Mastering Mathematics – Divisibility Rules

To master mathematics, you have to know the rules. The more tools you have in that tool shed, the more likely one will get the job done. Here, we explore divisibility properties for the numbers up to 11. Once you add these properties to your arsenal, you will be that much further along to mastering this most difficult subject.

Divisibility Tests for Numbers:

2: If the number is even, that is, if the number ends in 0, 2, 4, 6, or 8, then that number is divisible by 2. Thus, 358 and 4,034,032 are divisible by 2.

3: If the sum of the digits of the number is divisible by 3, then the given number is also. Thus, 324 and 1,345,611 are both divisible by 3 since the sums of their digits, 9 and 21, respectively, are both divisible by 3.

4: If the last two digits of the number are divisible by 4, then so is the number. Thus, 312 and 1,024 are both divisible by 4.

5: If the number ends in 0 or 5, then the number is divisible by 5. Thus, 1,000 and 405 are both divisible by 5.

6: If a number is divisible by both 2 and 3, then the number is divisible by 6. You can test divisibility by 2 and 3 using the tests above. Once this is established, you are certain that the number is divisible by 6. Thus, 312 and 4,002 are both divisible by 6. Another way of saying this is if the number is even and the sum of the digits is divisible by 3, then the number is divisible by 6.

7: This rule is probably the most labor intensive of all. Yet, this rule works very well, especially when dealing with large numbers. Let us illustrate it with a specific example. Take the number 2,667. To determine whether this number is divisible by 7, we do the following: we take the last digit, namely 7, multiply it by 2 to get 14 and subtract this from the three digits, namely 266, that remain after we remove the 7. Thus 266 – 14 = 252. Repeat the procedure and we have 2×2 = 4; 25 – 4 = 21, and 21 is divisible by 7. Generally, repeat the procedure until you get to a number that is a few multiples of 7, so that you recognize the divisibility by this number.

8: If the last three digits form a number divisible by 8, then the entire number is divisible by 8. Thus, 4,096 and 1,016 are divisible by 8.

9: As with 3, if the sum of the digits forms a number divisible by 9, then the number is too. Thus, 108 and 3,240 are divisible by 9.

10: This is probably the easiest rule. Simply, if the number ends in 0, then it is divisible by 10.

11: If the alternate sum of the digits results in a number that is divisible by 11, including 0, then the entire number is divisible by 11. For example, take the number 5,082. Perform 5-0+8-2 = 11. Since 11 is divisible by 11, obviously, then the entire number is as well.

Learn these divisibility properties and I guarantee that your knowledge in and ability with mathematics will grow exponentially. For those parents who want their children to perform better in math, then see that your children master these rules. For then, the sky truly will be the limit.

Las Camisetas de fútbol de adidas se encuentran entre las preferidas de muchos equipos. Descubre por qué visitando nuestra colección en la web. by Joe Pagano

Pre-Season Soccer Training – The Basics

Effective pre-season training is important for all soccer players of any age, whether you play for a team in the Premier League or your local college team and the work done in pre-season can define the competitive season ahead, making the difference between winning trophies or being also-rans.

The Pre-season soccer training schedule should be planned out by the coach in order to maximise each session. Ideally training should begin at least five to six weeks before the season actually starts.

Each training session should start with a thorough warm-up taking care not to strain any muscles in early pre-season. Ideally each session should begin with a five minutes gentle jogging followed by gentle static stretching, followed by more jogging followed by a more intensive stretching session, while taking care not to over stretch and cause damage to muscles, tendons or ligaments.

Stretching for soccer should include all major muscle groups, with a mixture of dynamic and static stretches. Dynamic stretching exercises that are perfect for soccer and include swinging the arms and circling the shoulders, twisting the upper body and swinging the legs as if kicking an imaginary ball, be careful not to over stretch with these exercises. Static stretches do not involve movement of the joint and are essential for the quadriceps and hamstrings. Ballistic stretches which involve bouncing to maximise the stretch are no longer advocated and should be avoided.

Running is excellent for aerobic conditioning and should be encouraged as improved fitness will pay dividends later in the season, this should involve distance work, sprinting and running that involves work with the soccer ball. Dribbling the soccer ball around cones or across a defined area will improve conditioning, speed and ball control at the same time.

Work with the soccer ball can be extended by spending time controlling the ball with the feet, knees and head, a perfect way to practice this is to divide players into pairs and have one player throw the ball while the other controls and returns to his partner.

Each session can be completed with a short game possibly integrating two touch soccer which will improve ball control and passing accuracy and also encourage thinking and movement off the ball. Following the game a cool down with stretching should take place to minimise aching and tired muscles which will aid recovery for your next session.

During early pre-season is it important not to over exert the players and to make the sessions fun which will motivate if players are tired not too push them too much, this can result in injury and lack of enthusiasm. Another important factor for any training session is adequate hydration, ensure all the players have a water bottle and keep adequately hydrated throughout the training session.

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The Case Against Using An Autoresponder

I've had to put on my best armor today.

Why? Because I'm no doubt gonna get one hell of a backlash from certain people. After all, email marketers are supposed to love autoresponders.

Aren't they?

Well, hold your horses. Because I'm here to tell you why you should be sending daily emails (as daily broadcasts) as opposed to relying on an autoresponder sequence.

Ready? Let's get straight into it …

1) You can't be "current" with an autoresponder

One of the best things about daily email, is that you get to talk about current events.

And when you talk to your prospects about current things that are happening in the world, they're gonna pay attention.

Want an example? Okay then. When Leicester won the Premier League, it gave me something current to talk about. And it turned out to be one of the most profitable emails I've written. I reckon this was just because people could relate to it, as it had only just happened.

TV series' and films also make for great email fodder. Again, clearly you have to be current when talking about these.

But if you relied on an autoresponder, you couldn't exactly be "current", could you …

2) You risk "losing" a lot of people because of one email

Look, even I write a poor email once in a while (I know, shock horror, right ?!).

But that doesn't matter. Because I can just make sales the next day with a better email. And that poor email would then be consigned to history.

But if that same email was in an autoresponder sequence, every single person who joined my list in the future would also receive it. Yes, I know you could take it out or change it. But that's making things harder than they need to be. Sending daily emails is just so less complicated.

3) Autoresponders don't tend to "pitch" in every single email

Look, I know you can easily make an autoresponder with a sales pitch in every email.

But the fact of the matter is, most autoresponders don't. Instead, they tend to tell a story that is told over the course of numerous emails, before then pitching a product / service.

Now, listen.

I'm sure this works.

There are certainly guys who do successfully use autoresponders. Andre Chaperon and John McIntyre spring to mind.

But I believe Ben Settle is the best email marketer in the world. And he does daily email. And, yes, he pitches every single day – without having to take anyone through a long-winded story sequence. Clearly, you're gonna make money faster doing it Ben's way. And I like fast. I'm sure you do, too.

Anyway, I'm not saying autoresponders are the devil.

Far from it.

In fact, they do have some advantages over daily broadcasts.

But you know what? For me personally, nothing has come even close to beating daily email when it comes to making sales.

And trust me, if you do it right, it'll be the same for you, too.

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Denis Law Was the King of Stretford End

The great Denis Law was born in Aberdeen on the 24th February 1940 and he began his soccer career as a wee boy playing for Aberdeen Lads Club. When Law left the Granite City to join the once great Huddersfield Town, he was only 15 years old and and it didn't take him long to make his debut for his native Scotland against Wales in 1958.

The legendary Sir Matt Busby reputedly wanted the promising Denis Law to play for Manchester United but was turned down by the Terriers. Bill Shankly, who was the manager at Huddersfield Town at the time, then tried to take Law with him to Liverpool. However, the Liverpudlians didn´t have the money to take the prolific marksman out of Yorkshire. Instead, the vastly talented Leeds Road youngster went to Manchester City when the Maine Road club paid a then British record transfer fee of £ 55,000 for him in March 1960. After a rather disappointing spell with famous Italian club Turin, he returned to Lancashire finally signing up for Busby´s Manchester United in 1962. Denis Law opened the 1963-64 season on a bright note and was deservedly picked out to play for a Rest of the World side against England at Wembley. As a Manchester United player, the Scottish international won every major domestic honor, although injury kept him out of the European Cup Final against Benfica at Wembley in 1968.

Denis Law returned to his old club Manchester City in 1973, and retired from football in 1974 after playing his last match in the World Cup in West Germany. During his 585 matches for his clubs, he managed to score a massive 300 goals. He also scored a total of 30 goals for Scotland in 55 matches. In 1964, Law was voted European Footballer of the Year as the only Scotsman to this day. Always in the best of spirits, Denis Law was no doubt one of the greatest entertainers ever witnessed on the British soccer scene. He was not only a Danny Kaye look alike, he also closely resembled the American comedian when performing some of his antics on and off the football pitch.

Las Camisetas de fútbol de adidas se encuentran entre las preferidas de muchos equipos. Descubre por qué visitando nuestra colección en la web. by Doug M Anderson