1

Algebra Homework: Chapter 1 (Homework is listed by date assigned; homework is due the following class period)

Day Date In-Class Homework

1 T

8/30

Introductions Operations on Decimals

Converting Decimals to Fractions Converting Fractions to Decimals

Multiplying and Dividing Fractions

HW1: Complete student info sheet

Parent signature on syllabus, academic honesty and electronics

contracts HW 1 Wkst

2 W

8/31

Adding and Subtracting Fractions Section 1.1: Translating Expressions and

Writing Rules

HW2: Complete student info

sheet Parent signature on syllabus,

academic honesty and electronics contracts

HW 2 Wkst

3 Th 9/1

Section 1.2: Exponents, Order of Operations Section 1.3: Classifying and Ordering Real Numbers

Section 1.4: Adding Real Numbers

HW3: Pg. 2: 1-21 odd

Pg. 6: 1-37 x3 (1, 4, 7, 10…) Pg. 12: 4-9, 17-19, 60

4 F

9/2

Section 1.5: Subtracting Real Numbers

Section 1.6: Multiplying and Dividing Real Numbers

HW4: Pg. 27: 1-22 x3 (1, 4, 7…) Pg. 34: 10-37x3 (10, 13,, 16…)

Pg. 61: 38-45 all

5 T

9/6 Sections 1.7 and 1.8: Properties of Real Numbers

HW5: Pg. 41: 1-4, 15-18, 25-27,

32-35, 40-43 Pg. 48: 15-33x3, 67-75 odd

Pg. 54: 1-8all, 16, 17

6 W 9/7

Solving 1-step equations

HW6: HW 6 Worksheet Print: Chapter 2 Notes

7 Th 9/8

Chapter 1 Review

HW7: Chapter 1 Study Guide Correct Study Guide online

Chp 1 Test and Notes Check Tomorrow

Print: Chp 2 Notes

8 F

9/9

Chapter 1 Test with 1-step equations Notes Check

HW8: Pg. 60: 29-63 all

Print: Chp 2 Notes

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Notes #1: Operations on Decimals, Converting Decimals to Fractions A. What are Decimals? Give some examples of decimals: Where do you see decimals outside of math class? When would you need to know how to add, subtract, multiply, or divide decimals? B. Adding and Subtracting Decimals To add or subtract decimals, follow these steps:

1. Align the numbers ______________ 2. Make sure that the _____________ _________ are lined up, use _________ as place holders 3. Add/Subtract as you do with integers 4. Make sure your answer has a ________________ ____________ and that your answer makes

sense. Estimate the following sums/differences. Then evaluate. 1.) 14.625 + 9.588 Estimate: ________ Solution: ________

2.) 124.08 – 56.2 Estimate: ________ Solution: ________

3.) 3 – 1.204 Estimate: ________ Solution: ________

C. Multiplying Decimals To multiply decimals, follow these steps:

1. Align the numbers ________________, with the “shorter” number on the ___________ 2. Multiply as you do with integers 3. In the original problem, count the number of digits to the __________ of the decimals points. 4. In your solution, move the decimal this many places to the ___________ 5. Make sure your answer has a ________________ ____________ and that your answer makes

sense. 6.

Estimate the following products. Then evaluate. 4.) (4.5)(2.07) Estimate: ________ Solution: ________

5.) (0.03)(12.64) Estimate: ________ Solution: ________

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D. Dividing Decimals To divide decimals, follow these steps:

1. The number before the division sign, or the number on the numerator of a fraction, is placed ________________ the division “house.”

2. The number after the division sign, or the number on the denominator of a fraction, is placed to the left of and ____________ of the division “house.”

3. Move decimals to the right in both numbers until the divisor (on the __________ of the “house”) is a whole number

4. Bring the decimal up top 5. Divide as you would with whole numbers; don’t worry about the decimal point.

Estimate the following division problems. Then evaluate. 6.) 33.54 ÷ 4.3 Estimate: ________ Solution: ________

7.) 40.3 ÷ 12.4 Estimate: ________ Solution: ________

Convert the following fractions into decimals by writing as a division problem.

8.) 7

8

Estimate: ________ Solution: ________

9.) 5

26

Estimate: ________ Solution: ________

E. Converting Decimals to Fractions Let’s first identify the place values in a decimal: _________ _________ __________ • _________ _________ __________ __________

4

To convert a decimal to a fraction, follow these steps: 1. Read the number out loud. The number to the left of the decimal point is a whole number. 2. When you get to the decimal point, say “and” and start writing your fraction. 3. Read the number to the right of the decimal point and the place value of the final digit. 4. This place value represents the denominator of the fraction (either 10, 100, 1000 etc) 5. As always, reduce your fraction to simplest form.

Example: 45.678 is read as “forty five and six hundred seventy eight thousandths” Convert the following decimals into simplified fractions: 10.) 3.8

11.) 10.062

Multiplying and Dividing Fractions A. Multiplying Fractions To multiply fractions, follow these steps:

1. Convert all mixed numbers to improper fractions 2. Multiply across the ________________ and across the _________________

(shortcut: cross-____________ first!) 3. Reduce your answer. You may leave the solution as an improper fraction or mixed number Multiply the fractions; leave in simplified form:

12.) 5 3

12 10

13.) 2 2

3 13 7

14.) ( )41 3

9

B. Dividing Fractions To divide fractions, follow these steps:

1. Convert all mixed numbers to improper fractions 2. ____________ the second fraction over and turn it into a multiplication problem 3. Remember, _______________________________ first! 4. Reduce your answer. You may leave the solution as an improper fraction or mixed number.

Divide the fractions; leave in simplified form:

15.) 6 2

25 5÷ 16.)

1 13 2

3 4÷

17.)

238

15

5

Notes #2: Adding, Subtracting Fractions and Section 1.1 A. Adding/Subtracting Fractions and Mixed Numbers with Like Denominators To add fractions with like denominators, follow these steps:

1. Add/Subtract the _________________ of the fractions (check to see if you have to borrow) 2. Keep the __________________ the same 3. Reduce your answer 4. Check to see if you need to carry (if the fraction is greater than _______ )

Add the fractions; leave in simplified form:

1.) 7 1 7

24 24 24+ +

2.) 1 3

3 118 8

+

3.) 5 1

3 112 12

−

4.) 5 7

2 129 9

+

5.) 1 5

7 26 6

− 6.) 3 15

317 17

−

B. The LCM (Least Common Multiple) of a Set of Numbers The LCM of a set of numbers is the smallest number that all of the given numbers can divide into evenly with no remainder. Find the LCM of each set of numbers: 7.) 2, 3, 6 8.) 2, 4, 5 9.) 8, 12 10.) 6, 10

6

C. Adding/Subtracting Fractions and Mixed Numbers with Unlike Denominators To add/subtract fractions with unlike denominators, follow these steps:

1. Find the LCM of the denominators 2. “un-reduce” each fraction so that it now has this new LCM as a denominator 3. Add/subtract as before (watch for borrowing, carrying, and reducing)

Add the fractions; leave in simplified form:

11.) 5 7

8 12+

12.) 1 1

3 28 2

−

13.) 4 5 7

2 1 35 12 10

+ +

14.) 2 3

10 33 4

−

Section 1.1: Translating Expressions and Writing Rules A. Writing Algebraic Expressions Write whether each expression implies addition, subtraction, multiplication, or division: 1.) sum 2.) difference 3.) more than 4.) quotient 5.) product 6.) twice 7.) added to 8.) less than 9.) total 10.) minus 11.) plus 12.) three times

7

Look for these key words and write an algebraic expression for each phrase: (if no variable is defined, define your own) 13.) the sum of m and 4 14.) twice y added to 17 15.) the quotient of 3 and the

sum of x and 5

16.) the product of 9 and 3 less than p

17.) a number divided by 7 18.) three times the sum of 11 and a number

Define variables and write an equation to model each situation: 19.) The total cost of gas is the number of gallons times $4.19

20.) The area of a rectangle is equal to the length of the base times the length of the height.

21.) Number of Hours

Total Pay

2 $15.00 4 $30.00 6 $45.00 8 $60.00

8

Notes #3: Sections 1.2, 1.3, 1.4 Section 1.2: Evaluating Exponents and Order of Operations A. Evaluating Exponents An exponent is indicates how many times to multiply a number by itself. Evaluate each expression: 1.) 23 2.) m2 when m = 8 3.) a4 when a = 3 B. Order of Operations When there are multiple operations to evaluate, follow this order: P E M D A S Evaluate each expression: 4.) 4 + 3(15 – 23) 5.) 4[4(8 – 2) + 5]

6.) 14 + 6 × 2 3 – 8 ÷ 22

7.) 5 + 42 × 8 – 23 ÷ 22 8.)

4(8 3)

3 2

−+

9.) 6 30

129 3

+ −

C. Evaluating Algebraic Expressions Be sure to follow PEMDAS when evaluating algebraic expressions. When you substitute a value for a variable, use ________________________.

10.) 2

5

a b+, for a = 1, b=2 11.) 3 2( )a b a+ ÷ , for a = 2, b = 6

12.)

2

3

2t

sfor s = 3, t=9

9

13.) Complete the table:

x 2x – 5 2 3 4

Section 1.3 A. Classifying Real Numbers We organize Real numbers into the following categories: Real Numbers Rational Numbers Integers Whole Numbers Natural Numbers State the set(s) of numbers to which each number belongs:

1.) 2.5 2.) -7 3.) 15

3 4.) 0

True or false? If false, provide a counterexample. 5.) All natural numbers are integers. 6.) All integers are natural numbers. E. Comparing Real Numbers If you are comparing fractions, make sure that they have the same denominator first! Compare the numbers using >, <, or = 7.) 12.45 ___ 12.44− −

8.) 4 5

___5 6

− −

Order the numbers in each group from least to greatest

9.) 3 7 2

, ,4 8 3

− − − 10.) 3 5

2 ,2 ,2.74 8

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Section 1.4 Adding Rational Numbers A. Adding Rational Numbers If the signs are the same, _________ the numbers and keep the __________ the same. If the signs are opposite, __________ the numbers and keep the _______ of the __________ number. *The same rules apply whether you are adding integers, fractions, or decimals* Add. Illustrate the addition for #1-3 on a number line. 1.) -3 + 6 2.) 7 + (-4) 3.) -2 + (-6)

Add. 4.) -2 + (-13) 5.) 27 + (-14) 6.) -12.2 + 31.9

7.) 9 + (-7.8) 8.) -3.4 + (-1.2) 9.)

7 1

12 6− +

10.) 3 1

3 14 2

− + 11.) 1 1

3 14 2

− + −

12.) 1 1 1

2 3 4 + − +

13.) a + (-3.4) for a = 9.8 14.) -2 + [7 + (-3)] 15.) 5 + 2[-7 + 4]

11

Notes #4: Sections 1.5 and 1.6 A. Subtracting Real Numbers Always turn a subtraction problem into an addition problem: “__________, __________” Then you can use the rules you already know from addition. Convert subtraction into an addition problem. Evaluate. 1.) 14 – 26 2.) -18 – (-3) – 5 3.) 2 – (-19)

4.) -6 – (-2) – (-4) – 12 + 3 5.) -4.2 – (-3.6) – 8.2 6.) – 3 – (-15)

7.) 3 1

14 4

− 8.) 7 1 5 3

12 2 6 4 − − − + −

9.) 7 4

10 15− −

10.) 1 1

3 4 − −

11.) 1 7

45 10

− − −

12.) (a – b) for a = -4 and b = 7

12

B. Absolute Value Absolute value describes how far a number is from zero on a number line. A distance is always ______________. Evaluate. 13.) 7 3− + − 14.) 11 4− − 15.) 8 5− − −

16.) -q – r + p for p = -1.5, q = -3, r = 2 C. Multiplying and Dividing Real Numbers (negative) × (negative) = ________________ (negative) ÷ (negative) = ________________ (negative) × (positive) = ________________ (negative) ÷ (positive) = ________________ Evaluate: 17.) (-3)(5)(-2) 18.) (-2)4

19.) -24

20.) 43 – (2 – 5)3 21.) 32 ÷ (-7 + 5)3

22.) (a + b)2 for a = 6, b = -8

23.) 4s ÷ (-3t) for s = -6, t = -2 24.) xy + z, for x = -4, y = 3, z = -3

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Notes #5: Sections 1.7 and 1.8 A. The Distributive Property The distributive property describes multiplying across an addition or subtraction problem. Simplify each expression. 1.) 2(x + 6) 2.) -5(8 – b)

3.) (5c – 7)(-3)

4.) -(4 – 2b) 5.) 0.4(3m – 8) 6.)

2(4 6 )

3p−

B. Combining Like Terms When adding or subtracting algebraic expressions, look for “buddies” (terms that have the same __________________). Add/subtract the coefficients but leave the variables the same. Simplify each expression. 7.) 4m – 3p – (-m) + 2p 8.) 17k – 4w + w – (-5k)

9.) 5 2 1 4

6 3 2 5x y x y− − +

10.) 2(3h + 2) – 4h

11.) 5(t – 3) – 2t 12.) 4(2 3 ) 0.5(6 )f g g f− − −

C. Properties of Numbers It is important to know the many rules that you use when you add and multiply numbers. Multiplication Property of Zero: Identity Property of Addition:

of Multiplication:

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Inverse Property of Addition:

of Multiplication: Commutative Property of Addition:

of Multiplication: Associative Property of Addition:

of Multiplication:

Name the property that each equation illustrates: 13.) 83 + 6 = 6 + 83 14.) (1)(4y) = 4y 15.) 15x + 15y = 15(x + y)

16.) (8 · 7) · 6 = 8 · (7 · 6) 17.) (8 · 7) · 6 = (7 · 8) · 6 18.) 0 + (-5m) = -5m

19.) 0 = 0 · 18 20.) -2xy + 2xy = 0 21.)

21.5 1

3 =

15

D. Algebraic Proof You use many of these properties when simplifying algebraic expressions. Next to each step, name the property illustrated: 22.) a. 4c + 3(2 + c) = 4c + 6 + 3c a. _______________________________

b. = 4c + 3c + 6 b. _______________________________

c. = (4c + 3c) + 6 c. _______________________________

d. = (4 + 3)c + 6 d. _______________________________

e. = 7c + 6 e. _______________________________

23.) a. 8w – 4(7 – w) = 8w – 28 + 4w a. _______________________________

b. = 8w + (-28) + 4w b. _______________________________

c. = 8w + 4w + (-28) c. _______________________________

d. = (8 + 4)w + (-28) d. _______________________________

e. = 12w + (-28) e. _______________________________

f. = 12w – 28 f. _______________________________

16

Notes#6 Review: Solving One-Step Equations A. Using Addition and Subtraction

• To “undo” a positive number (or addition), you must do the opposite: ________

• To “undo” a negative number (or subtraction), you must to the opposite: _______

Remember, whatever you do to one side of the equation,

you must do to the ________ _________!!

Addition Property of Equality

Subtraction Property of Equality

Solve each equation. Show your check step where indicated. 1.) x + 7 = 2 2.) 5 = −4 + a 3.) n – 0.6 = 4 (check): (check): (check):

4.) c + 4 = -2.5 5.) 1 8

3 3r + = 6.)

5 7

6 8x− =

7.) 4 1

5 10a + = 8.)

3 1

8 4x− =

17

B. Using Multiplication and Divison

• To “undo” a coefficient (multiplication), you must do the opposite: __________

• To “undo” a denominator (division), you must to the opposite: _____________

• For problems involving a variable multiplied by a fraction (i.e. 3

4x = 2 ),

multiply by the _________________

Solve each equation. Show your check step where indicated.

1.) 5x = 25 2.) –3y = -42 3.) 1

43

y− =

(check): (check):

4.) 5 2

6 3x= − 5.) 6x− = 6.) 10

5

x =

Remember, whatever you do to one side of the equation,

you must do to the ________ _________!!

Multiplication Property of Equality

Division Property of Equality

18

7.) 123

m = −−

8.) 64

t− = 9.) 2 4

5 15y− = −

(check): (check):

10.) 5 10

7 14x = − 11.) 6.3 44.1x = 12.) 3.1 21.7y− =

19

Algebra 1: Chapter 1 Test Topics 1.) Decimals (Add, subtract, multiply, and divide decimals. Apply these operations to word problems) 2.) *Fractions* (Add, subtract, multiply, and divide fractions. Know when to make fractions improper and know when you need common denominators. Know how to borrow or how to avoid borrowing by using improper fractions.) 3.) Convert (Convert decimals to fractions, convert fractions to decimals) 4.) *Translate* (Translate written expressions into mathematical expressions by finding key terms such as “sum,” “difference,” “product,” “quotient,” etc. Define a variable as necessary.) 5.) *Evaluate* (Evaluate numerical expressions or variable expressions using PEMDAS) 6.) Classify (Classify given numbers as Real, Rational, Integer, Whole, Natural) 7.) *Negatives* (add, subtract, multiply and divide negative integers, fractions, and decimals.) 8.) Order (Put given fractions and/or decimals in order from least to greatest) 9.) *Distribute and Combine* (Distribute a coefficient to all terms inside the parentheses and combine like terms) 10.) *Justify* (Justify a mathematical statement with the correct Algebraic property – Identity, Inverse, Associative, Commutative, Distributive, etc) 11.) *Solve* (solve one-step algebraic equations using addition, subtraction, multiplication and division of integers, decimals, and fractions.)

20

HW #7: Chapter 1 Study Guide Name: _________________________ Please show ALL of your work (this means no calculators). NO WORK = NO CREDIT Estimate an answer. Then, add/subtract/multiply/divide the decimals. Use your estimate to check your work. 1.) 412.36 73.99+ Estimate: _______ Solution: _______

2.) 82.6 – 14.7 Estimate: _______ Solution: _______

3.) (23.5)(0.04) Estimate: _______ Solution: _______

4.) 39.78 2.6÷

Estimate: _______ Solution: _______

Convert as directed: 5.) Convert to a fraction in simplest form: 2.16

6.) Convert to a decimal: 3

38

Add/subtract/multiply/divide the fractions; leave in simplest form.

7.) 3 5

2 58 6

+

8.) 3 5

7 210 6

−

21

9.) 2 1

3 53 2

÷

10.) 2 1

4 25 2

−

Write an expression for each phrase: 11.) twice the sum of 9 and p

12.) 4.3 less than the product of y and 3

13.) the quotient of m and the difference of w and 2

14.) the sum of three times j and twice b

Write a phrase for each expression: 15.) 3k – 6 16.) 4(d + 3)

17.) 5

4 p+

Simplify each expression: 18.) 2(3 7) [4 4 (1 ( 1))]+ + ÷ − −� 19.) 1 – 3[8 – 2(1 – 5)] 20.) 9 + [4 – (10 – 9)2]3

Evaluate each expression for a = -1, b = 2, c = -3: 21.) 2b ÷ a + 3c

22.) -c2 ÷ (a2 + b) 23.)

22

1

a b

c−

Name the set(s) of numbers to which each number belongs: 24.) 4.12

25.) 0

Order the numbers from least to greatest:

26.) 5 1 2

2 , 2 , 26 2 3

− −

22

Compare the numbers using >, <, or =:

27.) 5 7

____6 8

− −

28.) 1

_____ 0.3333

−

Simplify each expression: 29.) 6 ( 3) 4 9− − − + −

30.) 2 25 ( 3) 4− + − −

31.) 4 1

3 25 2

− − −

32.) 6 4 3− − + +

33.)

31

412

34.) 2(3a – b) – 4(2b + a)

35.) ( )14 3

2z− −

36.) 5 1

3 ( )12 2

m n m n− − − +

Which property does each equation illustrate? 35.) 3z + 0 = 3z

36.) 3a + (2b + c) = (3a + 2b) + c

37.) 3 3

02 2

− + =

38.) 3 2

12 3 =

23

39.) (2x + 3y)(4z) = (4z)(2x + 3y) 40.) -3(2m – n) = -6m + 3n

Give a reason to justify each step: 41.) 4[m – 2(2m + 3)] = 4[m – (4m + 6)] __________________________________

= 4[m + (-4m – 6)] __________________________________

= 4[(m + (-4m)) – 6] __________________________________

= 4[(-3m) – 6] __________________________________

= -12m – 24 __________________________________

Complete the table 42.)

c 13

2c−

Evaluate for x = -2, y = 3, z = -1 43.) 2x xy z− − −

44.) 3

5

xy z−−

24

Solve each equation. Show your check where indicated. 45.) 8 14x− = − 46.) 7.2 2.9y + = − 47.) 4.5 2.8z+ =

48.) 28 2m= − 49.) 4

2.5

n− =−

50.) 2 4

7 23 5

c− = −

51.) 19.6 2.3k − = − 52.)

2 13 6

7 2a − = 53.)

212

3x = −