I got 2 questions and I've been stuck on them for days and its due in 2 days.
1. For a quick way of doing multiplication, you can do:
for example: 81 x 89=? First you do 1x9=9 in which case you have to add '0' in front of it to make it 09. Then you add 1 to any of the 8s and multiply the tens digits making 72. You add the digits 72 to 09 making 7209.
Another one: 64x66=? 6x4= 24 and 6+1=7. Then I go 6x7=42. So the digits 42 and 24 makes 4224.
The question is WHEN can I do this. I already know that the last 2 digits must add up to 10, but what number does this method end? Over 100?
Second question. Why does 9+4=1? Because of clock arithmetic. 9o'clock + 4 hours= 1 o'clock, and the modulus is 12 for 12 hours for one cycle. I need to find out what other things uses a particular modulus. I've managed to think of a month(31,30,29,28) days.
What else?
Thanks heaps!
A math teacher will have to help you with your first question, but here are some ideas for your second one:
http://www.unc.edu/~rowlett/units/custom.html
16 ounces = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
etc.
inches, feet, yards, miles...
Ok thanks. The problem is, I'm from Australia and we don't use those measurements. But I MIGHT be able to use other Australian measurements.
just keep on trying
1. The method you described for quick multiplication can be applied to any two-digit numbers. However, it becomes less efficient for numbers beyond 100. The reason behind this method is that it helps in breaking down the multiplication into smaller, easier calculations.
Let's take an example beyond 100: 123 x 129.
First, we multiply the ones digits: 3 x 9 = 27. Write down the "7" and carry over the "2".
Next, we multiply the tens digits and add the carried over value: (1 + 2) x (2 + 1) = 9. Write down the "9" next to the "7".
Finally, we multiply the hundreds digits: 1 x 1 = 1.
So, combining all the results, we get 15927 as the answer for 123 x 129.
As you can see, this method can be extended to any two-digit numbers. However, for three-digit numbers or larger numbers, it becomes more time-consuming to apply this specific technique. In those cases, it may be more efficient to use the traditional long multiplication method.
2. The concept of modulus, as you mentioned in the second question, is widely used in various fields. Some examples of where modulus is used are:
a) Music theory: Modulus is used to calculate pitch classes and intervals in music. In this context, the modulus is typically 12 because there are 12 pitch classes in an octave.
b) Cryptography: The modulus operation is a fundamental part of many encryption and decryption algorithms, such as RSA. Large prime numbers are often used as the modulus to ensure security.
c) Computer programming: Modulus is frequently used in programming languages for various purposes. It can be used to determine remainders, cycles, or to perform certain calculations based on patterns.
d) Circular systems: Clock arithmetic, as you mentioned, is one example of a circular system where modulus is used. Other examples include navigating on a sphere (longitude and latitude) or measuring angles in a circle using degrees or radians.
These are just a few examples, and the concept of modulus has applications in many other fields as well. It is a fundamental mathematical concept that finds utility in various contexts.