Download presentation

Presentation is loading. Please wait.

Published byHerbert Baldwin Modified over 2 years ago

1
**Greatest Common Divisor Exponents Sections 1.2 & 1.3**

Review of Numbers Greatest Common Divisor Exponents Sections 1.2 & 1.3

2
**Whole Previous Information Types of numbers Natural Integers Rational**

Irrational

3
Purpose In later mathematics, you will want to work with numbers in simplest form. It is easier to work with small numbers rather than large numbers.

4
Prime Factorization Breaking a number down into it’s combination of prime factors To start prime factorization, ask yourself… “Will 2 divide this number…, Will 3 divide this number…, Will 5 divide this number…”

5
**Factors of 15 15 15 3 5 3 5 3 5 3 5 Alternate Method Factor Tree 3 5 1**

6
**Factors of 45 45 45 3 15 3 3 15 5 3 5 3 3 5 3 5 Alternate Method**

Factor Tree 3 5 45 45 3 15 3 3 15 5 2 1 3 5 3 3 5 2 1 3 5

7
**Greatest Common Divisor**

Largest factor of 2 or more numbers When finding – use prime factorization

8
**Greatest Common Divisor of 15 & 45**

3 5 45 15 Maximum number of common factors in each final row is one three and one 5 3 15 3 5 Therefore, the GCD is 3*5 = 15 3 3 5 1 1 3 5 GCD is 15 2 1 3 5

9
**Greatest Common Divisor of 8 & 27**

Note: there is no Common Divisor, 8 27 Therefore, The GCD =1 2 4 3 9 What number divides all numbers evenly? 2 2 2 3 3 3 1 3 3 2 3

10
TEST YOURSELF Find the GCD for the following pairs of numbers 12 & 18 12 & 24 18 & 32 32 & 64 12 & 54 18 & 54 18 & 64 32 & 54 24 & 64 54 & 72 14 & 15 6 12 2 32 18 2 8 18 1

11
**Exponents Repeated Multiplication be b = base e = exponent**

So you would multiply b e times b*b*b*b*b*…*b {e times}

12
Examples 24 72 x3 =2*2*2*2 =7*7 =x*x*x =16 =49 = x3

13
**Rules of Exponents: MULTIPLICATION**

Add exponents am+n 32+4 = 36 Multiply like Bases am * an 32 * 34

14
**Rules of Exponents: Exponents**

Multiply exponents am*n 32*4= 38 Exp raised to an Exp (am )n (32)4

15
**Rules of Exponents: DIVISION**

Subtract exponents am-n 34-2 = 32 Divide like Bases am an 34 32

16
**Distribute exponents Qty raised to an Exp ambm (ab)m (3x)4 34x4**

Rules of Exponents: Quantity to an Exponent Distribute exponents ambm 34x4 Qty raised to an Exp (ab)m (3x)4

17
**Rules of Exponents: Negative Exp**

= the reciprocal 1 am Number raised to a neg Exp a-m 3-2 =

18
**TEST YOURSELF: Rules of Exponents**

23 * 24 54/53 (2/5)2 -32 (-3)2 (6x)3 6x3 7(-2) 23+4 = 27 = 128 54-3 = 51 = 5 22/52 = 4/25 -32 = -9 (-1)2 * 32 63x3 = 216x3 6x3 1/72 = 1/49

19
**Terminology Factor Prime number Composite number Prime Factorization**

Exponential Form Greatest Common Divisor Expanded Form Sum Difference Product Quantity Reciprocal

20
**Conclusion Any two are more numbers have a Greatest Common Divisor**

(either 1 or some other Factor) To find the GCD use Prime Factorization (match factors using the smallest exponential value) Rules of Exponents

21
Assignment On-line 12 GCD & Exponents

Similar presentations

OK

Section 5.1 Prime Factorization and Greatest Common Factor.

Section 5.1 Prime Factorization and Greatest Common Factor.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on charge coupled device Ppt on phase sequence checker for three phase supply Ppt on grease lubrication procedure Ppt on preservation of public property band Science ppt on fibre to fabric Ppt on network topologies Ppt on time management training Ppt on thermal conductivity of insulating powder coat Ppt on event driven programming in java Ppt on steve jobs biography