[PDF] Introduction to Mathematical Reasoning Math 310 Spring 2006





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If a=b then a can be substituted for b in any equation. The Addition and Subtraction Properties. If a=b







Introduction to Mathematical Reasoning Math 310 Spring 2006

(e) (a/b)?1 = b/a if a and b are nonzero. 5. Properties of quotients. (a) a/1 = a. (b) (a/b)(c/d)=(ac)/(bd) if b and d are nonzero.



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a+b c = a c + b c but a b+c 6= a b + a c (b) Cancellation of the c here requires that it appears in each additive term of the numerator and denominator: ca+cb cd = c(a+b) cd = a+b d but ca+b cd 6= a+b d (c) Compound fractions can be simpli?ed by using the rule “division is the same as multiplication by the reciprocal”: a b c d = a b ÷ c



A B and C are polynomials where A = n B = 2n + 6 and

an ACT workbook for the classroom by Jeremy AikinandMatt Bennett This product was made possible by the National Science Foundation GK- 12 Fellows Program at Louisiana State University the Louisiana Education Quality Support Fund and the Gordon A Cain Center at Louisiana State University



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a# 1 b# c2= # # a # b = b # a a # a Z 0 1 a = 1 a # 1 = a a Z 0 a # 0 = 0 a +1 b c2= a + b = b + a a + 1-a2 = 0 a + 0 = a Key Words and Symbols The following words and symbols are used for the operations listed Addition Sum total increase plus addend 3addend = sum Subtraction minuend subtrahend = difference Multiplication Product of times



Searches related to a/b/c/d math PDF

ccomes from c 2= a2 + b and asymptotes that pass through the center y= b a (x h) + k (y 2k) a 2 (x 2h) b = 1 This graph is a hyperbola that opens up and down has center (h;k) vertices (h;k a); foci (h;k c) where ccomes from c 2= a2 + b and asymptotes that pass through the center y= a b (x h) + k Pythagorean Theorem A triangle with legs

What is a B B and C in math?

A, B, and C are polynomials, where A = n, B = 2n + 6, and C = n2 – 1. What is AB – C in simplest form?

What is the formula for a/B/C/D?

In the expression A/B/C/D, operations are done from left to right, so (A/B) is divided by C, yielding A/ (BC) and then this result is divided by D, yielding A/ (BCD). Of course, if the questioner was trying to get (A/B) / (C/D), we would end up with (AD)/ (BC).

What is ABCD in math?

ABCD is a rectangle. E, F, G and H are mid - point of sides AB, BC, CD and DA respectively. If ar (EFGH)= 16 cm2, find ar (ABCD). Find Math textbook solutions?

What is the fraction of a/B/C/D?

To simplify the fraction in the form of A/B/C/D, find the LCD, which is BD and multiply it to A/B and C/D to get (ABD/B)/ (CBD/D) which is equal to AD/CB. A fraction of the form A/B/C/D is basically nothing but A/ (B*C*D). Just multiply B, C and D together and divide A by the result obtained.

Introduction to Mathematical ReasoningMath310Spring 2006 Handout #5: Common Properties of Numbers (CORRECTED These are some of the elementary properties of numbers that can be proved from the axioms on Handout

#1. These can be proved in the order listed-that is, each statement can be proved using only the axioms

and statements that appear before it on the list. In all of the properties below,a,b,c,drepresent arbitrary real numbers unless otherwise specified.

1.Properties of zero

(a0 a=0. (bIf ab= 0, thena=0orb=0.

2.Properties of signs

(a-0=0. (b-(-a)=a. (c-a=(-1)a. (d( -a)b=-(ab)=a(-b). (e( -a)(-b)=ab.

3.Extensions of the distributive property

(a-(a+b)=(-a)+(-b)=-a-b. (b-(a-b)=b-a. (c-(-a-b)=a+b. (da+a=2a. (ea(b-c)=ab-ac=(b-c)a. (f) (a+b)(c+d)=ac+ad+bc+bd. (g( a+b)(c-d)=ac-ad+bc-bd=(c-d)(a+b). (h( a-b)(c-d)=ac-ad-bc+bd.

4.Properties of inverses

(a1 -1 =1. (b( a -1 -1 =aifais nonzero. (c( -a) -1 =-(a -1 )ifais nonzero. (d( ab) -1 =a -1 b -1 ifaandbare nonzero. (e( a/b) -1 =b/aifaandbare nonzero.

5.Properties of quotients

(aa/1=a. (b( a/b)(c/d)=(ac)/(bd)ifbanddare nonzero. (c( a/b)/(c/d)=(ad)/(bc)ifb,c, anddare nonzero. (d( ac)/(bc)=a/bifbandcare nonzero. (e( -a)/b=-(a/b)=a/(-b)ifbis nonzero. (f) (-a)/(-b)=a/bifbis nonzero. (ga/b+c/d=(ad+bc)/(bd)ifbanddare nonzero. (ha/b-c/d=(ad-bc)/(bd)ifbanddare nonzero.

6.Properties of inequalities

(a0 <1. (bIf a-b. (cIf ab -1 (gIf a0 if and only ifaandbare both positive or both negative. (pab <0 if and only if one is positive and the other is negative. (rThere do esnot exist a smallest p ositivereal n umber.

7.Properties of squares

(aIf a?= 0, thena 2 >0. (bF oran ya,a 2 ≥0. (cIf aandbare positive, thenab 2

8.Order properties of integers

(aIf nis a positive integer, thenn≥1. (bIf mandnare integers such thatm>n, thenm≥n+1. (cThere do esnot exist a largest in teger.

9.Laws of exponents

In statements(a-(dbelow,mandnare assumed to be nonnegative integers. (aa n b n =(ab) n (ba m+n =a m a n (c( a m n =a mn (da n /b n =(a/b) n ifbis nonzero. (eIden tities9(a dholdforarbitrary in tegers mandn, providedaandbare nonzero.

10.Divisibility properties of integers

In each of the following statements,m,n, andpare assumed to be integers. (aIf m|nandn|p, thenm|p. (bIf m|nandm|p, thenm|(n+p). (cIf m|norm|p, thenm|np. (dIf nis even, so isn 2 (eIf n 2 is odd, so isn. (f) Ifmandnare even, so ism+n. (gIf mis even, then so ismnfor any integern.quotesdbs_dbs24.pdfusesText_30
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