LOIF Technique

[chrishuff]

When should I use it? (@nsguy1350)

[nsguy1350]

LOIF is the FOIL you learn in Algebra 1, backwards, applied in multiplication. It's basically the same thing. This is for 2x2 multiplication, not 3x3, which you can learn once you get past 30 or 40. The steps:
1. Multiply the ones digits. Write the first digit (ones digit) of the result, and carry.
2. Multiply the inner and outer (the ones of the first, tens of the second, then the ones of the second, tens of the first) digits, then add the results, along with the carried result. Write only the ones digit of the result.
3. Multiply the first (tens digits) of both numbers, add the carried number (if one), then write the entire result.

Examples:
23 x 45
3 x 5 = 15, write 5, carry 1.
3 x 4 + 2 x 5 + 1 = 23, write 3, carry 2.
2 x 4 + 2 = 10, write 10.
Answer: 1025

67 x 33
7 x 3 = 21, write 1, carry 2.
3 x 7 + 6 x 3 + 2 = 41, write 1, carry 4.
6 x 3 + 4 = 22, write 22.
Answer: 2211

91 x 52
1 x 2 = 2. Write 2.
1 x 5 + 2 x 9 = 23, write 3, carry 2.
9 x 5 + 2 = 47, write 47.
Answer: 4732

Hopefully I executed correctly, if you think I made a mistake, tell me. Any questions, ask. Other than that, that should be a decent enough explanation, although I might have missed something.

[chrishuff]

Ah yes, I can do that. How fast should I be able to answer these kinds of questions?


I want to establish a goal by using the [url]arithmetic.zetamac.com[/url] game. It's highly addictive. I just disable the addition, subtraction, division, and change the values of the multiplication to whatever I am specifically practicing on..

[nsguy1350]

When I first developed the LOIF techinique (actually my coach showed me), my speed and accuracy were horrendous. I would take very long and miss almost all of the problems that I made for myself. WIth practice, it became second nature. It should take you no more than 5 seconds or so, even less, really. Still, 5 seconds would be excellent for your purposes, with good accuracy. These first column questions are questions you can't miss! If you can get to #30 by the next meet, you should be able to beat enough people (besides the 5A, it's ridiculous) to compete in your District and Region. Make sure you also study for the other events as well! I suggest you first work on memorization and these multiplication techniques, and then I and others, along with you own indepent discovery and derivation, will help you learn all of the tricks you need to know.

[chrishuff]

In other words, playing a two minute arithmetic game should yield a score of a 24 or higher

The Number Sense coach at my school is actually having the first ever Number Sense Team Meeting Tuesday After school. He said earlier at the UIL meet that he will go over "all the tricks" to the competition. I don't know about all the tricks, just probably the ones that are most common.

[chrishuff]

[nsguy1350]

There are a few tricks in adding and other things that you can use to help you in those situations. Post any question that you think you're slow on to see if there is something hidden that you didn't see.