question chessboard

Monday, November 30, 2009

Hi! I'm SO SORRY that this is REALLY late. I hope that I explain this question well. The Question I got is the chessboard question. THe first question talks about the diagonal lines of the small squares/rectangles.

A)Find the diagonal of all squares and rectanges possible in the first three rows. Then Arrange the squares/rectangles, from least to greatest by length of their diagonals.

As you can see, not all the little squares were "counted" because for example, row 3 and column 1 was already done by the first row, third column.(Do you get it?)
Now we need to find ALL the possible diagonals in the first three rows.
If it helps you draw a picture of the chess board and then do the math.
The picture(sorry that it's a bit blurry)on the bottom shows all the possible diagonal lines. IN ORDER from LEAST TO GREATEST

In order to get the diagonal of the squares/rectangle, you need to know that A squared + B squared = C squared (formula for a triangle)
The second part of this question is...
B) Consider the entire chessboard. When would you expect the square or rectangle to give a whole number diagonal?
The picture below shows how many squares/rectangles that give a whole number. When we did the three rows, we only found one.
Which was 3 squared + 4 squared = C squared
Then the square root of 10 = C squared
Then the answer was 5 = C squared
Then there's another diagonal with a whole number which was:
6 squared +8 squared = C squared
square root of 100 = C squared
Then you get the answer of 10 = C squared
If you look at the two diagonals that have a whole number as a diagonal, you could see that
6 squared +8 squared is four times as much as 3 squared + 4 squared. I don't really know how else I could explain part B of this that's all I'm going to say...

Scribe Post for November 30, 2009

Hello everyone! Nicky again to talk to you about homework. You see, homework is a good thing, because (believe it or not) it actually helps you learn. Yes, it does. So, you shouldn't mind one bit that today's class was mainly homework, right? Ahem... Despite the numerous stares that I'm sure I'm receiving from you all, I will still tell you the homework.
Workbook 2.3
Extra Practice 2.3

Seems like a lot, doesn't it? However, we get two days to do it! BUT! Don't wait until tomorrow at 10 o'clock to do them... Believe me, everyone (except me because I'm a good little boy) has done that. Still, I trust that "The Class" won't let me down.

So, still waiting for epicness? Well, say hello to my little friend. His name is Ned the Integoolie. Some of you may recall him from my integer story from last year.
So, you may be asking why Ned is here, aren't you? Well Ned is here for two things. The first is to tell you that you "should" have lots of stuff in your foldable (you can still be working on it) and the second is to recite a poem about dividing decimals. Yes, I am serious... Just listen...

The other day in math class,
I was pondering my math,
Dividing decimals,
Why must we take a long, hard path?

Is it that our math teachers,
Who appear so kind and nice,
Are really mean and nasty,
Waiting to watch us squirm like mice?

Or is it the curriculum?
With it's "required" things?
Is it really that necessary,
Does it help us earn our wings?

The answer is quite simple,
I tell you this is true,
It is to prepare us all,
Including me and you.

It'll prepare us for math much later,
When we are in high school,
So when we see hard questions,
We understand which is quite cool.

Sure, now we can use calculators,
But that won't help us much,
When the numbers turn to variables,
And such,

We must simply understand it,
So that when it's time to fly,
We can do it really easily,
And that my friends is why.

Bravo Ned, your poems are always great. However, to all of you rhymically challenged, or those to lazy to read it, here's a summary. Mr B told us today that we needn't do long division all the time and that we must simply know how to do it. So, for now, it's perfectly fine to be using your calculator.

So, here's a bit of a recap for you. You must complete 2.3 Extra Practice and in your Workbook and begin filling in your foldable. Also, you can expect a math test on either Monday or Tuesday.

And to that, I bid you all a good night and happy homework. Fare thee well until the morrow!

Question 12

Sunday, November 29, 2009
Hello. I kind of forgot about this, and so I shall be doing it late. I was assigned questions 12, and if you already know, it includes a lot of addition and subtraction. Here's what the question looks like. Anyways, the questions will be placed in the slide below, as it's easier to read as opposed to a long post.

Comment on mistakes, or if anything is misunderstood. Also comment if you just wanted to say good job. (: Keep up the good work 9-05!

Question 15

Hello 9-05 sorry for my late post, but better late then never right. Well Mr. B assigned me number 15. So here we go.

So the question is

Predict the next three numbers in the pattern,
Here is the question and answer

(bottom right corner says " To find the next number take the last number and add 5/8")

Now here is the second question

Well sorry for the short and late post also I'm sorry if my pictures are confusing/unreadable. Comment if you find anything mistakes. Well until my next blog post goodbye for now
Hey guys... sorry mine was so late, that's because I'm so busy the last two days. By the way Mr.B assigned me the gold bar question.
- A gold bar has a mass of 1 and 1/3 kg. You wish to cut off exactly 1/2 kg. What fraction of the bar should you cut off? Explain.
so what they really asking you is, what fraction would 0.5 kg be of 1.33?or how many 1/2 are there in 1 and 1/3 not how much would be left if you cut off 1/2 ot of 1 and 1/3
to figure that out al you have to do is devide them with each other (Note when you devide fractions you need to write division as multiplication by the reciprocal of the devisor)

What i did:

Well I'm done, hope you understand my scribe, plss comment if If i did something wrong. Okie I have to do my music presentation. - Text Generator
Text Generator - Fire Text - Counters - - Free League Management

Numbaa 19 :)

Hey guys! :) Sorry this is late, I haven't been home in a while. HAHHA, don't chop my head up "Mr.B" Anyways, I got number 19 for my post thing.

I got the answers by using that a+b=c method we learned.

c) 8/13

d) -1 1/2
I don't know how to show C and D. I need to ask "Mr.B" for help. I'll have it up tommorrow :)

Question #9

Friday, November 27, 2009
HI, EVERYONE !! Today I'm going to try and explain question #9 from the textbook.

Lori owed her mother $39. Lori paid back 1/3 of this debt and then paid back 1/4 of the remaining debt.

How much does Lori still owe her mother ?

It says here that Lori paid her mother back 1/3 of $39. Now, let's find out what 1/3 of $39.

39/1 x 1/3 = $13 So she paid $13 and she still owes 2/3 of $39.
So, we have to find out what 2/3 and here's how you find it, 39 - 13 = $26. She still owes her mom $26.

So, now its says here that she paid 1/4 of the remaining debt. Now, let's find out what 1/4 of $26.

26/1 x 1/4 = 6.50 She paid back $6.50 from $26. And she still owes 3/4. Now let's find out what 3/4 is. So you have to subtract $6.50 from $26 and this is how you do it, 26 - 6.50= $19.50.

So, Lori still owes her mother $19.50 .

I guess that's it. I hope you guys understand it :D PLEASE COMMENT ON MY MISTAKES !! Thank you for reading my post :)

Question 17

Hello everyone, I am going to try to make you understand this question.

My Blog question is:

To calculate -3/4 + (-2/ 3), Amy decided to convert the fractions to decimals and convert the decimals on a scientific calculator.
a) Explain why she had difficulty in determining the exact answer by this method.
b) How should she calculate to get an exact answer?

A) Amy had a problem with this question because -2/3 is a repeating number. She would have to round the decimal which would not give her an exact answer.


The decimal equivalent to -1 5/12 is -1.41666... repeating.

The fraction is in its lowest terms so it can't be simplified anymore. And I guess we are done.

Textbook Question #24

Hello Everybody,
Today I will be explaining question 24 in our Textbooks
The question is "Copy and Complete each statement".
For A)
To get the answer in the purple box you need to:
Use the Inverse operation and work backwards

Then you can simplify -1 and 1 quarter into -5 fourths and there's your answer

For B)

You have to use the Inverse operation and work backwards

Which should give you a answer of

For C)
You have to use the Inverse operation and work backwards

Which should give you a answer of

For D)
You have to use the Inverse operation and work backwards

Which should give you a answer of

Thanks for reading

Blinkie Text Generator at

Question #13

Hi 9-05! I'll be here to explain to you all how to do question 13 in our textbooks!

13. The diameter of Pluto is 6/17 of the diameter of Mars. Mars is 17/300 the diameter of Saturn.
a) What fraction of the diameter of Saturn is the diameter of Pluto?

Okay, so the first thing we do is organize our information.

What We Know:
Pluto = 6/17 diameter of Mars
Mars = 17/300 diameter of Saturn

Find Pluto's diameter of Saturn

Of - indicates multiplying
Fraction - indicates the answer form

Okay, now we can begin with actually answering the question.

How To, and Why?:
Since the word "of" is present, we need to multiply. Our goal is to find Pluto's diameter or Saturn so we multiply Pluto's diameter or Mars by Mars' diameter of Saturn because Mars' diameter is in relation to Saturn, and Pluto's diameter is in relation to Mars.

Wow, that was really ugly and time consuming. Let's try that again!
That's much better. Go ahead, try it on your calculator! It should work.

b) The diameter of Saturn is 120 000 km. What is the diameter of Pluto?
Okay, so we know Pluto's diameter of Saturn now, which is 1/50. But, just because, let's organize our information again, shall we?

What We Know:
Pluto's diameter of Saturn: 1/50
Saturn's diameter: 120 000 km
Measurement: Kilometers

To find Pluto's diameter in kilometers

Kilometer - indicates what unit of measurement the answer should be

Okay, so since we know what Pluto's diameter of Saturn, and we know what Saturn's diameter in kilometers, all we need to do is multiply.

So that's how you do it! Comment if you're confused, have any questions, or just because! :)

How to Solve Question # 22

Hi 9-05 it's Jai here coming to you with question #22. For those of you who didn't understand this question I will try to explain it to you so next time that you see question #22 you can say "Hey I know how to solve this!"

The question goes something like this......

Taj has three scoops for measuring flour. The largest scoop holds 2 1/2 as much as the smallest one. The middle scoop holds 1 3/4 as much as the smallest one.
Describe 2 different ways in which Taj could measure each of the following quantities. He can only use full scoops.
a) 3 1/4 as much as the smallest one.
b) 1/2 as much as the smallest one.

So to figure out question (a) out you are going to have to have the following things. Empty cups of each measuring cup, a flour bag, and any container that is big enough to hold more than 3 1/4.

Once you have completed this you have to now fill up the largest measuring cup.

After that fill up the middle measuring cup by pouring as much flour as you can from the largest cup into the middle cup. Once you have done this the largest cup will have 3/4 of flour left.

Once this is done, pour the flour from the largest measuring cup that is left into the random container. Once this is completed. Empty all of the measuring cups into the flour bag and repeat this process 2 more times ensuring that the random container is filled with 2 1/4 as much flour as the smallest measuring cup.

Now the last step into solving question (a) is to fill up the smallest measuring cup and pouring that flour into the random container filling it up to 3 1/4 which question (a) asks for.
Now that we have solved question (a) on to the easiest question to solve which is question (b). To solve this question all you have to do is fill up the largest measuring cup first. Then you empty that measuring cup twice into the smallest measuring cup. Each time that you fill up the smallest measuring cup remember to empty it into the flour bag afterwards.
Once this is completed, the amount of flour that you will have left in the largest measuring cup will be the amount that question (b) asks which is 1/2 as much as the smallest measuring cup.
If you still don't understand what I am trying to say, just ask me at school, and I will try to explain this question even better than I have in this post. Comment if I made any mistakes any mistakes. Thanks for reading!

Question #14

Hey 9-05! Today I'll be showing you how to answer question #14.

First of all you need to read the information given to you and pick out key words:

Li and Ray shared a vegetarian pizza and a Hawaiian pizza of the same size. The vegetarian pizza was cut into eight equal slices. The Hawaiian pizza was cut into six equal slices. Li ate two slices of the vegetarian pizza and one slice of the Hawaiian pizza. Ray ate two slices of the Hawaiian pizza and one slice of the vegetarian pizza.

a) Who ate more pizza?
-To find out who ate more pizza you need to add the sized pieces they ate together
-Li ate two slices of the vegetarian pizza (out of 8) and one slice of the Hawaiian pizza (out of 6)
-2/8 + 1/6=

-When adding fractions you must have a common denominator
-Add the numerators, leave the denominator as it is
-Simplify if possible

-This means Li ate 10/24 of the pizzas

-Ray ate two slices of the Hawaiian pizza (out of 6) and one slice of the vegetarian pizza (out of 8) -2/6 + 1/8=

-When adding fractions you must have a common denominator
-Add the numerators, leave the denominator as it is
-Simplify if possible
-This means Ray ate 11/24 of the pizzas

11/24 is larger than 10/24 so that means Ray ate more pizza.

b) How much more did that person eat?

-Since there are already common denominators,
all you need to do is subtract the numerators

Ray ate 1/24 more pizza than Li.

c) How much pizza was left over?

-There was a total of 2 pizzas (2/1)
-Li ate (10/24) of the pizzas
-Ray ate (11/24) of the pizzas
-The answer is how much pizza was left after they ate

There was 1 1/8 pizza left over.

Woot! That's it! Please COMMENT if I made any mistakes, you don't understand something, or if you just feel like commenting. ^__^

Question #18

Hey 9-05! Mr.B assigned us some math questions again, and I got number 18. Here it goes. Oh and make sure to comment about my post, please point out some of my mistakes to make my post better! :)

Here it goes!

One ninth of the height of an iceberg was above the surface of the water. The iceberg extended to a depth of 75.8 m below the surface. What was the height of the iceberg above the surface? Express your answer to the nearest tenth of a metre.

Here's a picture to help you out.

Okay, we know that the iceberg below the water is 75.8m and the iceberg above is one ninth. We need to find what the measurement of one ninth of the iceberg. So we have to divide the measurement of the iceberg below by 8. Now, if your wondering why we have to divide it by eight, it is because it is eight ninths of the iceberg. How do we know 75.8m is eight ninths? Well if you read the question, the question tells us that the iceberg that is above the water is one ninth, so that makes the bottom below the water eight ninths. So we have to divide the numbers.
So, when we divide the two numbers we get 9.475. Wait! The question tells us to round the measurement to the nearest tenth. When we round the number 9.475 we get 9.5. Also, we must not forget to add the unit value! Which is meters. One ninth of the iceberg is 9.5m. The height of the iceberg above the water is 9.5m. Now we've got the answer!
Thanks for reading guys. Reminder, please comment on my post to make it better! :)

Question #10

Hello 9-05! Abby here with question number 10! Okay so let's get started!

A carpenter has 64 m of baseboard. He installs 1/2 of the baseboard in one room. He installs another 3/5 of the original amount of the baseboard in another room. How much baseboard does he have left?

So first, we have to multiply 64 by 1/2 because we want to find out how much of the baseboa
rd the carpenter used in the first room. Here's how it goes:

The carpenter used 32 m of the baseboard for the first room.

Because the question says he used another 3/5 of the original amount (64), we just have to multiply 64 by 3/5 to find out how much of the baseboard the carpenter used in the other room using the original amount.

For this equation, I used a calculator to convert 38 and 2/5 to 38.4. So the carpenter used 38.4 m of the baseboard in the other room.

Now, we have to add the amount of baseboard the carpenter used in the first room (32) and the amount of baseboard the carpenter used in the other room (38.4). We have to do this because this will be a part of finding what the carpenter has left.

Then, we have to get the original amount of the baseboard (64) and subtract the amount of baseboard that was combined from the two rooms the carpenter used (70.4). This will help us find what the carpenter has left.

The answer is -6.4 m! Since the answer is negative, it means the carpenter needs or is short on baseboard.

So the word problem sentence would be..

The carpenter needs 6.4 m of baseboard.

Well, that's my blog post for question number 10! If there are any errors, and if you don't understand something, please feel free to comment! I will try my best to change my post to make you guys understand it better! Anyways, have a great weekend 9-05! (:

Question 21

Hey Everybody! Ok well let's get started...the question was,

Question #21:
a) 1/3(2/5-1/2)+3/10

b) 3/4 ./. 5/8-3/8 ./. 1/2 (./.=divided by)

c)one 1/2+one 1/2(-two 5/6+1/3)

Starting with A you have to do the parenthesis first which you equal -1/10 and then you just put them together...
1/3-1/10+3/10 which now looks pretty simple..when you add them up you get 8/15!!

Next is B first of all, you kind of break it apart like this, (3/4 ./. 5/8)-(3/8 ./. 1/2) next you do the parenthesis, the first would be one 1/5 and the second one would be 6/8, simplified would be 3/4 then you just put it together like this.
one 1/5-3/4=9/20!!

(edited)Next would be C and well I THOUGHT this would be hard...but now after Mr.B helped me and told me what I did wrong I get it now. You have to think BEDMAS or PEDMAS it's practically the same thing. But anyways you first have to do the brackets or the parenthesis. If you did it correctly, you should have gotten this answer= -two 1/2 then the next part in BEDMAS is multiplication because the bracket is touching the one 1/2. Then you should've got -three 3/4 by now. Then the last part would be adding the other one 1/2 which would equal= -two 1/4!!! YAY I finally got it.

Now please comment if there there are anymore mistakes~

Scribe Post for November 26, 2009

Hey guys! Guess what, I thought Linda's idea was really good. So I decided to follow in her awesome footsteps. Here's my scribe 905, don't forget to comment!

Well Mr. B, sorry it isn't on the day of, but hey, I tried. 30 minutes late isn't as worse as Sunday night, that's for sure. Well sorry for the lateness, but today was busy and I started around 9:30 because that's the time I came home. Anyways, whoever's reading this, make sure to leave a comment! Thanks!

Question 23

Thursday, November 26, 2009
Write a subtraction statement involving two negative fractions or negative mixed fractions so that the difference is -4/3.

So basically, it's a - b= -4/3.

You can just inverse the statement and make it -4/3 + b = a. B and A have to both be negatives so for B, I just chose a random negative fraction like -2/5.

-4/3 + (-2/5) = a

When I did this, a came out as -26/15.
So it's -4/3 + (-2/5) = -26/15.

If you make it back to a - b = -4/3, it'd become -26/15 - (-2/5) = -4/3. I even checked it. It's right.

I wasn't sure if it might work with other negative fractions so I tried it with -6/7.

-4/3 + (-6/7) = a

It came out as -4/3 + (-6/7) = -46/21.

I made it back to a - b =-4/3 again. It became -46/21 -(-6/7) = -4/3. It also works.

I'd make pictures but my paint isn't being cooperative with me and neither are my cameras. I'll try again tomorrow though...

Answering Mr. Backe's question, I think it will work everytime because it's a - b = -3/4, right? A and B have to be negatives. So when you inverse the statement to -3/4 + b = a, it should work because A has to be a negative and a negative plus a negative equals a negative.

Question Number 13

Hey 9-05,sorry for the latness.I just got home.I just want to get out that GOODLUCK to all volleyball teams this weekend and next weekend and lets hope you win!The question for homework I'm doing is question 13. The question is...

The diameter of Pluto is 6/17 the diameter of Mars.Mars is 17/300 the diameter of Saturn.
A)What fraction of the diameter of Saturn is the diameter of Pluto?
B)The diameter of Saturn is 120 00 km.What is the diameter of Pluto?

A) In order to get your answer you need take the diameter of Mars and the diameter of pluto and multiply them together then simplify to the lowest answer possible.
B) In order to get the answer for this question you'll need to take the answer 1/5 and multiply it by 120,000 and you'll get your answer.

A)6/17 * 17/300=102/5100=1/50
B)1/50(120 000)=2400km

Pluto has a diameter of 2400 km.