Download presentation

Presentation is loading. Please wait.

Published byKimberly Padilla Modified over 4 years ago

1
Division & Divisibility

2
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

3
If a|b and a|c then a|(b+c) If a divides b and a divides c then a divides b plus c a|b a.x = b a|c a.y = c b+c = a.x + a.y = a(x + y) and that is divisible by a Division

4
a|b a.m = b b.c = a.m.c which is divisible by a Division

5
a|b a.x = b b|c b.y = c c = a.x.y and that is divisible by a Division

6
Theorem 1 (page 202, 6 th ed, page 154, 5 th ed)

7
The Division Algorithm (aint no algorithm) a is an integer and d is a positive integer there exists unique integers q and r, 0 r d a = d.q. + r a divided by d = q remainder r dividend divisor quotient remainder NOTE: remainder r is positive and divisor d is positive

8
Division a = d.q + r and 0 <= r < d a = -11 and d = 3 and 0 <= r < 3 -11 = 3q + r q = -4 and r = 1 a = d.q + r and 0 <= r < d a = -63 and d = 20 and 0 <= r <= 20 -63 = 20q + r q = -4 and r = 17 a = d.q + r and 0 <= r < d a = -25 and d = 15 and 0 <= r < 15 -25 = 15.q + r q = -2 and r = 10

9
Division a = d.q + r and 0 <= r < d a = -11 and d = 3 and 0 <= r < 3 -11 = 3q + r q = -4 and r = 1 Troubled by this? Did you expect q = -3 and r = -2? What if 3 of you went to a café and got a bill for £11? Would you each put £3 down and then leg it? Or £4 each and leave £1 tip?

Similar presentations

OK

+ Division Objective: I can divide multi-digit whole numbers by whole numbers divisors with and without remainders.

+ Division Objective: I can divide multi-digit whole numbers by whole numbers divisors with and without remainders.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on industrial revolution in england Ppt on steps in designing hrd system Ppt on save environment posters Ppt on atrial septal defect closure Ppt on scientific calculator project in java Ppt on unipolar nrz Ppt on indian news channels Ppt on any one mathematical quotes Ppt on chapter 12 electricity company Ppt on motivation concepts