A Better Way to Learn Math
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To celebrate the release of our new
and free access to our 500+ fraction lessons, today we’re going to show you a handy shortcut for multiplying fractions. This easy trick will help you reduce and simplify the fraction without having to spend much time on it at all. The trick involves cross-dividing before cross-multiplying. The easiest way to show this is by example, so lets get right to it.
4 3
- x – = ?
5 8
If this equation were done normally (by “cross multiplying”), you would cross multiply to get 12/40, a somewhat ugly fraction that you’d then have to simplify:
4 3 12 3
- x – = - = -
5 8 40 10
But, if we use this fraction trick and “cross divide”, we’d save time and skip the last simplification step. We start by finding a numerator and denominator that could be simplified. In this case it’s the 4 and the 8, which will become 1 and 2:
4 3 1 3 3
- x – = – x – = –
5 8 5 2 10
Now the equation gives us the most simplified answer, with less work. This trick is even more effective with larger numbers. Let’s try it with a harder example:
128 72
- x – = ?
300 64
This is more like it. Multiplying these fractions the traditional way will give us a huge numbers in the nominator and denominator, (9216 / 19200 to be exact). But if we try our trick first, the numbers become simple enough to where this multiplication can be done more easily in your head. We first divide the 128 and 64 by 64, leaving only 2 and 1. Then both 300 and 72 are divided by 3, leaving 100 and 24. Then divide them both by two twice, simplifying them to 25 and 6:
128 72 2 72 2 24 2 12 2 6 12
- x - = - x - = - x - = - x - = - x – = -
300 64 300 1 100 1 50 1 25 1 25
Now instead of having a fraction in the thousands, we have the much more manageable 12/25. This trick works on all multiplying fractions, as long as there is something to simplify.
Lesson: Don’t just rush in and multiply. Look for simplification tricks first and you’ll be faster and more able to do math in your head.
5 
As many of you know, a week ago, on Friday, August 6th, Guaranteach took a monumental (for us) step and setup our first retail location in the Towson Town Center mall. We’ve generally been happy with the response, including the large number of kind conversations we’ve been able to have as we get the word out about our unique online, personalized method of tutoring and sell our new prepaid tutoring cards. And we have many people to thank, including those at the Towson Town Center mall who have been ever so helpful as our online company has made its first steps into the real world of retail.
One company that has been utterly unhelpful, however, is Verizon. Due to their numerous screw-ups we’ve had to go our entire first week without DSL – and it still isn’t working! Without DSL, we don’t have enough bandwidth to stream our videos and use our site. Given that we are, at our core, a video tutoring website, you can imagine that not being able to demo videos for potential customers is a HUGE handicap.
So, we’re taking the step of blogging about this to see if we can’t move Verizon to action. We’ve tried (so so many times) to get things done through the official channels – but the screw-ups just don’t end.
Verizon, if you reading this, we’re not happy. We’re paying for DSL and YOU are preventing us from using. Fix it. Fix it NOW. We still believe you CAN fix things. You just need to get out of your own way and decide to make it happen. Please. Pretty please with sugar on top. Help us!
How? By sending a Baltimore-area tech out to the Towson Town Center mall, (Suite 7503) to install a floor jack A – S –A – P!
When you do, we’ll forgive you for every mistake you’ve made over the past two weeks, including:
Selling us a speed (7.0 Mbps) that you realized later we couldn’t actually get. And then “solving” this problem by cancelling our order and starting a new one. Time lost: 5 days. (Because it took you THAT long to realize you couldn’t deliver on what you sold us)
Sending our DSL modem and startup kit to the wrong address, and not providing us with a tracking number or telling us that delivery had failed until we called to ask: “Hey, where is our modem!?” . And then you didn’t have a mechanism to correct the UPS address (in fact, you told us that we could call UPS and do it, except that when we tried, UPS rightly said that only the sender – YOU – could change the address. But you “have no process” for that). In the end, you had to send us a new modem to replace the one now lost in UPS purgatory. Time lost: 2 days
Destroying our hope. Once we finally got the modem and moved our mall cart to expose the floor jack we discovered that your technicians had LEFT ONLY WIRES AND NO JACK IN THE FLOOR when they’d been out a week before to setup the line. Since we discovered this just today in the evening, (we foolishly waited for the modem to come) your local office was closed for the weekend and we’ve been left with no option but to turn to the blogosphere. Time lost: AT LEAST 2 days
So here we are: with no DSL and no one who help us with more than a “We’re sorry sir, but you’ll have to call the local office when they open on Monday to schedule a time for a tech to come out... and we can't guarantee when that will be." Total time lost so far: 9 days. Will we make it to 10? Stay tuned.
UPDATE (08/17/09): Over this weekend, after posting the entry above to our blog and writing an email to Verizon CEO Ivan Seidenberg (and CC-ing bloggers over at Consumerist), we received a phone call from, Jackie, a very friendly (and apologetic) Verizon person based out of Baltimore. She made sure that a technician came out right away Monday morning to get things straightened out. We have DSL at our kiosk now and can happily demo videos for anyone who comes by!
I had a conversation yesterday with a Guaranteach user who made an interesting comment: “I wish you had more videos from students on your site.” She went on to explain how she feels that we’d be much more engaging to students if they felt they could also participate in the content of our site. It is a thought that we’ve heard before – and one that we agree with.
So we’re happy to announce a student video contest!
Send us a math video teaching any topic by October 15th, and you could not only have your video posted to Guaranteach, but you could also win $200. You can find the details, including instructions and tips on how to make a video, at http://www.guaranteach.com/community/video_contest
Note: This contest is open only to students. But if you are a teacher (or parent) you can enter our “teacher video contest.” Details about this second contest can also be found on http://www.guaranteach.com/community/video_contest.
Good luck!