[Modern Maths] F5 Chapter 1 : Number Bases (Part 3)

Continue from Part 2.

So, first, it's important to start from the right side, separate them to 3 digits one set. What does that means?

See, those separation lines! And then the answer come out should be taken from this list which I posted before.

So, the answer is 332 base 8.

Now, let's talk about addition and subtraction of base 2, 5 and 8 numbers. Remember, only the same base number can do so, other than that, you should convert one of the number to the same base of another number.

e.g: 

(a) Addition and subtraction of base 2 numbers.

This is only solving base 2 numbers manually, you can also try using calculator to solve base 2 addition and subtraction.

(b) Addition and subtraction of base 8 numbers.

This video I made it on my own.. I hope that there isn't any mistake but if there is, please point it out. I'm still learning and my words a bit mess, hope you don't mind.

(c) Addition and subtraction of base 5 numbers.

This time, all of the examples (except for the video one) I get from the Internet, because I found the explanation is much more easier to understand so I decided to share it out.

Anyway, if there is still problems stuck in your head, just share with us or leave us a comment = )

[Modern Maths] F5 Chapter 1 : Number Bases (Part 2)

In Part 1 we learnt all the bases (2,5,8  & 10) and how to convert the first three bases into base 10 numbers.

And for today, we're going to learn its reversible process, that is from base 10 number to another number with different bases. It also can be from base 5 number to base 2 number or base 8 number to base 5 number. We're going to learn it in two ways, one with calculator and another is manually. As for the manually process, you have to remember the LCM (Lowest Common Multiple) which we learnt in Form 1 Maths. But it's a little bit differ from Form 1 LCM. In this case, we need to write down the remainder, why? I'll show you the working first and then you'll understand.

(a) Base 10 number convert to base 2 number.

e.g. :

You can check your answer by using calculator. First, press mode twice, and then press on the number which refers to "Base". Then, press on x^2 which have a green capital letter DEC on it. Then, type the number which you want to convert. From the example, we type 397. And then press the equal symbol. After that, press on the log which have a green capital letter BIN on it. See, that's the answer.

(b) Base 2 number to base 5 number

e.g.:

In this case, you have to first convert the base 2 number into base 10 and then convert it to base 5 number. And it's sorry to say that there's no solution provided by using scientific calculator to convert any base of number to base 5 number or vice versa. I'm not going to show the working for this question, in fact, you should do it on your own haha! XD Post your answer in the comment part. 

(c) Base 2 number to base 8 number or vice versa

This time, we use the same number, because the answer come out can be different. But from base 2 to base 8 or vice versa is much more easier than other conversion of base actually. See how it works. Do you still remember the base 2 number sequence? Just list down the first 7 number of base 2 numbers, that is

But, in this case, you have to make it to become 3 digit numbers, that is

Then, look at the question.. ( to be continued in part 3 )

[Modern Maths] F5 Chapter 1 : Number Bases (Part 1)

So, below is what my maths teacher has taught me this week.

Normally, we are using base 10 numbers in addition, subtraction, division and multiplication. So, what does that mean? Take a look at an example below.

Example 1 : 17 + 15 = 32

So, take a look at the ones place value. 5 + 7 = 12 , right? Since the value exceeds ten, so it has to go into the tens place value. So, this example is using number of base 10. What if we use base 2, base 5 or base 8? Maybe it's a little bit too fast, let me first tell you what's that.

In this case, 4 is the base and 3 is the power. That's the mean of base.

Here some examples of number for each base.

Base 2 number sequence:

Look, in base 2 number sequence, there's no number 2 exist. The third number is not read as ten base two, the correct way of reading it is one ten base two. Remember, there's no something like two base two!!

Base 5 number sequence:

The same goes to base 5. There's no number 5 exist in base 5. It's just like the limit, it can't exceed. 

Base 8 number sequence:

  

Now, we talk about conversion, from base 2, 5 and 8 number convert to base 10 number.

(i) Base 2 --> Base 10

Watch out for the place value here. The ones we used to say in base 10 number is 2 to the power of zero in base 2. It looks like this.

So, how to convert? Below is the solution.

And that's it~ If you meet any problems, feel free to discuss with us  = D

[Modern Maths] F5C4 : Matrices (Addition&Subtraction)

First example : -

* Multiply first or expand and continue your addition as well as subtraction. Be careful when solving


Second example : -

If you master this, try this out!

That's it. Kinda easy right?