the new Common Core math. One of the algorithms listed was called lattice
addition. Here’s how you would add 297 + 45.
a. Start by writing the two numbers vertically. Under each place value, draw a box with a
diagonal (slash).
2
+
9
7
4
5
b. Add the digits in each place value and write the result in the corresponding box.
2
+
0
9
7
4
5
1
2
1
3
2
c. Now add down the diagonals to get the final result.
2
+
0
9
7
4
5
1
2
3
1
3
4
2
2
d. Do you see how this method works? What other algorithm is this similar to?
Math 52 – Homework Unit 3 – Page 4
13. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.3: Addition Properties
Vocabulary and symbols – write out what the following mean:


Commutative Property of Addition
Associative Property of Addition


Identity Property of Addition
Additive Identity Element
Concept questions:
1. Which property allows us to regroup the addends?
2. Which property allows us to change the order of the addends?
3. Which property allows us to add a number and not change the value?
Exercises:
4. Determine which property is being used in each step. [There may be more than one!]
a.
b.
c.
d.
e.
f.
g.
38 + 15 = 15 + 38
23 + (6 + 5) = (23 + 6) + 5
14 + (9 + 7) = 14 + (7 + 9) = (14 + 7) + 9
72  0  72
0+7=7+0=7
12 + (8 + 3) = (8 + 3) + 12
(99 + 273) + 1 = (273 + 99) + 1 = 273 + (99 + 1)
Wrap-up and look back:
5. If you were given the problem (99 + 273) + 1,
a. which numbers would you prefer to add first? Explain why.
b. Which property allows you to add the numbers you wanted to instead of the 99 and 273?
6. Which property do you use most?
7. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.4: Adding Integers using Chips
Vocabulary and symbols – write out what the following mean:


Value of a black chip
Value of a red chip

Zero Pair
Math 52 – Homework Unit 3 – Page 5
Concept questions:
1. When you put one red chip and one black chip together, what do you get?
2. Can you write the number 5 using chips in more than one way? How?
Exercises:
3. Represent the number listed using poker chips in at least two ways using zero pairs.
a. – 4
b. 1
c. 5
d. 6
e. – 2
f. 0
4. Draw a chip diagram and determine the value of the expression; use zero pairs when necessary.
a. (– 2) + 3
b. (– 3) + (– 4)
c. 5 + (– 6)
d. (– 1) + (– 3)
e. 4 + (– 6)
f. 7 + (– 2)
5. Using the chips, would you get the same result from 4 + (– 6) and (– 6) + 4? Explain what property
this relates to.
6. Could the chips be used to find the result of (– 3) + (– 4) + 5? Draw a diagram to illustrate this.
Wrap-up and look back:
7. How would you explain adding 3 + (– 5) with chips?
8. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.5: Adding Integers Without Chips
Vocabulary and symbols – write out what the following mean:




Additive Inverse (of a number)
Additive Inverse Property
Absolute Value
Size




Sign
 x 
Negative
x
Concept questions:
1. What is one way to interpret  3 ?
2. What is the additive inverse of – 13? Why?
Math 52 – Homework Unit 3 – Page 6
3. Does every number have an additive inverse? What about the number π?
4. What was your rule for adding integers and finding the sign of the sum?
5. If we want to find the sum more quickly by increasing the size of one addend by 4, what do we need to
do to the other addend? Why?
Exercises:
6. Find the following values and describe in words what it represents.
a.  17 
d.   197
c.  3,140
f.
e.  0
b.   19
  9,817
7. Combine the like objects quickly. Do not combine negatives and positives at this stage!
a.  11  5  3   5  8
d. 15  23   19  4   37
c.  31  87   9  12   3
f.
b. 3   5  2   1   3
e.  63  14   21   4  8 8  8
9  8   6  12   13
8. Find the following values and describe in words what it represents.
a.
 62
d.
0
b. 8.5
e.   514
c.  111
f.
   39
9. Fill out the table concerning value, size, and sign; the first is done as an example.
a.
Value
Absolute value (Size)
Sign
88
88
Positive
47
Positive
2,319
Negative
– 92
b.
c.
694
d.
e.
f.
  93
0
Math 52 – Homework Unit 3 – Page 7
10. Place the correct symbol (  ,  , or =) between the following numbers:
a.
 38
17
b.
–5
–9
c.
5
9
d.
 5
  5
e.
– 87
87
f.
 87
87
g.
 87
  87
h.
 213
 345
i.
– 213
– 345
j.
 213
– 345
k.
– 213
 345
l.
– 45
27
m.
 45
27
n.
 45
27
11. Identify the sign of the sum. Use the rule you created previously to help you circle the “sign” of the
sum… positive (P), negative (N), or zero (Z).
Sign
Sign
a.
 97  78
P
N
Z
c.
35   59
P
N
Z
e.
28   16
P
N
Z
g.
 96   32
P
N
Z
b.
 78  56
P
N
Z
d.
 43  43
P
N
Z
f.
43  726
P
N
Z
h.
6,197   3,342
P
N
Z
12. Find the value of the sums using the methods shown in this section.
a.  28  88
f.
 53  47
b. 49   59
g.
96   37
c. 43   26
h.
 74  167
d.
 13   56
i.
2,197   3,342
e.
 27  13
j.
3,568   342  1,739
Math 52 – Homework Unit 3 – Page 8
13. Practice finding these sums quickly by regrouping addends (as shown in this section – no calculator).
a. 37 + 89
b. 99 + 285
c. 4,392 + 499
d. 6,997 + 2,318
e. 689 + 497
f. 67,999 + 802
Wrap-up and look back:
14. Did the speedy method for regrouping addends during addition work well for you? How did it
compare with the other algorithms?
15. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.6: Adding Fractions (Rational Numbers)
Vocabulary and symbols – write out what the following mean:


Numerator
Denominator


FLOF
Common Denominators
Concept questions:
1. When we defined fractions as rational number, we showed that the denominator can’t be 0. Type this
into your calculator: 5 ÷ 0. What does the calculator say?
2. How could you describe the location of
3
on a number line from 0 to 1?
5
3. What does FLOF allow us to do?
4. Can two fractions be equal if they have different numerators and different denominators?
5. Can two fractions be equal if they have the same numerators and different denominators?
6. Can two fractions be equal if they have the same denominators and different numerators?
5
?
6
3
8. If you had a number line from 0 to 1, how could you find the location of ?
7
Exercises:
7. If you had a number line from 0 to 1, how could you find the location of
Math 52 – Homework Unit 3 – Page 9
9. Find some equivalent fractions using FLOF: (find at least 3 equivalent fractions for each)
a.
1

3


c.
1

6


b.
3

7


d.
3

8


10. Add the fractions; the first is been done for you.
3 2 5 3  2  5 10
a.
  

9 9 9
9
9
b.
3
6

17 17
c. 
2 9 8
 
19 19 19
d.
51  23 
 

613  613 
e.
47
52
13


984 984 984
11. Place the correct symbol (  ,  , or =) between the following numbers – no calculator!
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
7
13
8
9
8
9
5
16
2
9
2

9
4
7
4
13
4
3
11
5
1
2
10
11
9
11
3
8
1
4
1

4
5
7
2
13
4
9
11
7
12. Based on the table above, if two fractions have the same numerator with different denominators,
which is larger?
Math 52 – Homework Unit 3 – Page 10
13. Based on the table above, if two fractions have the same denominator with different numerators,
which is larger?
14. Regarding the number line below, label the missing tick marks using fraction notation.
a.
0
1
b.
0
1
c.
0
1
d.
0
1
15. Add the fractions – make sure you use a common denominator!
a.
b.
c.
d.
e.
f.
g.
h.
1 3

4 8
1 3

2 8
 1 5
  
 2 8
3  7
  
4  8
 8  1
    
 9  3
6 1

7 3
9  7 
  
20  30 
2 7

15 5
i.
j.
k.
l.
m.
n.
o.
p.
 7 8
  
 10  15
11 7

24 8
7 1

11 4
5 7

12 8
4 7
 
31 18
41  31 
  
49  42 
11 59

80 75
32 25

111 39
Wrap-up and look back:
16. If two numbers have the same denominator, does that mean they have the same value?
17. If two numbers have the same numerator, does that mean they have the same value?
Math 52 – Homework Unit 3 – Page 11
18. If the numerators are the same, why does a larger denominator make for a smaller fraction?
19. If the denominators are the same, why does a larger numerator make for a larger fraction?
20. Why do we need common denominators when adding fractions?
21. Will your calculator be able to handle all fraction problems? Explain when it will stop working in
fraction mode.
22. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.7: Adding Decimals
Vocabulary and symbols – write out what the following mean:

None
Concept questions:
1. Lamar added 0.5 and 2.3 and ended up with 2.8. Is this correct? Why or why not.
2. Mariam added 0.05 and 2.3 and ended up with 2.8. Is this correct? Why or why not.
3. What would the sign be for (6.3) + (– 2.8)? Explain your answer.
4. What would the sign be for (1.3) + (– 2.8)? Explain your answer.
Exercises:
5. Add the decimals; write additional 0’s where needed but don’t change the value of the addends.
a. 35.2 + 1.87
f. 5.2 + 3.94 + 2.814
b. 16.903 + 58.24
g. 14.93 + 0.0593 + 6.58
c. 0.0249 + 0.3942
h.
6.24394 + 29.934 + 1.58301 + 8.8695
d. 17.302 + 9.2483
+ 0.00342
e. 3,402.8 + 583.54
i. 5.82 + (– 3.11)
Wrap-up and look back:
6. Is there anything you need to do with decimals that is different than integers?
7. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
Math 52 – Homework Unit 3 – Page 12
3.8: Adding Values on a Number Line
Vocabulary and symbols – write out what the following mean:

Tip-to-Tail
Concept questions:
1. Will 4 + 2 end at the same place as 2 + 4? Explain.
2. Will 4 + 2 look the same with arrows as 2 + 4? Why or why not.
Exercises:
3. Use a number line, like the one below, to find the result of:
a. 4 + 2
d. 11 + 2
b. 6 + 3
e. 6 + 3 + 5
c. 8 + 5
f. 7 + 5 + 4
4. Use a number line, like the one below, to find the result of:
a. 4 + (– 2)
e. (– 4) + 7
b. 3 + (– 7)
f. 7 + (– 4)
c. (– 2) + (– 4)
g.
d. (– 8) + 5
h. 5   3   4
 3  6   2
5. Find the region that best approximates the following values.
a. 3.
e. A + B.
b. – 2.
f. D + (– 3).
c. B + 2.
g. B + (– A).
d. A + C.
h. C + C.
A
R1
B
R2
R3
0
C
R4
1
D
R5
R6
Math 52 – Homework Unit 3 – Page 13
6. Approximate the sum using the number line:
a.
4 5
0
b.
1
2
3 6
3
7 9
c.
4
5
Wrap-up and look back:
7. Is it true that
A  B  A  B ? Explain why it is true, or find some numbers that show it is NOT
true.
8. Conceptually, if we have A + B and B is positive, will the result be to the left or right of A on the
number line?
9. Conceptually, if we have A + B and B is negative, will the result be to the left or right of A on the
number line?
10. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.9: Applications of Addition and Concept Questions
Vocabulary and symbols – write out what the following mean:

Perimeter
Concept questions:
1. Mickey did the perimeter of a rectangle with sides of 8 inches and 10 inches and found the perimeter
was 18 inches by adding the numbers. Is he correct, and if not, what did he do wrong?
2. Maureen did the perimeter of a triangle with sides of 8 inches, 9 inches, and 10 inches and found the
perimeter was 27 inches by adding the numbers. Is she correct, and if not, what did she do wrong?
Exercises:
3. Where would the diver end up if…
a. He starts at a depth of 35 feet and rises 12 feet?
b. She starts at a depth of 15 feet and drops 30 feet?
c. She starts at a depth of 27 feet, then drops 41 feet, then rises 15 feet?
Math 52 – Homework Unit 3 – Page 14
4. Find the perimeter of the following shapes:
a. Rectangle with sides of 12 inches and 16 inches.
b. Rectangle with sides of 23 yards and 40 yards.
c. Rectangle with sides of 435 inches and 582 inches.
d. Rectangle with sides of K and M.
e. Rectangle with sides of P and .
f. Rectangle with sides of 3 feet and 16 inches (find the result in inches).
g. Triangle with sides of 17 inches, 28 inches, and 13 inches.
h. Triangle with sides of 7 feet, 8 feet, and 11 feet.
i. Triangle with sides of 13 miles, 10 miles and 12 miles.
j. Triangle with sides of A, B, and C.
5. How much money is in an account if…
a. It starts with $200 and the bank adds a fee of $25?
b. It starts with $310 and the bank adds a fee of $35?
c. It starts with $ – 84 and the owner puts in $42?
d. It starts with $ – 91 and the owner puts in $57?
e. It starts with $ – 91 and the owner puts in $107?
6. Postal applications:
For the US Postal Service (USPS), commercial parcels have a condition that the length (longest side) +
girth (distance around thickest part not including length) cannot exceed 108 inches.
Determine whether these parcels could be mailed:
a.
c.
4 inches
19 inches
8 inches
29 inches
16 inches
23 inches
b.
d.
6 inches
10 inches
9 inches
2 feet
19 inches
1 foot, 4 inches
NOTE: for part (a), the longest side is 16 inches. The girth would be the distance around the 4 inch by 8
inch rectangle. So the longest side is 16 inches and the girth is 24 inches, for a total of 40 inches. Since
this is less than 108 inches, it is able to be mailed with USPS.
Math 52 – Homework Unit 3 – Page 15
7. Application problems:
a. A football team runs the following plays starting on their 20 yard line: + 5 yards, – 6 yards, + 10
yards, – 15 yards. Where is the ball located after all four plays?
b. In a checking account, there is $ – 65. The account owner puts in $40. What is the ending balance?
8. Add the following expressions.

a. 27 x  4 y  9 x   5 y 
b.  19 x   5 y   9 x  15 y
c. 31x  7 y   12 x   9 y

d. 13x  11x 2  56 x   2 x 2
e.  13x  7 y  9   8x   7
f.  14 x  28 y   3x    52 y 
Wrap-up and look back:
9. Which of the application problems was your favorite? Why?
10. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.10: Addition Wrap-Up (Practice)
Vocabulary and symbols – write out what the following mean:










Perimeter
Tip-to-Tail
Numerator
Denominator
FLOF
Common Denominators
Additive Inverse (of a
number)
Additive Inverse Property
Absolute Value
Size




Sign
 x 
Negative
x




Value of a black chip
Value of a red chip
Zero Pair
Commutative Property of
Addition
Associative Property of
Addition









Addends
Sum
Algorithm
Regrouping
Like Terms
+
Identity Property of
Addition
Additive Identity Element
Concept questions:
1. Mickey found the perimeter of a rectangle with sides of 8 inches and 10 inches by adding the numbers
and got 18 inches. Is he correct, and if not, what did he do wrong?
2. Maureen found the perimeter of a triangle with sides of 8 inches, 9 inches, and 10 inches by adding the
numbers and got 27 inches. Is she correct, and if not, what did she do wrong?
Math 52 – Homework Unit 3 – Page 16
Exercises:
3. Complete the summary problems from the unit:
a. 7 + 19 + 25 + 41
b. 9,694 + 498
c. 297 + 573
j.
k.
d.  8   23
e.  28   43   7
f.
l.
m.
n.
o.
 68   41
g.  9  93   11  13   54
3 1

8 4
7  3
i.
  
11  4 
s. 3 oranges + 8 footballs + 6 oranges + 5 footballs
h.
 7 2
  
 10  15
31  16 

 
7 7
6.84 + 2.938
623.49 + 84.52
– 6.13 + (– 12.8)
16.2   38.9
p. 17  42   13 
q. 24 x   7 y   5 y   8x 

 
 
2 7   11 2   4 7   152 2
r.

4.
If B is…
Then A + B is…
a.
Positive
Greater than A
Less than A
Equal to A
b.
Negative
Greater than A
Less than A
Equal to A
c.
Zero
Greater than A
Less than A
Equal to A
5. More practice by type:
(Whole Numbers)
a. 4  11  16  9
b. 467  9,385
(Integers)
c.  4   11
e.  16   35
d.  42   59
f.
(Fractions)
3 7

g.
4 8
7  1
h.
  
8  12 
(Decimals)
k. 30.27  15.8
l. 39.21  3.8
i.
j.
 9  7   11  13   24
 9 7
  
 10  15
3  10 
   
7  7
m.  4.2  5.9
n. 2.3   42.6
Math 52 – Homework Unit 3 – Page 17
(Mixed Bag)
o. 7  9   3 
p. 13x   7 y   9 y   8x 
q. 3 oranges + 8 footballs + 6 oranges
r. 3 7  5 2   8 7  19 2


Wrap-up and look back:
11. Sums of integers are always positive (P), always negative (N), or sometimes positive and sometimes
negative (S). Determine the following:
Expression
pos + pos
Sign (circle one)
P
S
N
pos + neg
P
S
N
neg + pos
P
S
N
neg + neg
P
S
N
Examples or Explanation
3.11: Subtraction
Vocabulary and symbols – write out what the following mean:




Minuend
Subtrahend
Difference
“–”
Concept questions:
1. Why was the traditional algorithm not used with 5,000 – 251? What method was quicker and easier?
2. In the cashier algorithm, what does the first number said represent?
3. Why is the traditional algorithm presented in most classrooms? Do you feel there is an algorithm that
is easier to use?
4. Tracy said that 46m – 22m = 24, because 46 – 22 = 24, and then the m’s subtract. Is she correct?
Explain.
5. When using equal addends, how do you determine whether you add or subtract a number?
Exercises:
6. Use the cashier algorithm to solve these subtraction problems:
a. 47 – 29
c. 75 – 34
b. 45 – 21
d. 105 - 87
7. Use the equal addends to solve these subtraction problems:
a. 9,000 – 2,593
b. 784 – 399
c. 62 – 38
d. 294 – 199
e. 801 – 299
f. 60,000 – 5,204
Math 52 – Homework Unit 3 – Page 18
8. Solve these subtraction problems using different algorithms. You are in charge of picking different
algorithms based on the problems!
a. 737 – 349
f.
1,945,392 – 395,238
b. 3,752 – 2,631
g.
788,325,594 – 98,447,452
c. 784 – 458
h. 67x – 25x
d. 4,731 – 854
i. 156m – 89m
e. 200,000 – 15,874
j. 878w – 489w
Wrap-up and look back:
16. Do you need to use the same algorithm for each problem?
17. Is there only one way to find a difference?
18. Richard said that the subtrahend – minuend = difference. Is he correct?
19. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.12: Subtracting Integers using Chips
Vocabulary and symbols – write out what the following mean:

Zero pairs
Concept questions:
1. What is the hardest part about subtracting with the chips?
2. If you had BBB – BB, do you need to put in any zero pairs? Why or why not?
3. If you had BBBB – RR, do you need to put in any zero pairs? Why or why not?
4. If you had BB – BBBB, do you need to put in any zero pairs? Why or why not?
5. If you had RRRR – RRR, do you need to put in any zero pairs? Why or why not?
Exercises:
6. Draw a picture for each and indicate the putting in (addition) or taking away (subtraction). Use zero
pairs if needed!
a. (– 5) – (– 2)
d. 4 + (– 7)
b. (– 4) – (– 6)
e. 5 – (– 3)
c. 4 – 7
f. 5 + 3
Math 52 – Homework Unit 3 – Page 19
7. Rewrite all subtractions problems using addition, but do not compute the result.
a. 628 – 39
b. – 25 – 49
c. 51 – 23 – (– 59) –28
d. – 28 – 19
e. 74 – (– 21)
f. – 41 + 37 – 18 – (– 33)
Wrap-up and look back:
8. How can we rewrite a – b?
9. How can we rewrite X – (– M)?
10. Explain why a subtracting a negative number gives the same result as adding the opposite.
11. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.13: Subtracting Integers (without chips)
Vocabulary and symbols – write out what the following mean:

None
Concept questions:
1. When subtracting integers, do we write the number with the biggest size on top or bottom in
traditional algorithms?
2. If we add integers with the same sign, do we use addition or subtraction? Why?
3. If we add integers with the different sign, do we use addition or subtraction? Why?
Exercises:
4. Write these problems using addition, then combine with either addition or subtraction
a. – 415 – 58
b. – 415 – (– 58)
c. 75 – 143
d. 75 – (– 143)
e. 295 – 69
f. 295 – (– 69)
5. Rewrite all subtractions to turn the entire problem into additions, then combine all like terms, and then
perform the final computation.
a. – 4 – (– 8) – 7 + (– 11)
b. 13 – (– 7) – 12 + (– 35)
c. – 4 – (– 8) – 7 + (– 11) – 9 – (– 15)
d. – 4 + (– 8) + 7 + (– 11) – 9 – (– 15)
e. – 42 + (– 81) – 73 – (– 25) – 19 – (– 35)
Math 52 – Homework Unit 3 – Page 20
6. Find the additive inverse (opposite) of the following:
a. 15x
b. – 25x
c. 9 + x
d. – 5x + 91
e. m + n + 7
f. 19 – 25x
7. Explain in words what the expression means, and find the value.
a.  20  x 
b.   98x 
c.  5  77 x 
d.  23x  159
e.   23x  159
f.  23x  159
Wrap-up and look back:
8. Why is it quick to rewrite long problems (with subtraction and addition of positive and negative
numbers) as just addition?
9. Write a “+” under a term if we add it as a positive and “–” under a term if we add it as a negative. Try
to do this without rewriting each using addition or subtraction.
a. (– 42) + (– 81) – 73 – (– 25) – 19 – (– 35)
b. (– 4) – (– 8) – 7 + (– 11) – 9 – (– 15)
10. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.14: Number Sense and Addition/Subtraction
Vocabulary and symbols – write out what the following mean:


Size
Sign
Concept questions:
1. When subtracting integers, we can rewrite it using addition. How would we rewrite a – b?
2. If we add numbers with the same sign, then we add (size or sign) and keep the (size or sign).
3. If we add numbers with different signs, then we add (size or sign) and keep the (size or sign).
Exercises:
4. Determine if the result is larger or smaller.
a. 16 + (pos) is (larger/smaller) than 16.
b. – 45 + (pos) is (larger/smaller) than – 45.
c.
16 + (neg) is (larger/smaller) than 16.
d. – 45 + (neg) is (larger/smaller) than – 45.
Math 52 – Homework Unit 3 – Page 21
e. 16 – (pos) is (larger/smaller) than 16.
f. – 45 – (pos) is (larger/smaller) than – 45.
g. 16 – (neg) is (larger/smaller) than 16.
h. – 45 – (neg) is (larger/smaller) than – 45.
5. To summarize the results, we can make a list of what we saw with addition:
a.
If B is…
0
Then A + B will be …
Greater than A
Less than A
Equal to A
b.
Positive
Greater than A
Less than A
Equal to A
c.
Negative
Greater than A
Less than A
Equal to A
6. To summarize the results, we can make a list of what we saw with subtraction:
a.
If B is…
0
Then A – B will be …
Greater than A
Less than A
Equal to A
b.
Positive
Greater than A
Less than A
Equal to A
c.
Negative
Greater than A
Less than A
Equal to A
7. Determine the size and sign of the sum or difference without performing any operations.
Operation
Resulting Sign
Value is…
a.
 57   5
Pos
Neg
Zero
Greater than – 57
Less than – 57
b.
 32   5
Pos
Neg
Zero
Greater than – 32
Less than – 32
c.
 94  6.5
Pos
Neg
Zero
Greater than – 94
Less than – 94
d.
4.26  6.5
Pos
Neg
Zero
Greater than 4.26
Less than 4.26
e.
 89   89
Pos
Neg
Zero
Greater than – 89
Less than – 89
f.
23  65
Pos
Neg
Zero
Greater than 23
Less than 23
g.
23  115
Pos
Neg
Zero
Greater than 23
Less than 23
h.
523  149
Pos
Neg
Zero
Greater than 523
Less than 523
i.
 23   49.7
Pos
Neg
Zero
Greater than – 23
Less than – 23
Math 52 – Homework Unit 3 – Page 22
Wrap-up and look back:
8. Manny spilled some juice on his homework. He knows that he started with 24 and subtracted some
negative number. Will his result be bigger or smaller than 24?
9. Peyton starts with a number A and then subtracts “– 14.” Does he end higher or lower than A?
10. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.15: Subtracting with Number Lines
Vocabulary and symbols – write out what the following mean:

None
Concept questions:
1. Conceptually, if we have A – B and B is positive, will the result be to the left or right of A on the
number line?
2. Conceptually, if we have A – B and B is negative, will the result be to the left or right of A on the
number line?
3. Can we rewrite subtraction as adding the opposite even if there are no numbers, just variables? Can we
rewrite A – B with addition?
Exercises:
4. Use a number line to complete the subtraction.
a.
b.
c.
d.
e.
f.
Find the region that best approximates B – D.
Find the region that best approximates B – (– 2).
Find the region that best approximates D – 1.
Find the region that best approximates C – B.
Find the region that best approximates B – (– B).
Find the region that best approximates 1 – B.
A
R1
B
R2
R3
0
C
R4
1
D
R5
R6
Math 52 – Homework Unit 3 – Page 23
Wrap-up and look back:
5.
6.
7.
8.
Opie found the result of A – D on the number line, and it was right of A. What kind of number is D?
Calvin found the result of A – D on the number line, and it was left of A. What kind of number is D?
Grumpy found the result of A + D on the number line, and it was left of A. What kind of number is D?
Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.16: Subtracting Fractions, Decimals, and More
Vocabulary and symbols – write out what the following mean:

None
Concept questions:
1. Which part of A – B = C is the minuend? Which part is the subtrahend? Which part is the difference?
2. What way can we interpret the mathematical symbol “ – ”… there are 3 different ways to interpret.
Create an example of each!
3. Why can subtraction be thought of as very similar to addition?
4. In the problem 492 – (– 56), do you actually perform addition or subtraction?
5. In the problem – 492 – (– 56), do you actually perform addition or subtraction? What subtraction
problem are you really doing?
6. If you want to rewrite subtraction by adding 5 to the subtrahend, do you add 5 or subtract 5 from the
minuend? Explain.
7. If you want to rewrite subtraction by subtracting 11 to the subtrahend, do you add 11 or subtract 11
from the minuend? Explain.
Exercises:
8. Practice subtraction in a number of settings.
a.
b.
c.
d.
e.
f.
g.
h.
653 – 439
9,100 – 897
920 – 704
6,345 – 1,295
8,752 – 2,964
– 60 – 28
– 60 – (– 28)
60 – 28
i. 60 – (– 28)
j. 39 – 600
k. – 55 – (– 400)
l.
 28   35
m.  28   35
n.   28   35
o.  21  13  18   33   54
Math 52 – Homework Unit 3 – Page 24
9. Practice subtraction with fractions, decimals, and desks (oh my)!
a. 
7 3

8 4
g. 
3 
 
10 
3

4
b. 
7  3
  
8  4
h. 
3 
 
10 
3

4
c. 
2  1
  
3  6
i. 46.2 – 19.84
2 1

3 6
k. – 2.485 + 0.62
d. 
j. 46.2 – 30.847
l. – 2.485 – 0.62
3 2
e.

8 3
f.
m. – 15.3 + 7.85
n. 45.3 – 100
2 3

3 8
o. 7 tables – 3 desks + 12 tables – 8 desks
10. Practice subtraction with variables and roots.
a. 45x   9 y   11y   44 x 
b.  53x  17 y   33 y   25x 


c.  11 7  5 2   23 7  54 2
d.  4 71  21  23 71  33 21
e. Louis has $1,315 in his bank account. He purchased a fancy tablet computer for $858. How much
money would Louis have left in his account?
Wrap-up and look back:
11. When subtracting 603 – 852…
a. What is the sign of the difference?
b. To find the size of the difference, do we perform 852 – 603 or 603 – 852?
12. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.17: Estimation, Property Review, and Magic Boxes
Vocabulary and symbols – write out what the following mean:

Estimate
Concept questions:
1. Why do we estimate numbers instead of just using a calculator?
Math 52 – Homework Unit 3 – Page 25
Exercises:
2. Estimate the values and choose the appropriate answer.
Estimating the value of …
Is closest to…
a.
64.9184 + 32.09
60
68
b.
1
1

100 500
c.
– 115 – 123
10
0
– 10
– 220
d.
– 115 – ( – 123)
10
0
– 10
– 220
e.
– 115 + ( – 108)
10
0
– 10
– 220
f.
– 62 – ( – 33)
30
– 30
g.
135.4738 – 2.54 – 0.0694
h.
1,472.04 – 390.294
i.
7 1

5 3
1
2
97
2
130
110
0
2
1
– 90
13
11
9.7
14
1.1
1
2
0
90
140
1,100
1
3. Determine if the property name matches the equation, and if it is used correctly.
Property Name
Using it like this…
Is…
a.
Additive Identity
53 0  53
Incorrect
Correct
b.
Additive Inverse
3   3  0
Incorrect
Correct
c.
Commutative Property
3  45  19  3  19  45
Incorrect
Correct
d.
Associative Property
3  45  19  3  19  45
Incorrect
Correct
e.
Associative Property
5  3  7  5  3  7
Incorrect
Correct
f.
Commutative Property
5  3  7  3  7  5
Incorrect
Correct
g.
Additive Identity
0  50  50
Incorrect
Correct
Math 52 – Homework Unit 3 – Page 26
4. Fill in the empty boxes.
a.
–5
–9
e.
+6
–7
–9
–4
b.
–8
f.
– 13
+9
+ 25
–8
– 13
c.
16
– 43
g.
– (–5)
– 43
d.
31
– (–5)
25
h.
– 67
+ 17
– 67
+ 84
– 31
Wrap-up and look back:
5. If Joan found A – B and Karl found B – A, would their answers be similar or exactly the same? What
would be the same (sign/size)?
6. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
3.18: Subtraction Summary
To summarize the results, we can make a list of what we saw with subtraction:
If B is…
Then A – B will be …
a.
Positive
Greater than A
Less than A
Equal to A
b.
Negative
Greater than A
Less than A
Equal to A
c.
0
Greater than A
Less than A
Equal to A
Math 52 – Homework Unit 3 – Page 27
Concept Questions
1. When dealing with integers, the sign of the sum depends on the value of the addends. The sum could
be always positive (P), always negative (N), or sometimes positive and sometimes negative (S). Label
each of the following expressions as P, S, or N. If the answer is P or N, explain why. But if the
answer is S, give one example that shows a positive result and one example that shows a negative
result.
Expression
Sign (circle one)
a.
pos – pos
P
S
N
b.
neg + pos
P
S
N
c.
pos + neg
P
S
N
d.
neg – neg
P
S
N
e.
pos + pos
P
S
N
f.
pos – neg
P
S
N
g.
neg – pos
P
S
N
h.
neg + neg
P
S
N
Examples or Explanation
2. What are all the ways to end with P using addition?
3. What are all the ways to end with N using addition?
4. What are all the ways to end with S using addition?
5. What are all the ways to end with P using subtraction?
6. What are all the ways to end with N using subtraction?
7. What are all the ways to end with S using subtraction?
8. Did you have any questions remaining that weren’t covered in class? Write them out and bring them
back to class.
Math 52 – Homework Unit 3 – Page 28