math fundamentals for statistics i (math 52) homework … · 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 Attribution-

NonCommercial-ShareAlike 4.0 International License

3rd Edition (Summer 2016)


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:

a. 650

b. 9,800

c. 510,000

d. 3,800,000


4. Re-write the following in standard notation. “16 tens” would be written as 160 in standard place value

notation.

a. 8.3 tens

b. 6.2 hundreds

c. 57 thousands

d. 13.25 million

e. 0.413 ten thousand

f. 400 tenths

g. 2,900 hundredths

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


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. 191936519762

e. 4 sevenths + 9 fifths + 3 sevenths + 2 fifths

f. ADBCDBDCBA 3564343234

g. 1061520976


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

b. 629 + 421

c. 89 + 53

d. 54 + 25

e. 3,944 + 899

f. 8,384 + 2,998

g. 5,204 + 3,788

h. 984,483,62135,388,19


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 9 7

+ 4 5

c. Now add down the diagonals to get the final result.

2 9 7

+ 4 5

d. Do you see how this method works? What other algorithm is this similar to?

0 1 1

2 3 2

0 1 1

2 3 2

3 4 2



back to class.

3.3: Addition Properties


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. 38 + 15 = 15 + 38

b. 23 + (6 + 5) = (23 + 6) + 5

c. 14 + (9 + 7) = 14 + (7 + 9) = (14 + 7) + 9

d. 72072

e. 0 + 7 = 7 + 0 = 7

f. 12 + (8 + 3) = (8 + 3) + 12

g. (99 + 273) + 1 = (273 + 99) + 1 = 273 + (99 + 1)


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?


back to class.

3.4: Adding Integers using Chips


Value of a black chip

Value of a red chip

Zero Pair


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.


7. How would you explain adding 3 + (– 5) with chips?


back to class.

3.5: Adding Integers Without Chips


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?


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

b. 19

c. 140,3

d. 197

e. 0

f. 817,9

7. Combine the like objects quickly. Do not find the end result at this stage!

a. 853511

b. 31253

c. 31298731

d. 374192315

e. 63 14 21 4 8 7

f. 1312689

8. Find the following values and describe in words what it represents.

a. 62

b. 5.8

c. 111

d. 0

e. 514

f. 39

9. Fill out the table concerning value, size, and sign; the first is done as an example.

Value Absolute value (Size) Sign

88 88 Positive

a. – 92

b. 47 Positive

c. 694

d. 2,319 Negative

e. 93

f. 0


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. 7897 P N Z

b. 5678 P N Z

c. 5935 P N Z d. 4343 P N Z

e. 1628 P N Z f. 72643 P N Z

g. 3296 P N Z h. 342,3197,6 P N Z

12. Find the value of the sums using the methods shown in this section.

a. 8828

b. 5949

c. 2643

d. 5613

e. 1327

f. 4753

g. 3796

h. 16774

i. 342,3197,2

j. 739,1342568,3


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


14. Did the speedy method for regrouping addends during addition work well for you? How did it

compare with the other algorithms?


back to class.

3.6: Adding Fractions (Rational Numbers)


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 5

3 on a number line from 0 to 1?

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?

7. If you had a number line from 0 to 1, how could you find the location of 6

5?

8. If you had a number line from 0 to 1, how could you find the location of 7

3?

Exercises:


9. Find some equivalent fractions using FLOF: (find at least 3 equivalent fractions for each)

a.

3

1

b.

7

3

c.

6

1

d.

8

3

10. Add the fractions; the first is been done for you.

a. 9

10

9

523

9

5

9

2

9

3

b. 17

6

17

3

c. 19

8

19

9

19

2

d.

613

23

613

51

e. 984

13

984

52

984

47

11. Place the correct symbol ( , , or =) between the following numbers – no calculator!

a.

13

7

2

1

b.

9

8

11

10

c.

9

8

11

9

d.

16

5

8

3

e.

9

2

4

1

f.

9

2

4

1

g.

7

4

7

5

h.

13

4

13

2

i.

3

4

9

4

j.

5

11

7

11

12. Based on the table above, if two fractions have the same numerator with different denominators,

which is larger?


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. 8

3

4

1

b. 8

3

2

1

c. 8

5

2

1

d.

8

7

4

3

e.

3

1

9

8

f. 3

1

7

6

g.

30

7

20

9

h. 5

7

15

2

i. 15

8

10

7

j. 8

7

24

11

k. 4

1

11

7

l. 8

7

12

5

m. 18

7

31

4

n.

42

31

49

41

o. 75

59

80

11

p. 39

25

111

32


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?


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.


back to class.

3.7: Adding Decimals


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

b. 16.903 + 58.24

c. 0.0249 + 0.3942

d. 17.302 + 9.2483

e. 3,402.8 + 583.54

f. 5.2 + 3.94 + 2.814

g. 14.93 + 0.0593 + 6.58

h. 6.24394 + 29.934 + 1.58301 + 8.8695 + 0.00342

i. 5.82 + (– 3.11)


6. Is there anything you need to do with decimals that is different than integers?


back to class.


3.8: Adding Values on a Number Line


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

b. 6 + 3

c. 8 + 5

d. 11 + 2

e. 6 + 3 + 5

f. 7 + 5 + 4

4. Use a number line, like the one below, to find the result of:

a. 4 + (– 2)

b. 3 + (– 7)

c. (– 2) + (– 4)

d. (– 8) + 5

e. (– 4) + 7

f. 7 + (– 4)

g. 263

h. 435

5. Find the region that best approximates the following values.

a. 3.

b. – 2.

c. B + 2.

d. A + C.

e. A + B.

f. D + (– 3).

g. B + (– A).

h. C + C.

R1 R2 R3 R4 R5 R6

A B 0 C 1 D


6. Approximate the sum using the number line:

a. 54 b. 63 c. 97

0 1 2 3 4 5


7. Is it true that BABA ? 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?


back to class.

3.9: Applications of Addition and Concept Questions


Perimeter

Concept questions:

1. Mickey calculated 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 calculated 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? 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?


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 W 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.

b.

c.

d.

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.

16 inches

8 inches

4 inches

19 inches

10 inches

6 inches

23 inches

29 inches

19 inches

1 foot, 4 inches

2 feet

9 inches


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. yxyx 59427

b. yxyx 159519

c. yxyx 912731

d. 22 2561113 xxxx

e. 789713 xyx

f. yxyx 5232814


9. Which of the application problems was your favorite? Why?


back to class.

3.10: Addition Wrap-Up (Practice)


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 36 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 54 inches. Is she correct, and if not, what did she do wrong?


Exercises:

3. Complete the summary problems from the unit:

a. 7 + 19 + 25 + 41

b. 9,694 + 498

c. 297 + 573

d. 238

e. 74328

f. 4168

g. 541311939

h. 4

1

8

3

i.

4

3

11

7

j. 15

2

10

7

k.

7

16

7

31

l. 6.84 + 2.938

m. 623.49 + 84.52

n. – 6.13 + (– 12.8)

o. 9.382.16

p. 134217

q. xyyx 85724

r. 21527421172

s. 3 oranges + 8 footballs + 6 oranges + 5 footballs

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. 916114 b. 385,9467

(Integers)

c. 114

d. 5942

e. 3516

f. 24131179

(Fractions)

g. 8

7

4

3

h.

12

1

8

7

i. 15

7

10

9

j.

7

10

7

3

(Decimals)

k. 8.1527.30

l. 8.321.39

m. 9.52.4

n. 6.423.2


(Mixed Bag)

o. 397

p. xyyx 89713

q. 3 oranges + 8 footballs + 6 oranges

r. 219782573


6. Sums of integers are always positive (P), always negative (N), or sometimes positive and sometimes

negative (S). Determine the following:

Expression Sign (circle one) Examples or Explanation

a. pos + pos P S N

b. pos + neg P S N

c. neg + pos P S N

d. neg + neg P S N

3.11: Subtraction


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

b. 45 – 21

c. 75 – 34

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


8. Solve these subtraction problems using different algorithms. You are in charge of picking different

algorithms based on the problems!

a. 737 – 349

b. 3,752 – 2,631

c. 784 – 458

d. 4,731 – 854

e. 200,000 – 15,874

f. 1,945,392 – 395,238

g. 788,325,594 – 98,447,452

h. 67x – 25x

i. 156m – 89m

j. 878w – 489w


9. Do you need to use the same algorithm for each problem?

10. Is there only one way to find a difference?

11. Richard said that the subtrahend – minuend = difference. Is he correct?


back to class.

3.12: Subtracting Integers using Chips


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)

b. (– 4) – (– 6)

c. 4 – 7

d. 4 + (– 7)

e. 5 – (– 3)

f. 5 + 3


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)


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.


back to class.

3.13: Subtracting Integers (without chips)


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)


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. x 20

b. x98

c. x775

d. 15923 x

e. 15923 x

f. 15923 x


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)


back to class.

3.14: Number Sense and Addition/Subtraction


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 subtract (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.


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:

If B is… Then A + B will be …

a. 0 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:

If B is… Then A – B will be …

a. 0 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. 557 Pos Neg Zero Greater than – 57 Less than – 57

b. 532 Pos Neg Zero Greater than – 32 Less than – 32

c. 5.694 Pos Neg Zero Greater than – 94 Less than – 94

d. 5.626.4 Pos Neg Zero Greater than 4.26 Less than 4.26

e. 8989 Pos Neg Zero Greater than – 89 Less than – 89

f. 6523 Pos Neg Zero Greater than 23 Less than 23

g. 11523 Pos Neg Zero Greater than 23 Less than 23

h. 149523 Pos Neg Zero Greater than 523 Less than 523

i. 7.4923 Pos Neg Zero Greater than – 23 Less than – 23



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 on the number line and then subtracts “– 14.” Does he end higher or

lower than A?


back to class.

3.15: Subtracting with Number Lines


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. Find the region that best approximates B – D.

b. Find the region that best approximates B – (– 2).

c. Find the region that best approximates D – 1.

d. Find the region that best approximates C – B.

e. Find the region that best approximates B – (– B).

f. Find the region that best approximates 1 – B.

R1 R2 R3 R4 R5 R6

A B 0 C 1 D



5. Opie found the result of A – D on the number line, and it was right of A. What kind of number is D?

6. Calvin found the result of A – D on the number line, and it was left of A. What kind of number is D?

7. Grumpy found the result of A + D on the number line, and it was left of A. What kind of number is D?


back to class.

3.16: Subtracting Fractions, Decimals, and More


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 from the minuend, do you add 11 or subtract 11

from the subtrahend? Explain.

Exercises:

8. Practice subtraction in a number of settings.

a. 653 – 439

b. 9,100 – 897

c. 920 – 704

d. 6,345 – 1,295

e. 8,752 – 2,964

f. – 60 – 28

g. – 60 – (– 28)

h. 60 – 28

i. 60 – (– 28)

j. 39 – 600

k. – 55 – (– 400)

l. 3528

m. 3528

n. 3528

o. 5433181321


9. Practice subtraction with fractions, decimals, and desks (oh my)!

a. 4

3

8

7

b.

4

3

8

7

c.

6

1

3

2

d. 6

1

3

2

e. 3

2

8

3

f. 8

3

3

2

g.

4

3

10

3

h.

4

3

10

3

i. 46.2 – 19.84

j. 46.2 – 30.847

k. – 2.485 + 0.62

l. – 2.485 – 0.62

m. – 15.3 + 7.85

n. 45.3 – 100

o. 7 tables – 3 desks + 12 tables – 8 desks

10. Practice subtraction with variables and roots.

a. xyyx 4411945

b. xyyx 25331753

c. 25472325711

d. 2133712321714

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?


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?


back to class.

3.17: Estimation, Property Review, and Magic Boxes


Estimate

Concept questions:

1. Why do we estimate numbers instead of just using a calculator?


Exercises:

2. Estimate the values and choose the appropriate answer.

Estimating the value of … Is closest to…

a. 64.9184 + 32.09 60 68 97 9.7

b. 500

1

100

1

2

1 2 0 1

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 – 90 90

g. 135.4738 – 2.54 – 0.0694 130 13 14 140

h. 1,472.04 – 390.294 110 11 1.1 1,100

i. 3

1

5

7 2

2

1 0 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 35035 Incorrect Correct

b. Additive Inverse 033 Incorrect Correct

c. Commutative Property 4519319453 Incorrect Correct

d. Associative Property 4519319453 Incorrect Correct

e. Associative Property 735735 Incorrect Correct

f. Commutative Property 573735 Incorrect Correct

g. Additive Identity 50500 Incorrect Correct


4. Fill in the empty boxes.

a.

b.

c.

d.

e.

f.

g.

h.


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)?


back to class.

3.18: Subtraction Summary

0. 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

– 9 + 6

– 5

+ 9 – 13

– 8

– 43 – (–5)

16

+ 17 – 67

31

– 7 – 4

– 9

+ 25 – 13

– 8

– 43 – (–5)

25

+ 84 – 67

– 31


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) Examples or Explanation

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

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?


back to class.

math fundamentals for statistics i (math 52) homework … · math fundamentals for statistics i...

Documents