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by: Anna Kolar

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# Schaum's Math Quiz 1 Notes for Chapter 1 CS200

Marketplace > Boston University > Computer science > CS200 > Schaum s Math Quiz 1 Notes for Chapter 1
Anna Kolar
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## About this Document

These notes cover Chapter 1 of Schaum's Outlines College Algebra Fourth Edition, which will be included in Math Quiz 1
COURSE
Fundamentals of Information Technology
PROF.
Bragg
TYPE
Class Notes
PAGES
6
WORDS
CONCEPTS
Algebra, sum, subtracting, adding, products, multiplication, dividing, fractions, Positive, Negative, absolute, value, imaginary, real, commutative, associative, exponents, power, Reciprocal, numerator, denominator, common denominator
KARMA
25 ?

## Popular in Computer science

This 6 page Class Notes was uploaded by Anna Kolar on Saturday September 10, 2016. The Class Notes belongs to CS200 at Boston University taught by Bragg in Fall 2016. Since its upload, it has received 20 views. For similar materials see Fundamentals of Information Technology in Computer science at Boston University.

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Date Created: 09/10/16
Schaum’s College Algebra Fourth Edition – Chapter 1 – Module 1 Term Definition Example Example  Page #  Section using #s of  Exampl es Sum When two numbers are added together A + B =C 1+1=2 1.1 Difference When one number is subtracted from another number A – B = C 4­3=1 1.1 How do you define  In A – B = C, C + B = A 5 – 2 = 3 1.1 addition through  3 + 2 = 5 subtraction? Product When two numbers are multiplied by each other A x B = C (2)(2) = 4 1.1 A ∙ B = C A(B) = C (A)(B) = C Quotient Dividing a number by another number. A ÷ B = C 10 / 2 = 5 1.1 A / B = C A/ B  C Dividend The number which is being divided by another number In A / B, A is the  1.1 dividend Divisor The number you are dividing by In A / B, B is the  1.1 divisor Fraction A number over another number A / B 1.1 Numerator The number on the top of the fraction In A / B, A is the  1.1 numerator Denominator The number on the bottom of the fraction In A / B, B is the  1.1 denominator Division by 0 Cannot be defined; you cannot divide by zero 1.1(b)  1.1 and (e) How do you define  If A / B = C, C(B) = A 6 / 3 = 2 1.1 multiplication through  2(3) = 6 division? Natural numbers 1, 2, 3, 4, etc. 1.2 … Etc 1.2 Positive rational  Quotient of two positive integers (can be written as a ratio) 2/3, 8/5, etc. 1.2 numbers/fractions Positive irrational  Positive and aren’t rational (doesn’t terminate of repeat) Pi, sqrt 2, etc. 1.2 numbers Zero (0) Any number multiplied by 0 = 0 BUT any number divided by 0 DOES  5*0 = 0 1.2 Schaum’s College Algebra Fourth Edition – Chapter 1 – Module 1 NOT equal 0 5/0 = ERR Negative Integers Can be rational and irrational; a number less than 0; denotated with a  ­2 5­6 = ­1 1.2 negative sign (­) in front of the number – assume the number is positive if this is not present Real number system All positive and negative rational and irrational numbers AND zero 1.2 Imaginary numbers Opposite of real numbers (will be described later) 1.2 Graphical  Number line with 0 in the middle, positive integers on the right and  Fig 1.1 1.3 represenatation of real  negative integers on the left numbers Greater Larger; a number further to the right on the number line than another  A > B 5 > 3 1.3 number ( >) Less Smaller; a number further to the left on the number line than another  A < B 2 < 10 1.3 number (<) Absolute/Numerical  Number is the distance of the number from the origin on a number line | A | | ­4 | = 4 1.3 Value Commutative property  The order of addition does not change the result A+B=B+A 3+4+3 = 10 1.4 for addition 4+3+3=10 Associative property  You may group without any change in result A+B+C = A+ 4+3+3=10 1.4 for addition (B+C) 4+(3+3) = 10 Commutative property  The order of numbers doesn’t effect a result AB = BA 2*5 = 10 1.4 for multiplication 5*2 = 10 Associative property  You may group without any change in result A*B*C =  3*4*5=60 1.4 for multiplication A(B*C) 3*(4*5)=60 Distributive property  Multiplying a number with the sum of two numbers is the same as  A(B+C) = AB +  1.4 for multiplication over  multiplying a number with the two numbers individually while adding AC addition Adding two numbers  Add absolute values and prefix the common sign 4+1 = 5 1.5 with like signs ­4 + ­1 = ­5 Adding numbers with  Find the difference between absolute values; prefix with the greater  2­5 = ­3 1.1 1.5 unlike signs absolute value Subtracting Change operation to addition and replace with opposite a­b = a + ­b 1.2 1.5 Multiplying/dividing  Multiply or divide absolute values; prefix a plus sign (or no sign) 5*2 = 10 1.3 1.5 with like signs (­5)*(­2) = 10 Multiplying/dividing  Multiply/divide and prefix with negative sign 5* (­2) = ­10 1.4 1.5 with unlike signs Exponents/Powers Multiplying a number by itself n times (A ) A*A*A = A 3 2  = 8 1.5 1.6 Base In an exponent, the number being multiplied (A) 1.6 Schaum’s College Algebra Fourth Edition – Chapter 1 – Module 1 Exponent In an exponent, the number of times you are multiplying by (n) 1.6 Multiplying exponents Add the exponents A * A = A p+q 1.6 Dividing exponents Subtract the exponents (A )/ (A ) = A p­q 1.6 p q pq Multiplying by  Multiply the exponents (A )  = A 1.6 exponents Exponents on  Each number gets an exponent before the multiplication/division function (ab)  = a  * b 1.6 n  n n multiplied/divided  (a/b) = (a ) / (b ) numbers Multiplying/dividing  Value of a fraction is the same (as long as you aren’t multiplying/dividing 3/4 * 2/2  1.6 1.7 fractions by the same  by zero) = 6/8  number = 3/4 Changing sign of  Changes sign of fraction ­2/3 = ­(2/3)  1.7 1.7 numerator/denominator = 2/­3 Adding fractions with  Sum the numerator; keep the common denominator A/B + C/B =  1/5 +2/5 1.8 1.7 common denominator (A+C)/B = 3/5 Sum/difference of  Give each fraction the same denominator and then subtract ½ + 2/3 1.9 1.7 fractions with different  = 3/6 + 4/6  denominators = (3+4)/6 Product of two  Multiply the numerators and denominators then simplify A/B * C/D = 2/5 * ½ 1.10 1.7 fractions AC/BD = 2/10 = 1/5 Reciprocal of a fraction A fraction where the numerator is the denominator and the denominator  A/B becomes  1.7 is the numeral B/A Dividing fractions Cross multiply; multiply the first by the reciprocal of the second (A/B) / (C/D) (2/5) / (1/2) 1.11 1.7 = AD / BC = (2*2) / (5*1) = 4/5 Example Problems: See pages 5­10 1.1 Find the sum, difference, product, and quotient 2, 10 Sum = 2+10 = 12 Difference = 2­10 = ­8 Product = 2*10 = 20 Quotient = 2/10 = 1/5 1.2 Perform an operation using order of operations 2+(4*1)­6/3 Parenthesis: 2+4­6/3 Multiplication and Division: 2+4­2 Addition and Subtraction: 4 1.3 Classify numbers as real, positive integer, negative integer, rational,  5 Real, positive integer, rational number irrational, or none of these ­2 Real, negative integer, rational number Schaum’s College Algebra Fourth Edition – Chapter 1 – Module 1 √­1 None of these options 0.2468 Real, rational 7∏ Real, irrational 1.4 Be able to place numbers on a number line 1.5 Show whether a number is greater than, or less than, another number  4,8 4 < 8 through the use of greater than or less than symbols ­4, ­8 ­4 > ­8 1.6 Arrange real numbers based on their magnitude (ascending) 1.7 Write absolute values ­1 |­1| = 1 4 |4| = 4 2.5 |2.5| = 2.5 √­1 |­√1| = √ 2∏ |2∏| = 2∏ 1.8 Addition and subtraction of real numbers ­1 + ­2 = ­3 1+2 = 3 ­1+2 = 1 1­2 = ­1 ­1 – 2 =  ­3 ­1 ­ ­2 = 1 1.9 Find the sum, difference, product, and quotient (positive and negative  2,­10 Sum: ­8 numbers) Difference: 12 Product: ­20 Quotient: 2/­10 = 1/­5 5,0 Sum: 5 Difference: 5 Product: 0 Quotient: 0 1.1 Solve using order of operations 3(­4)          6(­4)     ­12         ­24                ­24 0 ­­­­­­    +  ­­­­­­­­­ = ­­­­­­   +  ­­­­­  = ­6 +  ­­­­­­ = ­12 2               5(1)­3       2           5­3                 2 1.1 Evaluating exponents 43 =4*4*4 = 64 2 3 5 1 2  * 2 = 2  = 32 3 /38 = 3  = 1/3  = 1/729 2 1 3 6 3 (2 /4 ) = 2 /4  = 64/64 = 1 3  * 33 =    3         ­­­­­1       ­­­­­­­­ =  3  = 3     3    3      4 Schaum’s College Algebra Fourth Edition – Chapter 1 – Module 1 1.1 Create equivalent fractions (fractions with the same denominator) 3/4, 20 = 3*5/4*5 = 15/20 2 1.1 Finding the sum, difference, product, and quotient of fractions ½, ­5/24 = 12            5 3   ­­­­­  +  ­ ­­­­­   = 7/24     24           24 = 12             5         ­­­­   ­  ­  ­­­­     = 17/24     24            24 =  ­5/48 =  ½ * ­24/5   = ­24/10 = ­12/5 = ­2 2/5 1.1 Evaluate if x=1, y= ­2, z= 4, a= 1/3, and b= ­1/2 4  – 2x         4  – 2(1) 4 ­­­­­­­­­­ = ­­­­­­­­­­­­­­­­­­­­­ 3 2 5x y ­3a     5(1) (­2) – 3(1/3) =        16 – 2(1)     ­­­­­­­­­­­­­­­­­­­     5(1)(­2) – 3(1/3) =      16­2     ­­­­­­­­­­­­­      ­10 – (3/1 * 1/3) =   16­2     ­­­­­­­­    ­10 – (3/3) = 16­2   ­­­­­­­­ Schaum’s College Algebra Fourth Edition – Chapter 1 – Module 1   ­10 – 1 =   14/­11

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