WIKIPEDIA HAS MANY MORE DIVISIBILITY RULES. EXAMPLE 123452 Since 52=13(4) is divisible by 4, 123452 is divisible by 4 Since 452=56(8)+4 is not divisible.

Slides:

Advertisements

Similar presentations

Division & Divisibility. a divides b if a is not zero there is a m such that a.m = b a is a factor of b b is a multiple of a a|b Division.

Advertisements

Dividing Whole Numbers 1.Arrange the numbers as a divisor and a dividend. Example: If 6 people sit at each table at a banquet, how many tables are required.

Partial Quotients Division Algorithm. Quick Slate Review Solve the following problems. ……. Ready……… …………..Set………….. ………Go!

Thinking Mathematically

5.1 Number Theory. The study of numbers and their properties. The numbers we use to count are called the Natural Numbers or Counting Numbers.

Section 5-4 Greatest Common Factor and Least Common Multiple.

Long and Synthetic Division of Polynomials Section 2-3.

Division Algorithms By: Jessica Nastasi.

Dividing a Decimal by a Decimal Lesson 2-5. Dividing a Decimal by a Decimal We NEVER want a decimal in the divisor. –If you have a decimal in the divisor,

Chapter II. THE INTEGERS

Division with remainders Meaning ContextExploration 3.18 Calculators.

By Jennifer Adams. The traditional approach (or algorithm) for large number division is the most abstract and difficult approach to division. Yet many.

division algorithm Before we study divisibility, we must remember the division algorithm. r dividend = (divisor ⋅ quotient) + remainder.

Everyday Mathematics Partial-Quotients Division Partial-Quotients Division Partial-quotients is a simpler way to do long division. Many children like.

Division of Polynomials Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Dividing Polynomials Long division of polynomials.

BY MISS FARAH ADIBAH ADNAN IMK

5.5 Apply the Remainder and Factor Theorem

Divisibility October 8, Divisibility If a and b are integers and a  0, then the statement that a divides b means that there is an integer c such.

CSCI 1900 Discrete Structures

February 24, 2015Applied Discrete Mathematics Week 4: Number Theory 1 Modular Arithmetic Let a be an integer and m be a positive integer. We denote by.

Short Division.

HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 1.9.

Synthetic Division. This method is used to divide polynomials, one of which is a binomial of degree one.

The Integers. The Division Algorithms A high-school question: Compute 58/17. We can write 58 as 58 = 3 (17) + 7 This forms illustrates the answer: “3.

Repeated Subtraction: Division

Real Zeros of Polynomial Functions

Ch 11.5 Dividing Polynomials

The “traditional” algorithm

Copyright © Cengage Learning. All rights reserved. 1.5 Prime Factorization.

MAT 320 Spring 2008 Section 1.2.  Start with two integers for which you want to find the GCD. Apply the division algorithm, dividing the smaller number.

Dividing Polynomials.

Dividing Decimals by a Whole Number 3.6 ÷ 3.

177 8 Start by setting up the problem like this. It looks just like the traditional long division method, except for the long line that is drawn to the.

The Forgiveness Method & Partial Quotients Division

Partial Quotients.

PARTIAL QUOTIENT DIVISION

Partial Quotient Method In this division algorithm the children record on the right side of the problem. The first thing they do is divide. They ask themselves.

In this case, the division is exact and Dividend = Divisor x Quotient

Euclidean Algorithm How to find a greatest common divisor in several easy steps.

Math 409/409G History of Mathematics Books VII – IX of the Elements Part 1: Divisibility.

Factor Theorem Using Long Division, Synthetic Division, & Factoring to Solve Polynomials.

The Steps… 1.Divide2. Multiply 3. Subtract4. Bring Down And an easy way to remember them… D ad M om S ister B rother.

The Real Zeros of a Polynomial Function Section 5.2 Also Includes Section R.6 : Synthetic Division 1.

DIVISION. Standards G4.1M.C2.PO4A. Use multiple strategies to divide whole numbers using 4-digit dividends and divisors from 1 to 12 with remainders.

Polynomial and Synthetic Division Objective: To solve polynomial equations by long division and synthetic division.

Dividing Rational Numbers Rational Numbers ~. Dividing Rational Numbers RULES: RULES: 1. When multiplying or dividing integers with the same signs, the.

Divisibility Rules. What Are Divisibility Rules? They are a quick way to tell if one number can be completely divided into another without a remainder.

Slide Copyright © 2009 Pearson Education, Inc. 5.1 Number Theory.

1 Discrete Structures – CNS2300 Text Discrete Mathematics and Its Applications Kenneth H. Rosen (5 th Edition) Chapter 2 The Fundamentals: Algorithms,

Hangman Division (Partial Quotient)

5th Grade Module 2 – Lesson 21

Reminder steps for Long Division

Dividing larger Numbers

Greatest Common Divisor

Greatest Common Divisor

5 Rational Numbers: Positive and Negative Decimals.

Long Division With 2 Digit Divisor

Partial Quotients Division Algorithm

Standard Algorithm By: Ally, Zoey, and Maha.

Reminder steps for Long Division

Tests of Divisibility 1 - All integers can be divided by 1

Everyday Mathematics Partial-Quotients Division

Objective: Learn to test for divisibility.

Everyday Mathematics Partial-Quotients Division

Division Dividing 3 and 4 Digits by 2 Digits.

Miniconference on the Mathematics of Computation

Chapter 1 Whole Numbers.

DIVISION OF INTEGERS 1-9.

Presentation transcript:

WIKIPEDIA HAS MANY MORE DIVISIBILITY RULES

EXAMPLE Since 52=13(4) is divisible by 4, is divisible by 4 Since 452=56(8)+4 is not divisible by 8, is not divisible by twice the last digit is 2(2)=4 and = – twice the last digit is 2(1)=2 and = – twice the last digit is 2(2) =4 and 123-4= – twice the last digit is 2(9)=18 and 11-18=-7 is divisible by IS DIVISIBLE BY 7

EXAMPLE IS DIVISIBLE BY 13? USE THE LIST 1,10,9,12,3,4 REPEATEDLY AS NEEDED 1x7 + 10x6 + 9x5 + 12x4 + 3x3 + 4x2 + (start over) + 1x1 = = =160+18=178 NOW DO IT AGAIN! 1x8 + 10x7 + 9x1 = =70+17=87 NOW DO IT AGAIN! (DOESN’T HELP) 1x7+10x8=7+80=87 Since 87=6(13)+9 The remainder when dividing 87 by 13 is 9 and so the remainder when dividing by 13 is also 9.

The Euclidean Algorithm To Find Greatest Common Divisors WITHOUT FACTORING!

IF YOU WANT TO FIND GCD(a,b) then Note that if any number D divides a and b then it will also divide a-Nb for any positive integer N. So this means that GCD(a,b)=GCD(b,a-Nb) We make these numbers smaller and continue the thinking!

SO NOTE THE FOLLOWING! IN EVERY SLIDE WE WILL ASK A QUESTION WITH THE SAME ANSWER! THE QUESTIONS ARE GETTING EASIER AND EASIER! THIS IS COMMON IN MATHEMATICS – FOR EXAMPLE WE MIGHT ASK HOW DO YOU SOLVE 2X+3=19? WE CHANGE THE QUESTION TO HOW DO YOU SOLVE 2X=16? THEN HOW DO YOU SOLVE X=8? I.E. YOU KEEP GOING UNTIL THE ANSWER IS OBVIOUS!

FIND GREATEST COMMON DIVISOR OF AND 6307 WHAT IS THE QUOTIENT AND REMAINDER WHEN DIVIDING BY 6307? 15158=2(6307)+2544

NOW FIND GREATEST COMMON DIVISOR OF 6307 AND 2544 WHAT IS THE QUOTIENT AND REMAINDER WHEN DIVIDING 6307 BY 2544? 6307=2(2544)+1219

NOW FIND GREATEST COMMON DIVISOR OF 2544 AND 1219 WHAT IS THE QUOTIENT AND REMAINDER WHEN DIVIDING 2544 BY 1219? 2544=2(1219)+106

NOW FIND GREATEST COMMON DIVISOR OF 1219 AND 106 WHAT IS THE QUOTIENT AND REMAINDER WHEN DIVIDING 1219 BY 106? 1219=11(106)+53

NOW FIND GREATEST COMMON DIVISOR OF 106 AND 53 WHAT IS THE QUOTIENT AND REMAINDER WHEN DIVIDING 106 BY 53? 106=2(53)+0 The zero says we are done so GCD(15158,6307)=53

EXAMPLES FOR YOU TO TRY! FIND THE GCD OF 23 and 123. FIND the GCD of and FIND the GCD of TWO SOCIAL SECURITY NUMBERS.

Divisibility Puzzle Form an integer by using each of {1,2,3,4,5,6,7,8,9} Exactly once so that The first k-digits are divisible by k for k=1,2,…,9

Divisibility Puzzle EXAMPLE The first k-digits are divisible by k For Example Partially works since 1 is divisible by 1 12 is divisible by is divisible by 3 BUT 1234 is not divisible by 4.

WIKIPEDIA HAS MANY MORE DIVISIBILITY RULES