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Math 0106

Basic

In Class Worksheets

Spring 2015

Math 0106 Worksheets  2015 Houston Community College

Table of Contents Geometric Formulas ...... 1 Algebraic Formulas ...... 2 Statistical Formulas ...... 3 Syllabus Quiz ...... 4 Student Information Sheet ...... 5 Multiples and Divisibility ...... 7 Prime Factorization ...... 9 Prime Factorization Pracce ...... 10 Understanding ...... 11 Reducing Fractions ...... 12 Multiplying Fractions ...... 13 Dividing Fractions ...... 14 Least Common Multiples ...... 15 Adding and Subtracting Fractions – Common Denominators ...... 16 Adding and Subtracting Fractions – Unlike Fractions ...... 17 Notation – and Rounding...... 18 Adding and Subtracting ...... 19 Multiplying Decimals ...... 20 Dividing Decimals ...... 21 Using Fractional Notation with Decimal Notation ...... 22 and Proportion...... 23 Percent Notation ...... 24 Solving Percent Problems and Applications ...... 26 Order of Operations ...... 28 Review of Order of Operations Worksheet ...... 29 Getting Ready for Factoring Polynomials 1 ...... 30 Getting Ready for Factoring Polynomials 2 ...... 31 Week 1 Quiz ...... 32 Week 1 Quiz - Solutions ...... 34

Math 0106 Worksheets  2015 Houston Community College

Week 2 Quiz ...... 35 Week 2 Quiz - Solutions ...... 37 Week 3 Quiz ...... 38 Week 3 Quiz - Solutions ...... 40 Worksheet Answer Key ...... 41

Math 0106 Worksheets  2015 Houston Community College

Geometric Formulas

PLANE GEOMETRY SOLID GEOMETRY Rectangle Area: A = lw Rectangular Solid Perimeter: P = 2 l + 2 w Volume: V = lwh w SA = 2lw+2wh+2lh w l h Square 2 l Area: A = s s Perimeter: P = 4 s Cube s 3 Triangle s Volume: V = s s s 2 Area: SA = 6s b • h A = h 2

b Sum of Angle Measures Right Circular Cylinder 2 h A + B + C = 180 o C Volume: V = πr h A 2 SA =2 πr + 2 πrh Right Triangle r B Pythagorean Theorem: c a2 + b2 = c2 a

b Right Circular Cone h Parallelogram 1 2 Volume: V = /3πr h Area: A = bh h SA = πr2 + πrh r

Trapezoid b a 1 Area: A = /2h(a+b ) h Sphere r Volume: b 4 3 Circle V = /3πr Area: A = πr2 SA = 4πr Circumference: d r angle = π or = 2 π arc length C d C r = 0 22 circumfere nce 360 π.= /7 or π.=3.14

Math 0106 Worksheets 1  2015 Houston Community College

Algebraic Formulas

Interest Formula: I= Prt ⋅ ⋅ r  nt Compound Interest Formula: A= P 1 +  n  part % Percent Formulas: = whole 100 Amount of Change New Amount − Original Amo unt Percent Increase/Decrease = = Original Amount Original Amount rise y− y Slope Formula m = = 2 1 run x2− x 1 To find the x-intercept of a line, complete the ordered pair (___, 0). To find the y-intercept of a line, complete the ordered pair (0, ___). Slope-Intercept Form of an Equation of a Straight Line: y= mx + b

Point-Slope Form of an Equation of a Straight Line: y− y1 = mx( − x 1 )

2 2 Distance Formula: d=()() xx21 − +− yy 21

−b ± b2 − 4 ac Quadratic Formula: If ax2 + bx + c = 0 then x = 2a

Math 0106 Worksheets 2  2015 Houston Community College

Statistical Formulas

n! P = n r n− r ! Permutation of n things taken r at a time () n! Combination of n things taken r at a time C = n r r!() n− r ! number of outcomes of an event Theoretical Probability P( E ) = total number of possible outcomes number of observed outcomes Empirical Probability P( E ) = total number of observed occurrences ∑ x Mean = x = n ∑( xf ) Mean of a Frequency Distribution = x = n min + max Midrange = 2 ∑()x− x 2 Standard Deviation =s = n −1 data value - mean z−score x = standard deviation

Math 0106 Worksheets 3  2015 Houston Community College

Syllabus Quiz

Student Name ______

1) What is the course instructor’s office phone number?

2) On what day(s) and time(s) are office hours held?

3) What is the attendance policy for the course?

4) What overall will result in a C grade for the semester?

5) True or False? For any false statement, please correct the statement.

a) Attendance is crucial for success in this course.

b) You will complete the entire midterm and the entire final exam in class.

c) Late assignments can be handed in up to three weeks after the due date.

d) Any student who attends class, takes good notes, completes assignments,

and studies outside of class should receive a good grade in this course.

6) What are the criteria for receiving maximum points for participation?

7) Homework assignments account for what portion of your final grade?

8) When are the tests scheduled for this class?

Math 0106 Worksheets 4  2015 Houston Community College

Student Information Sheet

Personal

Full name:

Current address:

Contact information (please complete at least one):

Home phone:

Cell phone:

Email:

Other:

Do you work? (yes / no)

If yes: full-time or part-time?

How many hours?

Are there other outside obligations you would like for me to know about?

Academic

What is your major? (put “undeclared” if relevant):

Where did you go to high school?

What year did you graduate from high school?

Do you plan to transfer from this college? circle one: Yes / No

If yes, where do you plan to transfer?

What other colleges (if any) have you attended?

Math 0106 Worksheets 5  2015 Houston Community College

Course Specific

Have you taken a math course at the community college level?

When was the last time you took a math course?

What course was it?

Where did you take this course?

What is your level of comfort with math? 1 2 3 4 5 6 7 8 9 10 Not comfortable Very comfortable

List the courses you are enrolled in this semester

What grade do you intend to earn in this course?

What strengths or assets do you have that will help you achieve your goal in this course? These strengths/assets can include things about you such as being a hard worker or things about your life such as having a supportive family or having a flexible work schedule.

Math 0106 Worksheets 6  2015 Houston Community College

Multiples and Divisibility A multiple of a number is a product of that number and an . Multiples of 5 are 5, 10, 15, 20, 25, … Multiples of 3 are 3, 6, 9,12, 15, 18, 21, …

Find the first four multiples of each number. 1) 2 4) 8

2) 4 5) 9

3) 6 6) 10

A number is divisible by another number if it is a multiple of that number. 45 is divisible by 5 since 45 is a multiple of 5 (45 = 9 ⋅ 5) and 20 is divisible by 4 since 20 is a multiple of 4 (20 = 5 ⋅ 4). Saying that 20 is divisible by 4 also means that 20÷4 results in a remainder of zero. When this happens, we sometimes say that 4 divides 20 evenly.

Divisibility Rules Knowing the divisibility rules for common numbers will save you time when determining if one number is divisible by another number. Let’s look at the divisibility rules for 2, 3, 5, 6, 9, and 10.

Divisibility by 2: A number is divisible by 2 if it has a one’s digit of 0, 2, 4, 6, or 8. Every even number is divisible by 2.

Example: Which of the following numbers is divisible by 2? 945 3488 3200 Solutions: 94 5 is NOT divisible by 2, because the last digit is odd. 348 8 is divisible by 2, because the last digit is even. 320 0 is divisible by 2, because the last digit is even.

Divisibility by 3: A number is divisible by 3 if the sum of its digits is divisible by 3.

Example: Which of the following numbers is divisible by 3? 54 480 923 Solutions: 54 is divisible by 3, because the sum of the digits is 5 + 4 = 9 is divisible by 3. (9 ÷ 3 = 3 ) 480 is divisible by 3, because the sum of the digits is 4 + 8 + 0 = 12 is divisible by 3. (12 ÷ 3 = 3 ) 923 is NOT divisible by 3, because the sum of the digits is 9 + 2 + 3 = 14 is not divisible by 3.

Math 0106 Worksheets 7  2015 Houston Community College

Divisibility by 5: A number is divisible by 5 if its one’s digit is 0 or 5.

Example: Which of the following numbers is divisible by 5? 945 3,488 3,200 Solutions: 94 5 is divisible by 5, because the last digit is 5. 3,48 8 is NOT divisible by 5, because the last digit is not 0 or 5. 3,20 0 is divisible by 5, because the last digit is 0.

Divisibility by 6: A number is divisible by 6 if its ones digit is 0, 2, 4, 6, or 8 (is even) and the sum of its digits is divisible by 3. In other words, a number is divisible by 6 if it is divisible by both 2 and 3.

Example: Which of the following numbers is divisible by 6? 945 3,488 4,200 Solution: 945 is NOT divisible by 6, because the last digit is odd. Thus, it is not divisible by 2. 3,488 is NOT divisible by 6, because the sum of the digits 3 + 4 + 8 + 8 = 23 is not divisible by 3. Although, it is divisible by 2. 4,200 is divisible by 6, because the last digit is even and the sum of the digits 4 + 2 + 0 + 0 = 6 is divisible by 3.

Divisibility by 9: A number is divisible by 9 if the sum of its digits is divisible by 9.

Examples: Which of the following numbers is divisible by 9? 945 3,488 3,200 Solution: 945 is divisible by 9, because the sum of the digits 9 + 4 + 5 = 18 is divisible by 9. 3,488 is NOT divisible by 9, because the sum of the digits 3 + 4 + 8 + 8 = 23 is not divisible by 9. 3,200 is NOT divisible by 9, because the sum of the digits 3 + 2 + 0 + 0 = 5 is not divisible by 9.

Divisibility by 10: A number is divisible by 10 if its ones digit is 0.

Examples: Which of the following numbers is divisible by 10? 945 3,488 3,200 Solution: 94 5 is NOT divisible by 10, because the last digit is not 0. 3,48 8 is NOT divisible by 10, because the last digit is not 0. 3,20 0 is divisible by 10, because the last digit is 0.

Determine if each number is divisible by 2, 3, 5, 6, 9, or 10. 1) 34 4) 4386

2) 210 5) 1473

3) 280 6) 56,484

Math 0106 Worksheets 8  2015 Houston Community College

Prime Factorization A number c is a factor of a if a is divisible by c. A factorization of a expresses a as a product of two or more numbers. Factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. Factorizations of 24 are 1 ⋅24, 2 ⋅12, 3 ⋅8, and 4 ⋅6.

Prime and Composite Numbers  A natural number that has exactly two factors, one and itself, is called a .  Any natural number, other than one, that is not prime, is composite .

Determine whether each number is prime, composite, or neither.

1) 8 2) 13 3) 24 4) 33 5) 89

ListList of of Primes Primes from from 2 2to to 100 100

2, 2, 3, 3, 5, 5, 7, 7, 11, 11, 13, 13, 17, 17, 19, 19, 23, 23, 29, 29, 31, 31, 37, 37, 41, 41, 43 43, 47,, 47, 53, 53, 59, 59, 61, 61, 67, 67, 71, 71, 73, 73, 79, 79, 83, 83, 89, 89, 97. 97

Prime Factorization Each has a unique prime factorization. The prime factorization of a number is the product of factors where each factor is a prime number.

Example: Give the prime factorization for 84 using prime factors. 84 is divisible by 2: 84 = 2 ⋅ 42 42 is divisible by 2: 84 = 2 ⋅ 2 ⋅ 21 21 is divisible by 3: 84 = 2 ⋅ 2 ⋅ 3 ⋅ 7 7 is prime. The prime factorization for 84 is 2 ⋅ 2 ⋅ 3 ⋅ 7 or 2 2 ⋅ 3 ⋅ 7

Example: Give the prime factorization for 300 using a factor tree. 300 300 can be written as 10 ⋅ 30 10 ⋅ 30 10 can be written as 2 ⋅ 5 and 30 can be written as 5 ⋅ 6 2 ⋅ 5 5 ⋅ 6 2 and 5 are primes. Circle them. 2 ⋅ 3 6 can be written as 2 ⋅ 3. 2 and 3 are both primes. Circle them. The prime factorization is found by multiplying all circled prime numbers. 300 = 2 2 ⋅ 3 ⋅ 52

Math 0106 Worksheets 9  2015 Houston Community College

Prime Factorization − Practice

List all factors.

1) 25 2) 49 3) 7 4) 13

5) 24 6) 48 7) 168 8) 135

Determine whether each number is prime, composite, or neither.

9) 36 10) 40 11) 47 12) 31

13) 55 14) 57 15) 28 16) 13

Find the prime factorization of each number.

17) 25 18) 81 19) 45 20) 12

21) 189 22) 450 23) 242 24) 338

Math 0106 Worksheets 10  2015 Houston Community College

Understanding Fractions

A represents a part of a whole. The circle is broken into 8 equal−sized portions. The shaded region represents 3 of the 8 regions. 3 = 8

Express each shaded region as a number in fraction form.

1) 12)

2) 13)

3) 14)

4) 15)

5) 16)

6) 17)

7) 18)

8) 19)

9) 20)

10) 21)

11) 22)

Math 0106 Worksheets 11  2015 Houston Community College

Reducing Fractions

1 4 22⋅ 22 ⋅ 2 To reduce fractions , cancel out = = = 10 25⋅ 251 ⋅ 5 the common denominator

Simplify each of the following fractions by cancelling out the common factor. 16 20 1) = 2) = 36 30

4 5 3) = 4) = 10 15

10 8 5) = 6) = 15 22

16 12 7) = 8) = 34 18

36 40 9) = 10) = 45 48

200 420 11) = 12) = 320 560

210 121 13) = 14) = 350 154

90 84 15) = 16) = 84 144

12 15 17) = 18) = 360 450

224 315 19) = 20) = 364 360

Math 0106 Worksheets 12  2015 Houston Community College

Multiplying Fractions

1 29 295 29 5 29 It is much easier to multiply ⋅=5 ⋅= ⋅= 30 301 651⋅ 1 6 after reducing common factors.

Multiply each of the following fractions by first cancelling out common factors. 3 3 1) 5⋅ = 2) 4⋅ = 8 4

5 4 3) ⋅12 = 4) ⋅14 = 6 7

3 5 5 7 5) ⋅ = 6) ⋅ = 4 2 6 11

2 4 5 7 7) ⋅ = 8) ⋅ = 9 5 6 4

6 21 5 24 9) ⋅ = 10) ⋅ = 7 48 6 25

32 7 2 9 5 11) ⋅ = 12) ⋅ ⋅ = 21 8 3 10 8

1 15 6 14 45 12 13) ⋅ ⋅ = 14) ⋅ ⋅ = 4 20 9 27 16 35

7 12 7 15) 32 ⋅ = 16) ⋅ = 8 7 8

17) Determine the area of a rectangle. 18) Determine the area of the triangle.

4 inches 3/4 inch 4 cm

10/3 cm 7 19) Give the area of the rectangular garden that measures 6 yards by yards. 3

20) Common Ground Catering anticipates 45 couples eating salmon at a year−end banquet.

Allowing 2/3 pound of salmon per couple, how many pounds of salmon should be prepared?

Math 0106 Worksheets 13  2015 Houston Community College

Dividing Fractions

To divide fractions , multiply by the reciprocal.

Rewrite each using multiplication. Then complete the operation. 3 1 2 7 1) ÷= ⋅ = 2) ÷= ⋅ = 5 2 4 9

4 2 6 1 3) ÷= ⋅ = 4) ÷= ⋅ = 5 7 7 2

3 1 2 3 5) ÷= ⋅ = 6) ÷= ⋅ = 4 8 3 4

7 7 5 2 7) ÷= ⋅ = 8) ÷= ⋅ = 12 9 6 3

3 4 10 5 9) ÷= ⋅ = 10) ÷ = ⋅ = 4 5 11 66

6 12 11) 2 ÷= ⋅ = 12) ÷=5 ⋅ = 5 15

4 3 13) 3÷= ⋅ = 14) 18 ÷ = ⋅ = 5 14

2 15) How many sections of foot−long pipe can be cut from a pipe that is 20−feet long? How much pipe 3 will be left over? 3 16) After her raise, Shannon earned more than she previously made. If Shannon’s weekly wages 4 totaled $2100 after her raise, what was Shannon’s original weekly wage?

Math 0106 Worksheets 14  2015 Houston Community College

Least Common Multiples The of two or more numbers is the smallest number that is divisible by each of the given numbers.

Using Listing to find the Least Common Multiple (LCM) Find the LCM of 4 and 6. Multiples of 4: 4, 8, 12, 16, 20, 24, 28, … Multiples of 6: 6, 12, 18, 24, 30, 36 Common Multiples of 4 and 6 are 12, 24, 36, … The LCM of 4 and 6 is 12.

Using Prime Factorization to find the LCM. Find the LCM of 20 and 24. The prime factorization of 20 is 2 2 ⋅ 5 The prime factorization of 24 is 2 3 ⋅ 3 To find the LCM, multiply the prime factors raised to the highest degree that it occurs in using multiplication. Then complete the operation.

Find the least common multiple for each list of numbers.

1) 20, 30 2) 4, 6

3) 8, 12 4) 12, 20

5) 5, 7 6) 11, 13

7) 2, 3 8) 4, 10, 15

9) 6, 8, 10 10) 12, 20, 30

11) 8, 12, 20 12) 5, 7, 11

13) 2, 3, 5 14) 7, 13, 91

15) 2, 5, 10 16) 6, 12, 18

17) 20, 50, 45 18) 98, 50, 40

19) 4, 9, 36 20) 12, 75, 100

Math 0106 Worksheets 15  2015 Houston Community College

Adding and Subtracting Fractions – Common Denominators

To add fraction with common denominators: (1) Add numerators, (2) Place the sum over the common

3 1 31+ 4441 ÷ denominator, + = === 8 8 8 8842÷ (3) If possible, reduce.

Add or subtract. Be sure to reduce your answers. 1 2 3 2 1) + = 2) + = 5 5 7 7

2 2 3 1 3) + = 4) + = 9 9 4 4

2 1 5 4 5) + = 6) + = 4 4 13 13

2 1 3 3 7) − = 8) − = 6 6 8 8

3 1 7 3 9) − = 10) − = 10 10 20 20

2 4 1 1 11) + = 12) + = 15 15 4 4

33 11 18 10 13) − = 14) − = 42 42 19 19

1 3 5 17 4 1 15) + + = 16) − + = 16 16 16 20 20 20

14 4 2 16 8 4 17) − − = 18) − − = 45 45 45 32 32 32

18 12 20 9 3 5 19) + − = 20) + − = 23 23 23 20 20 20

Math 0106 Worksheets 16  2015 Houston Community College

Adding and Subtracting Fractions – Unlike Fractions

To add unlike fractions : (1) Rewrite each fraction using the same denominator, (2) Add fractions, (3) If possible, reduce.

Add or subtract. Be sure to reduce your answers. 1 1 1 5 1) + = 2) + = 2 3 3 12

1 3 3 5 3) + = 4) + = 2 10 4 16

3 3 5 1 5) − = 6) − = 8 16 6 2

2 4 5 9 7) − = 8) − = 3 9 6 20

7 11 13 6 9) − = 10) − = 10 20 14 7

5 3 11) +2 = 12) 3− = 8 4

5 10 13) 1− = 14) 4 + = 8 11

1 1 1 1 1 1 15) + + = 16) − − = 2 4 8 3 9 27

3 1 3 5 5 17) − + = 18) +2 − = 4 2 5 6 9

13 8 17 5 19) + = 20) − = 30 45 24 42

Math 0106 Worksheets 17  2015 Houston Community College

Decimal Notation – Order and Rounding

Write the word name for the number in the sentence.

1) One gallon is equal to 3.7853 liters. 2) The sales tax in Houston is 8.25 percent.

Convert Decimals to Fractions. Do not simplify.

3) .572 4) 67.023

5) 0.00045 6) 9.875

Convert Decimals to Mixed Numbers. Do not simplify.

7) 43.7 8) 5.0123

Convert Fractions to Decimals.

9) 10)

, 11) 12) ,

Which number is greater? (Order of decimals)

13) 67.89 and 67.98 14) 0.0342 and 0.04

15) 9.79 and 9.97 16) 0.00000045 and 0.00001

Round the decimal number to the indicated place

17) Round 72.3846 to the nearest hundredth. 18) Round 0.03445 to the nearest thousandth.

19) Round 19.97 to the nearest tenth. 20) Round 24.74 to the nearest one.

Math 0106 Worksheets 18  2015 Houston Community College

Adding and Subtracting Decimals

Add. 231.074 2.1523 1) +12.637 2) +9.6237

3) 56.314 + 17.78 4) 10.07 + 0.538

35.8 15.4 512.615 5) 319.725 6) 6427.5 +53.614 +23.427

Subtract. 46.974 231.074 7) −12.632 8) −12.637

9) 40.05 – 0.71 10) 6.007 – 3.2

11) 456 – 2.467 12) 23 – 3.198

Add or subtract, as indicated. 13) 6.72 + 1.62 14) 7.74 – 2.34

15) 35.6 + 47.12 16) 8.7 – 7.8

Math 0106 Worksheets 19  2015 Houston Community College

Multiplying Decimals

Multiply. 6.4 5.6 1) 2) × 3 × 0.4

35.3 5.026 3) 4) × 0.05 × 0.01

123.3 47.013 5) × 0.1 6) × 100

Multiply. 7) 2.3 × 1.12 8) (4.32)(2.34)

9) 2.037 × 10000 10) 7421.3 × 0.001

15.3 0.326 11) 12) × 142 × 512

Convert dollars to cents. 13) $19.43 14) $0.73

Convert cents to dollars. 15) 58¢ 16) 172¢

Find the area of a rectangular room with given dimensions. 17) 7.2ftwide, 12.5ftlong 18) 5.4mwide, 6.6mlong

Simplify. 19) 4.1+5×3.2 20) 82.1 − 2.1(5.25 + 6.2 × 4.7)

Math 0106 Worksheets 20  2015 Houston Community College

Dividing Decimals

Divide. 1) 4)35 2) 24)82.08

3) 2.6)104 4) 2.7)129.6

5) 8.6)5.848 6) 0.74)0.37

Divide by 10, 100, 1000, 0.1, 0.01, or 0.001 . . 7) 8)

. . 9) 10) .

. . 11) 12) . .

Simplify using order of operations. 13) 2.3 × (12.1 + 2.7) 14) (3.4 − 1.3) × 0.2

15) (5 − 0.06 ) ÷2+3.42×0.1 16) 0.07+ 2.01 ÷0.1

17) 5.4+0.32÷0.1 18) (4.5 − 3.2) + 7.4 × 0.2

19) 2.1 + 1.2 − 3.5 20) 3.4−1.3×0.2

Math 0106 Worksheets 21  2015 Houston Community College

Using Fractional Notation with Decimal Notation Convert each fraction to a terminating decimal. 1) 2) 3)

4) 5) 6)

Convert each fraction to a . 7) 8) 9)

10) 11) 12)

Convert each fraction to a decimal and round as indicated. 13) , round to the nearest thousandth 14) , round to the nearest tenth

15) , round to the nearest hundredth 16) , round the nearest ten thousandth

Simplify and write the result as a decimal. 17) (15.4) 18) (0.576 )

19) (10.6) + (7.4) 20) (0.058 ) + (7.83 )

Math 0106 Worksheets 22  2015 Houston Community College

Ratio and Proportion

1) Write as a unit rate: 350 miles on 10 12) Solve: = gallons of gas. 2) Find fraction notation for the ratio. 13) Joan can mow a 6-acre field in 2 hr. How long would it take her to mow a 3-acre Don’t simplify. 3 to 6 . field? 3) Of a family's $ 815 weekly income, $ 14) Jim drove 168 mi in 4 hr. If he can keep 125 usually goes toward groceries. the same pace, how long will it take him What is the ratio of the amount spent to drive 504 mi? on groceries to weekly income? 15) On a map of the Thunderbird Country 4) In the rectangle shown below, what is Club golf course, 0.5 in. represents 45 the ratio of length to width? Of width to yd. How long is the 7th hole if the map length? shows 3 in.? 16) In the rectangles below, the ratio of length to width is the same. Find the length of the larger rectangle.

5) Find the rate, or speed, as a ratio of distance to time. 45m, 15 sec. Simplify 6) Find the ratio of the first number to the second and simplify. 8 to 18. 17) On a test of 18 items, Charles got 15 7) If Alison's company charged $ 197.94 for correct. What is the ratio of the 6 hours of work, what rate did the incorrect to the correct ones? company charge in dollars per hour? 18) If 3 dozen eggs cost $6.27, how much 8) Determine whether the two pairs of will 2 dozen eggs cost? numbers are proportional. 19) To control a fever, a doctor suggests that a child who weighs 28 kg be given 24, 18 and 4, 3 320 mg of Tylenol. If the dosage is proportional to the child’s weight, how 9) Determine whether the two pairs of much Tylenol is recommended for a numbers are proportional. child who weighs 35 kg? 5 , 6 and 2 , 7 20) A leaky hose loses 35 gal of water in a week. What is the rate of gallons per 10) Solve : = day? 11) Solve: =

Math 0106 Worksheets 23  2015 Houston Community College

Percent Notation

Write each decimal as a percent. 1) 1. 0.00554 2) 0.119

3) The Swayed family saves 0.1217 of their income. Write this decimal as a percent

Write each percent as a decimal. 4) 35% 5) 0.39% 6) 170%

Write each fraction or mixed number as a percent. 7) 8)

9) Round to the nearest hundredth percent.

Write each percent as a fraction or mixed number in simplest form. 10) 10.276% 11) 185 % 12) 16 %

Solve. Round decimals to the nearest thousandth and percents to the nearest tenth of a percent. 13) Write the equivalent decimal and percent for .

14) Write the equivalent fraction and percent for 0.12.

15) Write the equivalent fraction and decimal for 33 %.

16) 54% of 74 is what?

17) What is 14.4% of 86?

18) Give three kinds of notation for the percent: 24%

Math 0106 Worksheets 24  2015 Houston Community College

19) The pie chart gives the fraction of a company’s total yearly sales by employee. What

percentage of yearly sales was attributed to Fred?

20) Complete the conversion table (Fraction/ Decimal/ Percent)

Fraction Decimal Percent

3/8 a) ? b) ? c) ? 0.65 d) ? e) ? f) ? 13.5%

4/9 g) ? h) ?

Math 0106 Worksheets 25  2015 Houston Community College

Solving Percent Problems and Applications

1) Translate to a percent equation. Then solve. What is 11% of 49?

2) Jennifer invests $10,000 at 7% simple interest. How much is in her account after 2 year?

3) Find the better buy (lower cost per ounce) by finding each unit price rounded to three decimal places, if necessary. Assume that different sizes of the same brand are being compared. Shampoo: $6.72 for 12 ounces $9.90 for 18 ounces

4) A bag of fertilizer covers 2000 square feet of lawn. Find how many bags of fertilizer should be purchased to cover a rectangular lawn 110 feet by 140 feet.

5) A fire fighter needs to estimate the height of a burning building. She estimates the length of her shadow to be 8 feet long and the length of the building’s shadow to be 72 feet long. Find the height of the building if the fire fighter is 5 feet tall. Round to the nearest tenth if necessary.

6) In a survey of 100 people, 4 preferred relish on their hot dogs. What percent preferred relish?

7) A basketball player made 30 out of 100 attempted free throws. What percent of free throws was made?

8) 71 is 0.71% of what number?

9) 2 is what percent of 16?

10) An inspector found 12 defective cameras during an inspection. If this is 0.012% of the total number of cameras inspected, how many cameras were inspected?

11) What percent of 46 is 458?

12) At one point in 2004, a quarterback had completed 46.3% of his passes throughout his career. He had attempted 2206 passes. How many did he complete?

Math 0106 Worksheets 26  2015 Houston Community College

13) Last year, Maria earned $ 323 per week. This year, her salary increased to $345 per week. What is the percent of increase?

14) The sales tax rate in Houston is 8.255%. How much tax will be charged on a purchase of 3 chairs at $61 a piece? Round your answer to the nearest cent.

15) Find the missing value: Marked Price Rate of Discount Discount Sale Price $157 10%

16) The Dow Jones Industrial Average (DJIA) plunged from 11,143 to 10,365 on September 29, 2009. This was the largest one-day drop in its history. What was the percent of decrease?

17) A kitchen table costs $ 230. The sales tax is $ 6.90. What is the sales tax rate and what is the total price paid?

18) 45 % of 92 is what?

19) 21 is 6% of what?

20) If a flagpole 12 feet tall casts a shadow that is 16 feet long, find the length of the shadow cast by an antenna which is 30 feet tall. Round to the nearest tenth if necessary.

Math 0106 Worksheets 27  2015 Houston Community College

Order of Operations Parentheses Exponents and Roots Multiplication & Division Addition &

Simplify each of the following expressions.

2 1) ()5 15) 42÷( 24 −⋅ 2 5) + 2 3

2) 102− 5 2 16) 9+ 25

4 2 3) 2− 4 17) 4( 200− 100) ÷ 64 + 36

4) 2 − ⋅ 2 12 2() 4 2 2 18) ()()7− 4 + 128 −

2 5) 22 + 5 ( ) 11  11  19) +  − −  48  48  2  6) 10+ 22 −() 4 − 3  22  1 4  20) ÷  ⋅  3  2 3  2 9  7)   5  3+() 54 −2 − 2 21) 8) 6− 3 − 2 − 1 9− 2 − 5

2 2 9) ()()4− 3 32⋅2 − 5 2 ÷( 61 − ) 22) 2+ (5 + 7) 10) 62 − 6

11) 10− 3( 6 − 4 )

12) 8− 2 ⋅ 3

13) 3⋅ (4 + 4) − 7

14) 512( − 7)( 7 − 2 )

Math 0106 Worksheets 28  2015 Houston Community College

Review of Order of Operations Worksheet

1) 14 – 2(3)

2) 3 + 4(5) – 2

3) 16 − 3 2

4) 3(6 – 4) + 3 − 6

5) 2 × 32 – 4 ÷ [8 + 2(2)]

6) 32 – 22 – 22 + 32

7) 90 – 8 × 7 + 6 ÷ ( 5 – 4 + 3 − 2)

4(3)+ 3 2 8) 2+ 22 + 1

9) (2 + 3) 2 – (16 – 42)

10) 2{10 – [14 – (8 – 3)]}

11) (10 2 – 1) – (10 – 1) 2

12) 5 + 3[5(5) – 2]

Math 0106 Worksheets 29  2015 Houston Community College

Getting Ready for Factoring Polynomials 1 In Math 0409, you will learn how to factor polynomials. The key to being able to factor is to be able to find the relationship between two numbers: the product and the sum. This worksheet will help you to practice this concept. For each pair of numbers, give the product and the sum.

Product Sum Product Sum 3 11 33 14 2 10 9 3 12 11 10 3 6 5 4 7 11 1 10 12 10 10 7 9 2 11 4 10 7 2 5 6 2 8 7 3 9 6 5 8 10 8 2 6 4 1 5 9 11 1 5 2 8 2 5 7 8 7 3 9 9 5 3 0 6 3 10 12 9 1 9 9 11 8 12 9 12 5 12 4 4 3 10 11 6 0 2 12 5 2 5 12 7 12

Math 0106 Worksheets 30  2015 Houston Community College

Getting Ready for Factoring Polynomials 2 In order to factor polynomials, you need to be able to determine which two factors of a number will give a specific sum. This worksheet will help you to practice this concert. For each product and the sum, determine the pair of numbers.

Product Sum Pair of Numbers Product Sum Pair of Numbers 28 11 4, 7 60 16 110 21 10, 11 30 13 81 18 42 13 18 11 56 15 16 10 24 11 50 15 14 9 48 14 54 15 16 8 90 19 22 13 10 7 96 22 8 9 1 2 70 13 36 12 63 16 132 23 40 14 35 12 21 10 36 12 12 7 11 12 45 14 22 13 36 13 16 10 15 8 100 20 54 15 63 16 110 21 22 13 77 18 10 11 121 22 12 7 66 17 10 7 18 9

Math 0106 Worksheets 31  2015 Houston Community College

Week 1 Quiz

1) Of 99 cars making up a freight train, 62 are boxcars. What fraction of the cars are not boxcars?

8 2) Identify the numerator and denominator in the fraction 7

3) Circle all proper fractions in the following list. Place a box around all improper fractions.

15 15 6 7 9 2 , , , , , 13 16 5 6 14 5

4) Fill in the blanks to complete the sentence. 7 The fraction represents ______of the ______equal parts into which a whole is 17 divided.

13 5) Convert to a mixed number. 3

6) Find all factors of 375.

7) Determine whether 25 is prime, composite, or neither.

8) Find the prime factorization of 200.

9) Circle each number that is divisible by 3.

95, 171, 57, 285, 114, 38, 456, 1368, 760, 380, 76, 152

80 10) Write in lowest terms. 112

16 24 11) True or false. = 36 54 930 12) Write in lowest terms. 186

Math 0106 Worksheets 32  2015 Houston Community College

22 21 8 13) Multiply. Give your answer in lowest terms. ⋅ ⋅ 49 52 33

4 14) Multiply. Give your answer in lowest terms. 63⋅ 9

15) Find the area of the rectangle. Give your answer in yd 2.

27 yards

yard

1 4 16) A rectangular laboratory tray is feet by feet. Find the area. 2 3

7 17) Give the reciprocal of . 3 5 3 18) Divide. Give your answer in lowest terms. ÷ 3 2

36 19) Divide. Give your answer in lowest terms. 4 7

20) A topical cream is sold in a 22-gram container. The average amount of topical cream used per 2 application is grams. How many applications can be made with the container? 9

Math 0106 Worksheets 33  2015 Houston Community College

Week 1 Quiz - Solutions 5 10) 7 37 11) True 1) 99 12) 5 2) numerator: 8; denominator: 7 4 13) 91 15 15 6 7 9 2 14) 28 3) , , , , , 13 16 5 6 14 5 15) 21 2 16) 4) 7, 17 3 1 3 5) 4 17) 3 7 6) 1, 3, 5, 15, 25, 75, 125, 375 10 18) 7) composite 9 8) 23 · 5 2 19) 63 20) 99 9) 95, 171, 57, 285, 114, 38, 456, 1368, 760, 380, 76, 152

Math 0106 Worksheets 34  2015 Houston Community College

Week 2 Quiz

15 1 4 1) Add and simplify. + + 23 23 23

21 7 2) Subtract and simplify. − 16 16

4 15 12 3) A forester planted acre in seedlings in the morning and acre in the afternoon. If acre of 17 17 17 seedlings were destroyed by frost, how many acres remained?

4) Find the least common multiple of 4 and 5.

5) Rewrite the fraction with the denominator of 33. 6 = 11 33

3 1 6) Add and simplify. + 8 6

2 5 7) Subtract and simplify. − 3 12

4 2 8) Monica spent hours listening to tapes of Beethoven and Brahms. She spent hours listening to 7 5 Beethoven. How many hours were spent listening to Brahms?

7 9) Plot on the number line. 6

30 1 10) Fill in the blank with < or > to make a true statement. ____ 75 15

3  3 11) Evaluate.   5 

Math 0106 Worksheets 35  2015 Houston Community College

1 1  2 2 12) Use the order of operations to simplify. +  − 5 5  125

2  2 13) Evaluate.   5 

14) List the digit that has the given place value for the number, 8240.7513

thousands:______thousandths:______hundredths:______

15) Write the decimal number that has the specified place values.

7 hundredths, 3 hundreds, 1 ten, 0 tenths, 2 thousandths, 1 thousand, 0 ones

16) Write 0.6 as a fraction in lowest terms.

17) Write “two hundred eighty and seven tenths” in numbers.

18) Corn is 3 cans for $1.12, so each can of corn is $0.3733. How much, to the nearest cent, does it cost for each can of corn?

19) Use the list of Olivia’s expenses to find Olivia’s total expenses for the month.

Rent $922 Car payment $192.67 Car repairs/gas $211 Cable TV $39.14 Internet $15.95 Electricity $47.53 Telephone $53.41 Groceries $184.26 Entertainment $92.47 Clothing/laundry $101

20) Use estimation to choose the most reasonable answer. DO NOT solve the problem. 2006.008 + 54.7167

a) 20.607247 b) 206.07247 c) 2060.7247

Math 0106 Worksheets 36  2015 Houston Community College

Week 2 Quiz - Solutions

20 1) 23 7 2) 8 7 3) 17 4) 20 5) 18 13 6) 24 1 7) 4 6 8) 35

9) 10) > 27 11) 125 28 12) 125 4 13) 25 14) 8, 1, 5 15) 1310.072 3 16) 5 17) 280.7 18) $0.37, or 37 ₵ 19) 1859.43 20) C

Math 0106 Worksheets 37  2015 Houston Community College

Week 3 Quiz

$55.68 1) Multiply. × 685

2) Paper for the copy machine at the library costs $0.064 per sheet. How much will the library pay for 2000 sheets? Round to the nearest cent.

3) Use the fact that 136 ÷ 17 = 8 to divide 1.36 ÷ 0.17

4) A food company will give a school 5 ₵ for each box top that the students bring in to the school. Each school can earn up to $2000. How many box tops do students have to collect in order to earn the maximum amount?

5) Simplify using order of operations. 48.1 + 13.5 · (15.2 – 13.2)

1 6) Write as a decimal. 4

3 7) Write as a decimal. 5

8) Change the measurement on the drawing from fraction form to decimal form. Round to the nearest tenth.

3 in 4 9) Arrange in order from smallest to largest. 2.446, 24.123, 1.46, 3.825

10) Compare the ratio of the longest side to the shortest side. 1 3 12 8 Simplify the ratio. 2 4

6

1 3 2 3 4 4 11) Write the rate as a fraction in lowest terms: 6 persons for 32 dresses

Math 0106 Worksheets 38  2015 Houston Community College

12) A grocery store sells four different jars of peanut butter. Determine which is the best buy, based on the cost per unit.

14 ounces for $1.60 20 ounces for $2.14 30 ounces for $2.76 38 ounces for $4.83

13) Three brands of cornflakes are available. You have a coupon for 50 ₵ off Brand P, and a coupon for 60 ₵ off Brand G. Which cereal is the best buy?

Brand G: $2.39 for 9 ounces Brand K: $3.99 for 16.6 ounces Brand P: $3.39 for 15.1 ounces

14) Write the proportion: 7.5 hours is to 4.5 hours as 8.5 hours is to 5.1 hours Do not simplify.

3 12 15) True or False? = 10 20

16) Solve using a proportion: If 3 pounds of grass seed cover 407 square feet, how many pounds are needed for 7733 square feet?

17) Write 6.3% as a decimal.

18) There are 25 children in the preschool class. 100% of the children are served breakfast and lunch. Find the number of children who are served both meals.

19) Convert 9.25% to fraction form. Simplify your answer.

20) Sharon needs 64 credits to graduate from her community college. So far she has earned 40 credits. What percent of the required credits does she have?

Math 0106 Worksheets 39  2015 Houston Community College

Week 3 Quiz - Solutions 1) $38,140.80

2) $128.00

3) 8

4) 40,000

5) 75.1

6) 0.25

7) 0.75

8) 0.8

9) 1.46, 2.446, 3.825, 24.123

50 10) 9 3 persons 11) 16 dresses

12) 30 ounces for $2.76

13) Brand P: $3.39 for 15.1 ounces

7.5 8.5 14) = 4.5 5.1

15) False

16) 57

17) 0.063

18) 25

37 19) 400 20) 62.5

Math 0106 Worksheets 40  2015 Houston Community College

Math 0106

Basic Mathematics

In Class Worksheets

Spring 2015

Worksheet Answer Key

Math 0106 Worksheets 41  2015 Houston Community College

Multiples and Divisibility - Key 1) 2, 4, 6, 8 3) 6, 12, 18, 24 5) 9, 18, 27, 36

2) 4, 8, 12, 16 4) 8, 16, 24, 32 6) 10, 20, 30, 40

7) Divisible by 2 9) Divisible by 2, 5, 10 11) Divisible by 3

8) Divisible by 2, 3, 5, 6, 10 10) Divisible by 2 12) Divisible by 2, 3, 6, 9

Prime Factorization

1) Composite 3) Composite 5) Prime

2) Prime 4) Composite

Prime Factorization - Practice 1) 1, 5, 25 8) 1, 3, 5, 9, 15, 27, 45, 135 17) 52

2) 1, 7, 49 9) Composite 18) 34

3) 1,7 10) Composite 19) 32 ⋅5

4) 1, 13 11) Prime 20) 22 ⋅3

5) 1, 2, 3, 4, 6, 8, 12, 24 12) Prime 21) 33 ⋅7

6) 1, 2, 3, 4, 6, 8, 12, 24, 48 13) Composite 22) 2⋅32⋅52

7) 1, 2, 3, 4, 6, 7, 8, 12, 14, 14) Composite 23) 2⋅11 2

21, 24, 28, 42, 56, 84, 15) Composite 24) 2⋅7⋅17

168 16) Prime

Math 0106 Worksheets 46  2015 Houston Community College

Understanding Fractions 1 1 1 9 1 = 2 1) 2 7) 4 13) 6 19) 4 4

3 1 5 1 11 5 6 = 1 = 1 = 1 = 3 2) 2 2 8) 4 4 14) 6 6 20) 2

1 9 1 19 3 11 3 = 2 = 2 = 3 3) 3 9) 4 4 15) 8 8 21) 4 4

5 2 11 3 9 1 11 2 = 1 = 2 = 1 = 3 4) 3 3 10) 4 4 16) 8 8 22) 3 3

7 1 10 2 1 3 = 2 =2 = 2 = 1 5) 3 3 11) 4 4 2 17) 3

11 2 2 = 3 = 1 6) 3 3 18) 2 11 3 = 2 12) 4 4

Reducing Fractions 4 4 5 7 1) 9 6) 11 11) 8 16) 12

2 8 3 1 2) 3 7) 17 12) 4 17) 30

2 2 3 1 3) 5 8) 3 13) 5 18) 30

1 4 11 8 4) 3 9) 5 14) 14 19) 13

2 5 15 1 7 = 1 5) 3 10) 6 15) 14 14 20) 8

21)

Math 0106 Worksheets 47  2015 Houston Community College

Multiplying Fractions

15 7 8 4 1 3 1 = 1 = 1 = 1 1) 8 8 7) 45 11) 3 3 16) 2 2

2) 3 35 11 3 17) 3 square inches = 1 8) 24 24 12) 8 3) 10 202 2 2 cm= 6 cm 3 1 18) 3 3 4) 8 9) 8 13) 8

15 7 = 1 4 1 5) 8 8 19) 14 yd 2 10) 5 14) 2

35 15) 28 20) 30 pounds

6) 66

Dividing Fractions

31 32 6 1 2 3 24 8 12 12 1 4 1) ÷ = ⋅ = = 1 6) ÷ = ⋅ = ÷=5 ⋅ = 52 51 5 5 3 4 33 9 12) 15 15 5 25 2 7 29 9 7 7 79 3 4 3 5 15 3 2) ÷ = ⋅ = 7) ÷ = ⋅ = 3÷ =⋅= = 3 4 9 4 7 14 12 9 12 7 4 13) 514 4 4

4 2 47 14 4 52 53 5 1 3 18 14 3) ÷=⋅= = 2 ÷ = ⋅ = = 1 18÷ = ⋅ = 84 5752 5 5 8) 63 62 4 4 14) 14 1 3

3 4 3 5 15 ÷ = ⋅ = 15) 30 sections; none left 4 5 4 4 16 6 1 62 12 5 9) 4) ÷=⋅= = 1 7271 7 7 10 5 10 66 over ÷ = ⋅ = 12 11 66 11 5 10) 16) $1200 6 25 5 2 3 1 38 2÷ = ⋅ = = 1 5) ÷ = ⋅ = 6 4 8 41 11) 5 16 3 3

Math 0106 Worksheets 48  2015 Houston Community College

Least Common Multiples

1) 60 6) 143 11) 120 16) 36

2) 12 7) 6 12) 385 17) 450

3) 24 8) 30 13) 30 18) 9800

4) 60 9) 120 14) 91 19) 36

5) 35 10) 60 15) 10 20) 300

Adding and Subtracting Fractions – Common Denominators

3 9 2 7 1) 6) 11) 16) 5 13 5 10

5 1 1 8 2) 7) 12) 17) 7 6 2 45

4 8) 0 11 1 3) 13) 18) 9 21 8 1 9) 4) 1 5 8 10 14) 19) 19 23 3 1 5) 10) 4 5 9 7 15) 20) 16 20

Adding and Subtracting Fractions – Unlike Fractions

5 1 21 5 5 1) 6) 11) = 2 16) 6 3 8 8 27 3 2 9 1 17 2) 7) 12) = 2 17) 4 9 4 4 20 4 23 3 41 5 3) 8) 13) 18) = 2 5 60 8 18 18 17 1 3 54 10 11 4) = 1 9) 14) = 4 19) 16 16 20 11 11 18 3 1 7 33 5) 10) 15) 20) 16 14 8 56

Math 0106 Worksheets 49  2015 Houston Community College

Decimal Notation – Ordering and Rounding

1) Three and seven thousand, eight hundred fifty-three ten-thousandths 2) Eight and twenty-five hundredths 572 9875 10) 1.03 17) 72.38 3) 6) 1000 1000 11) 0.00137 18) 0.034 67 ,023 7 12) 12.3067 19) 20.0 4) 7) 43 1000 10 13) 67.98 20) 25 45 123 14) 0.04 5) 8) 5 15) 9.97 100 ,000 10 ,000 16) 0.00001 9) 0.03

Adding and Subtracting Decimals

1) 243.711 5) 409.139 9) 39.34 13) 8.34 2) 11.776 6) 6978.942 10) 2.707 14) 5.4 3) 74.094 7) 34.542 11) 453.533 15) 79.72 4) 10.608 8) 218.437 12) 19.802 16) 0.9

Multiplying Decimals

1) 19.2 6) 4701.3 11) 2172.6 16) $1.72 2) 2.24 7) 2.576 12) 166.912 17) 90 ft 2 3) 1.765 8) 10.1088 13) 1943 ₵ 18) 35.64 m 2 4) 0.05026 9) 20,370 14) 73 ₵ 19) 20.1 5) 12.33 10) 7.4213 15) $0.58 20) 9.881

Dividing Decimals

1) 8.75 6) 0.5 11) 0.0453 16) 20.17 2) 3.42 7) 3.58 12) 2465 17) 37.4 3) 40 8) 0.000128 13) 34.04 18) 3.17 4) 48 9) 0.53147 14) 0.42 19) 2.35 5) 0.26 10) 1380.7 15) 125.208 20) 3.14

Using Fractional Notation with Decimal Notation

1) 3.25 7) 6.0 12) .1 142857 17) 9.625 2) 0.15 18) 0.384 8) 27.0 13) 0.533 3) 0.275 14) 1.2 19) 16.4 9) 35.0 4) 10.3 15) 0.43 20) 9.4395 10) 36.1 5) 0.25 16) 1.7143 6) 0.125 11) 0.83

Math 0106 Worksheets 50  2015 Houston Community College

Ratio and Proportion

1) 35 mi/gal 4) 251/129, 9) No 15) 270 yd 7 129/215 10) 12 16) 15 ft 3 5) 3 m/sec 11) 84 17) 1/5 2) 8 1 6) 4/9 12) 3/2 18) $4.18 6 4 7) $32.99/hr 13) 1 hr 19) 400 mg 3) 25/163 8) Yes 14) 12 hr 20) 5 gal/day

Percent Notation 1) 0.554% 7) 58% 3 15) 1/3, 0.333 11) 27 2) 11.9% 2 5 16) 39.96 8) 41 % 3) 12.17% 3 1 17) 12.384 12) 4) 0.35 9) 46.67% 6 18) 24%, 6/25, 0.24 5) 0.0039 10) 27.6 13) 0.053, 5.3% 19) 2/25 6) 1.7 14) 3/25, 12% 4 20) a) 0.375, b) 37.5%, c) 13/20, d) 65%, e) 27/200, f) 0.135, g) 0.4 , h) 44 % 9

Solving Percent Applications 1) 0.11 × 49 = x, 5.39 6) 4% 11) 995.65% 16) 6.98% 2) $10,700 7) 30% 12) 1021 17) 3% 3) $9.90 for 18 ounces 8) 10,000 13) 6.81% 18) 41.584 4) 8 bags 9) 12.5% 14) $15.11 19) 350 5) 48 ft 10) 100,000 15) $15.70, $141.30 20) 40 ft

Order of Operations 1) 25 7) 9/25 13) 17 19) ¼ 2) 75 8) 0 14) 125 20) 2 3) 0 9) 7 15) 15 21) 1 4) 112 10) 30 16) 8 22) 1/2 5) 81 11) 4 17) 20 6) 12 12) 2 18) 5

Review of Order of Operations Worksheet 1) 8 4) 3 7) 37 10) 2 2) 21 5) 17 2/3 = 53/3 8) 3 11) 18 3) 7 6) 10 9) 25 12) 74

Math 0106 Worksheets 51  2015 Houston Community College

Getting Ready for Factoring Polynomials 1 - Key In Math 0409, you will learn how to factor polynomials. The key to being able to factor is to be able to find the relationship between two numbers: the product and the sum. This worksheet will help you to practice this concept. For each pair of numbers, give the product and the sum.

Product Sum Product Sum 3 11 33 14 2 10 20 12 9 3 27 12 12 11 132 23 10 3 30 13 6 5 30 11 4 7 28 11 11 1 11 12 10 12 120 22 10 10 100 20 7 9 63 16 2 11 22 13 4 10 40 14 7 2 14 9 5 6 30 11 2 8 16 10 7 3 21 10 9 6 54 15 5 8 40 13 10 8 80 18 2 6 12 8 4 1 4 5 5 9 45 14 11 1 11 12 5 2 10 7 8 2 16 10 5 7 35 12 8 7 56 15 3 9 27 12 9 5 45 14 3 0 0 3 6 3 18 9 10 12 120 22 9 1 9 10 9 9 81 18 11 8 88 19 12 9 108 21 12 5 60 17 12 4 48 16 4 3 12 7 10 11 110 21 6 0 0 6 2 12 24 14 5 2 10 7 5 12 60 17 7 12 84 19

Math 0106 Worksheets 52  2015 Houston Community College

Getting Ready for Factoring Polynomials 2 - Key In order to factor polynomials, you need to be able to determine which two factors of a number will give a specific sum. This worksheet will help you to practice this concert. For each product and the sum, determine the pair of numbers.

Product Sum Pair of Numbers Product Sum Pair of Numbers 28 11 4, 7 60 16 10,6 110 21 10, 11 30 13 3,10 81 18 9,9 42 13 6,7 18 11 9,2 56 15 7,8 16 10 8,2 24 11 3,8 50 15 5,10 14 9 2,7 48 14 6,8 54 15 9,6 16 8 4,4 90 19 10,9 22 13 11,2 10 7 2,5 96 22 16,6 8 9 8,1 1 2 1,1 70 13 None 36 12 6,6 63 16 7,9 132 23 11,12 40 14 4,10 35 12 7,5 21 10 7,3 36 12 6,6 12 7 3,4 11 12 11,1 45 14 9,5 22 13 2,11 36 13 9,4 16 10 8,2 15 8 3,5 100 20 10,10 54 15 9,6 63 16 7,9 110 21 10,11 22 13 11,2 77 18 7,11 10 11 10,1 121 22 11,11 12 7 3,4 66 17 6,11 10 7 2,5 18 9 6,3

Math 0106 Worksheets 53  2015 Houston Community College